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Class 11 • Physics
Thermodynamics & KTG
Chapter-11
1000 Questions
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1
Medium
The temperature of food material in refrigerator is 4$^\circC and temperature of environment is 15^\circ$C. If carnot cycle is used in its working gas, then find its carnot efficiency.
Options:
A) 0.038
B) 0.028
C) 0.053
D) 0.072
2
Medium
If $7 \mathrm{~gm} \mathrm{~N}_2 is mixed with 20 \mathrm{~gm} \mathrm{~Ar}, there \frac{C_p}{C_V}$ of mixture will be
Options:
A) \frac{17}{6}
B) \frac{11}{7}
C) \frac{17}{11}
D) \frac{17}{13}
3
Medium
In an isobaric process, the work done by a di-atomic gas is 10 J, the heat given to the gas will be
Options:
A) 35 J
B) 30 J
C) 45 J
D) 60 J
4
Medium
Calculate radiation power for sphere whose temperature is 227$^\circ$C, radius 2 m and emissivity 0.8.
Options:
A) 142.5 kW
B) 1500 W
C) 1255 W
D) 1575 W
5
Medium
An ideal gas initially at pressure 1 bar is being compressed from $30 \mathrm{~m}^3 to 10 \mathrm{~m}^3 volume and its temperature decreases from 320 \mathrm{~K} to 280 \mathrm{~K}$, then find final pressure of the gas.
Options:
A) 2.625 bar
B) 3.4 bar
C) 1.325 bar
D) 4.5 bar
6
Medium
Assertion : Vibrational degree of freedom of a di-atomic gas molecule appears at every high temperature. Reason : Di-atomic gas has two vibrational degree of freedom in one direction.
Options:
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true, but reason is not the correct explanation of assertion.
C) If assertion is true, but reason is false.
D) If both assertion and reason are false.
7
Medium
Assertion : $\mathrm{NH}_3 is liquidities more easily than \mathrm{CO}_2. Reason : Critical temperature of \mathrm{NH}_3 is more than \mathrm{CO}_2$.
Options:
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true, but reason is not the correct explanation of assertion.
C) If assertion is true, but reason is false.
D) If both assertion and reason are false.
8
Medium
Assertion : In adiabatic process work is independent of the path. Reason : In adiabatic process work done is equal to negative of change in internal energy.
Options:
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true, but reason is not the correct explanation of assertion.
C) If assertion is true, but reason is false.
D) If both assertion and reason are false.
9
Medium
An ideal gas of mass $m in a state A goes to another state B via three different processes as shown in figure. If Q_1, Q_2 and Q_3$ denote the heat absorbed by the gas along the three paths, then
Options:
A) Q_1< Q_2< Q_3
B) Q_1< Q_2=Q_3
C) Q_1=Q_2 >Q_3
D) Q_1>Q_2 >Q_3
10
Medium
A gas consisting of a rigid diatomic molecules was initially under standard condition. Then, gas was compressed adiabatically to one-fifth of its initial volume. What will be the mean kinetic energy of a rotating molecule in the final state?
Options:
A) 1.44 J
B) 4.55 J
C) 787.98 \times 10^{-23} \mathrm{~J}
D) 757.3 \times 10^{-23} \mathrm{~J}
11
Medium
Assertion In isothermal process, whole of the heat energy supplied to the body is converted into internal energy. Reason According to the first law of thermodynamics, $\Delta Q=\Delta U+\Delta W
Options:
A) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion
B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C) Assertion is correct and Reason is incorrect
D) Assertion is incorrect and Reason is correct
12
Medium
Assertion Internal energy of an ideal gas does not depend on volume of gas. Reason Internal energy depends only on temperature of gas.
Options:
A) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion
B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C) Assertion is correct and Reason is incorrect
D) Assertion is incorrect and Reason is correct
13
Medium
The coefficient of cubical expansion of mercury is $0.00018 /{ }^{\circ} \mathrm{C} and that of brass 0.00006 /{ }^{\circ} \mathrm{C}. If a barometer having a brass scale were to read 74.5 \mathrm{~cm} at 30^{\circ} \mathrm{C}, find the true barometric height at 0^{\circ} \mathrm{C}. The scale is supposed to be correct at 15^{\circ} \mathrm{C}$.
Options:
A) 74.122 \mathrm{~cm}
B) 79.152 \mathrm{~cm}
C) 42.161 \mathrm{~cm}
D) 142.39 \mathrm{~cm}
14
Medium
One mole of an ideal diatomic gas undergoes transition from A to B along a path AB as shown below. The change in internal energy of the gas during the transition is
Options:
A) 20 kJ
B) -$12 kJ
C) -$20 kJ
D) 20 J
15
Medium
Assertion : It is hotter over the top of a fire than at the same distance on the sides. Reason : In the upward direction, the heat propagate through convection.
Options:
A) Both assertion and reason are true and reason is the correct explanation of assertion
B) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false
D) Both assertion and reason are false.
16
Medium
Assertion : In adiabatic expansion the product of $p and V$ always decreases. Reason : In adiabatic expansion process, work is done by the gas at the cost of internal energy of gas.
Options:
A) Both assertion and reason are true and reason is the correct explanation of assertion
B) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false
D) Both assertion and reason are false.
17
Medium
Assertion : The molecules of a monoatomic gas has three degrees of freedom. Reason : The molecules of diatomic gas has five degrees of freedom.
Options:
A) Both assertion and reason are true and reason is the correct explanation of assertion
B) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false
D) Both assertion and reason are false.
18
Medium
Assertion : Molar heat capacity cannot be defined for isothermal process. Reason : In isothermal process $p-V versus T$ graph is a dot.
Options:
A) Both assertion and reason are true and reason is the correct explanation of assertion
B) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false
D) Both assertion and reason are false.
19
Medium
In the given cycle A B C D A , the heat required for an ideal monoatomic gas will be
Options:
A) p_{0} V_{0}
B) \frac{13}{2} p_{0} V_{0}
C) \frac{11}{2} p_{0} V_{0}
D) 4 p_{0} V_{0}
20
Medium
In a mixture of gases, the average number of degree of freedoms per molecule is 6 . The rms speed of the molecule of the gas is c , then the velocity of sound in the gas is
Options:
A) \frac{c}{\sqrt{3}}
B) \frac{c}{\sqrt{2}}
C) \frac{2 c}{3}
D) \frac{3 c}{3}
21
Medium
A vessel containing 1 mole of $\mathrm{O}_2 gas (molar mass 32) at temperature T. The pressure of the gas is p. An identical vessel containing one mole of He gas (molar mass 4) at temperature 4 T$ has a pressure of
Options:
A) p/8
B) p
C) 4p
D) 8p
22
Medium
A Carnot's heat engine works between the temperature $527^{\circ} \mathrm{C} and 127^{\circ} \mathrm{C}. What amount of heat should it consume per second to deliver mechanical work at the rate of 1.0 \mathrm{~kW}$ ?
Options:
A) 0.477 kcal/s
B) 4.77 kcal/s
C) 447.7 kcal/s
D) 0.2385 kcal/s
23
Medium
A monoatomic gas of molar mass m is kept in a insulated container. Container is moving with velocity v. If the container is suddenly stopped, then the change in the temperature of the gas is
Options:
A) mv2/4R
B) mv2/2R
C) mv2/R
D) mv2/3R
24
Medium
One mole of an ideal diatomic gas undergoes a process as shown in the figure. The molar specific heat of the gas in the process is
Options:
A) 3R/2
B) R/2
C) 5R/2
D) 7R/2
25
Medium
An ideal monoatomic gas is taken round the cycle ABCDA as shown in the p-diagram The work done during the cycle is
Options:
A) pV
B) 2pV
C) {{pV} \over 2}
D) zero
26
Medium
Which of the following graphs show the correct relation between conductivity and temperature for a metallic conductor?
Options:
A)
B)
C)
D)
27
Medium
The ratio of the specific heats ${{{C_v}} \over {{C_p}}} = {1 \over \gamma }$ in terms of degrees of freedom (n) is given by
Options:
A) \left( {1 + {n \over 3}} \right)
B) \left( {1 + {2 \over n}} \right)
C) \left( {1 + {n \over 2}} \right)
D) \left( {1 + {1 \over n}} \right)
28
Medium
A black body radiates energy at the rate E Wm$-2 at high temperature TK. When the temperature is reduced to \left( {{T \over 4}} \right)$ K, the new radiant energy is
Options:
A) {E \over {256}}
B) 4E
C) {E \over {4}}
D) {E \over {16}}
29
Medium
In an adiabatic process, where pressure is decreased by ${3 \over 4}%, if {{{C_p}} \over {{C_v}}} = {4 \over 3}$, then the volume increases by
Options:
A) {3 \over 4}$%
B) {9 \over 16}$%
C) {16 \over 9}$%
D) {4 \over 3}$%
30
Medium
A Carnot engine has the same efficiency between 600 K to 300 K and 1600 K to x K, then the value of x is
Options:
A) 1600 K
B) 800 K
C) 819 K
D) 900 K
31
Medium
A vessel contains one mole of O2 gas (molar mass 32) at a temperature T. The pressure of the gas is p. An identical vessel containing one mole of He gas (molar mass 4) at a temperature 2T has a pressure of
Options:
A) {p \over 8}
B) p
C) 2p
D) 8p
32
Medium
The figure shows graphs of pressure (p) versus density (d) for an ideal gas at two temperatures T1 and T2, then
Options:
A) T1 > T2
B) T1 < T2
C) T1 = T2
D) None of these
33
Medium
When 2 moles of a monoatomic gas are mixed with 3 moles of a diatomic gas, the value of adiabatic exponent for the mixture is
Options:
A) {{15} \over {16}}
B) {{7} \over {5}}
C) {{31} \over {21}}
D) {{38} \over {59}}
34
Medium
The total number of degrees of freedom associated with 2 \mathrm{~cm}^3 of Nitrogen gas at normal temperature and pressure is: [Given Avogadro number as ' N ' ]
Options:
A) \frac{N}{44800}
B) \frac{N}{4480}
C) \frac{N}{2240}
D) \frac{N}{22400}
35
Medium
The rms velocity of the gas molecule at 327^{\circ} \mathrm{C} is same as the rms velocity of the oxygen molecules at 27^{\circ} \mathrm{C}. If the molecular weight of oxygen is 32 then the molecular weight of the given gas molecule is:
Options:
A) 32
B) 64
C) 96
D) 128
36
Medium
A given volume of gas at NTP is allowed to expand 6 times of its original volume, first under isothermal condition and then under adiabatic condition. Which of the given statement is correct? [Given \frac{c_p}{c_v}=\gamma=1.4 ]
Options:
A) The final pressure after the adiabatic expansion is 1.4 times greater than the final pressure after the isothermal expansion.
B) The final temperature after the adiabatic expansion is 1.4 times less than the final temperature after the isothermal expansion.
C) Pressure remains same in both adiabatic and isothermal expansion
D) The final pressure after the adiabatic expansion is less than the final pressure after the isothermal expansion.
37
Medium
The rate of heat conduction in the given two metal rods having the same length is found to be the same when the temperature difference between the ends is kept 30^{\circ} \mathrm{C} If the area of cross section of the first rod is 8 \times 10^{-2} \mathrm{~m}^2 then what will be area of cross section of the second rod? [ Given that the ratio of the thermal conductivity of the first rod to that of the second rod is 1: 4 ]
Options:
A) 2 \times 10^{-2} \mathrm{~m}^2
B) 4 \times 10^{-4} \mathrm{~m}^2
C) 2 \times 10^{-4} \mathrm{~m}^2
D) 4 \times 10^{-2} \mathrm{~m}^2
38
Medium
The heat required to increase the temperature of 4 moles of a mono-atomic ideal gas from 273^{\circ} \mathrm{C} to 473^{\circ} \mathrm{C} at constant volume is
Options:
A) 1600 R
B) 600 R
C) 1200 R
D) 400 R
39
Medium
Rods A and B have their lengths in the ratio 1: 2. Their thermal conductivities are K_1 and K_2 respectively. The temperatures at the ends of each rod are \mathrm{T}_1 and \mathrm{T}_2. If the rate of flow of heat through the rods is equal, the ratio of area of cross section of A to that of B is
Options:
A) \frac{2 K_2}{K_1}
B) \frac{K_2}{4 K_1}
C) \frac{K_2}{K_1}
D) \frac{K_2}{2 K_1}
40
Medium
A monoatomic ideal gas, initially at temperature T_1, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature \mathrm{T}_2 by releasing the piston suddenly. If L and 2 L are the lengths of the gas column before and after expansion respectively, then \frac{T_1}{T_2} is
Options:
A) 2^{3 / 2}
B) 2^{2 / 3}
C) \left(\frac{1}{2}\right)^{2 / 3}
D) \left(\frac{1}{2}\right)^{3 / 2}
41
Medium
An ideal gas is expanding such that P T^2= constant. The coefficient of volume expansion of the gas is
Options:
A) \frac{2}{T}
B) 3 T
C) \frac{T}{3}
D) \frac{3}{T}
42
Medium
A block of metal A is connected in series with another block of metal B such that the two metal blocks have the same area of cross sections. The thermal conductivity of metal A is K and the free end of metal A is at 80^{\circ} \mathrm{C}. The temperature of the interface is 60^{\circ} \mathrm{C} and the free end of metal B is at 20^{\circ} \mathrm{C}. Assuming the two metals have the same thickness, the conductivity of metal B is:
Options:
A) 2 K
B) 4 K
C) \frac{K}{2}
D) \frac{K}{4}
43
Medium
The mean energy per molecule for a diatomic gas is:
Options:
A) \left(\frac{5}{2}\right) \mathrm{K}_{\mathrm{B}} \mathrm{T}
B) \left(\frac{3}{2}\right) \mathrm{K}_{\mathrm{B}} \mathrm{T}
C) \left(\frac{3}{2 N}\right) \mathrm{K}_{\mathrm{B}} \mathrm{T}
D) \left(\frac{5}{2 N}\right) \mathrm{K}_{\mathrm{B}} \mathrm{T}
44
Medium
The ratio of specific heat capacities at constant pressure to that at constant volume for a given mass of a gas is \frac{5}{2}. If the percentage increase in volume of the gas while undergoing an adiabatic change is \frac{3}{2}, then the percentage decrease in pressure will be:
Options:
A) \frac{15}{4}
B) \frac{3}{5}
C) \frac{4}{15}
D) \frac{5}{3}
45
Medium
A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure below. It absorbs 60 J of heat during the part AB and rejects 80 J of heat during CA . There is no heat exchanged during the process \mathrm{BC} . \mathrm{A} work of 40 J is done on the gas during the part BC . If the internal energy of the gas at A is 1450 J , then the work done by the gas during the part CA is:
Options:
A) 10J
B) 20J
C) 40J
D) 30J
46
Medium
The coefficient of volume expansion of glycerine is $49 \times 10^{-5} \mathrm{~K}^{-1}. The percentage change in its density for a 50^{\circ} \mathrm{C}$ rise in temperature is
Options:
A) 3.54
B) 5.24
C) 4.25
D) 2.45
47
Medium
The latent heat of vaporisation of water is $2240 \mathrm{~J}. If the work done in the process of vaporisation of 1 \mathrm{~g} is 168 \mathrm{~J}$, the increase in internal energy is
Options:
A) 1408 J
B) 2072 J
C) 2208 J
D) 2408 J
48
Medium
Internal energy of $\mathrm{n}_1 moles of hydrogen at temperature T is equal to internal energy of \mathrm{m}_2 moles of helium at temperature 2T. The ratio \frac{n_1}{n_2}$ is
Options:
A) \frac{6}{5}
B) \frac{3}{7}
C) \frac{5}{3}
D) \frac{3}{2}
49
Medium
A cylinder of fixed capacity 44.81 contains hydrogen gas at STP. What is the amount of heat needed to raise the temperature of the gas in the cylinder by $20^{\circ} \mathrm{C} ? (R=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$)
Options:
A) 541 J
B) 374 J
C) 831 J
D) 743 J
50
Medium
An iron piece of mass $200 \mathrm{~g} is kept inside a furnace for some time and then put in a calorimeter of water equivalent 20 \mathrm{~g} containing 230 \mathrm{~g} of water at 20 \mathrm{C}. The steady state temperature attained by the mixture is 60^{\circ}. The temperature of the furnace is (Specific heat capacity of iron is 470 \mathrm{~J~kg}^{-1} \mathrm{C}^{-1}$ )
Options:
A) 464.7$^\circ$C
B) 893.6$^\circ$C
C) 506.8$^\circ$C
D) 953.6$^\circ$C
51
Medium
An ideal gas changes its state from $\mathrm{A} to \mathrm{C} in two different paths \mathrm{ABC} and \mathrm{AC}. The internal energy of the gas at state \mathrm{C} is 20 \mathrm{~J} and at state \mathrm{B} is 10 \mathrm{~J}. Heat supplied to the gas to go from \mathrm{B} \rightarrow \mathrm{C}$ is
Options:
A) 90 J
B) zero
C) 70 J
D) 60 J
52
Medium
If pressure of an ideal gas is increased by keeping temperature constant the kinetic energy will
Options:
A) Vary quadratically
B) Increase
C) Not change
D) Decrease
53
Medium
A cubical box of side $2 \mathrm{~m} contains helium gas. It was observed that in a time of 1 second, an atom travelling with the root-mean-square speed parallel to one of the edges of the cube, made 250 hits with one of the walls, without any collision with other atoms. The average kinetic energy of the helium gas is Take R=\frac{25}{3} \mathrm{~J} / \mathrm{mol}-\mathrm{K} and \mathrm{kB}=1.38 \times 10^{-23} \mathrm{JK}{ }^{-1}
Options:
A)
82.8 \times 10^{-21} \mathrm{~J}
B)
3.31 \times 10^{-21} \mathrm{~J}
C)
82.8 \times 10^{-19} \mathrm{~J}
D)
1 \times 10^{-21} \mathrm{~J}
54
Medium
A glass of hot water cools from $90^{\circ} \mathrm{C} to 70^{\circ} \mathrm{C} in 3 minutes when the temperature of surroundings is 20^{\circ} \mathrm{C}. What is the time taken by the glass of hot water to cool from 60^{\circ} \mathrm{C} to 40^{\circ} \mathrm{C} if the surrounding temperature remains the same at 20^{\circ} \mathrm{C}$ ?
Options:
A) 15 minutes
B) 6 minutes
C) 12 minutes
D) 10 minutes
55
Medium
A cubical box of side $1 \mathrm{~m} contains Boron gas at a pressure of 100 \mathrm{~Nm}^{-2}$. During an observation time of 1 second, an atom travelling with the rms speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms. The total mass of gas in the box in gram is
Options:
A) 30
B) 0.3
C) 3
D) 0.03
56
Medium
A one \mathrm{kg} block of ice at $-1.5^{\circ} \mathrm{C} falls from a height of 1.5 \mathrm{~km} and is found melting. The amount of ice melted due to fall, if 60 \% energy is converted into heat is (Specific heat capacity of ice is 0.5 \mathrm{~cal} \mathrm{~g}^{-1} \mathrm{~C}^{-1}, Latent heat of fusion of ice =80 \mathrm{~cal~g}^{-1}$ )
Options:
A) 1.69 g
B) 10 g
C) 16.9 g
D) 17.9 g
57
Medium
An electric bulb of volume $300 \mathrm{~cm}^3 was sealed off during manufacture at a pressure of 1 \mathrm{~mm} of mercury at 27{ }^{\circ} \mathrm{C}. The number of air molecules contained in the bulb is, (\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} and N_A=6.02 \times 10^{23})
Options:
A) 9.67 \times 10^{16}
B) 9.65 \times 10^{15}
C) 9.67 \times 10^{17}
D) 9.65 \times 10^{18}
58
Medium
The mean energy per molecule for a diatomic gas is
Options:
A) \frac{5 k_B T}{N}
B) \frac{5 k_B T}{2 N}
C) \frac{5 k_B T}{2}
D) \frac{3 k_B T}{2}
59
Medium
A gas is taken through the cycle $A \rightarrow B \rightarrow C \rightarrow A$, as shown in figure. What is the net work done by the gas?
Options:
A) 2000 J
B) 1000 J
C) Zero
D) -2000$ J
60
Medium
The gases carbon monoxide $(\mathrm{CO}) and nitrogen at the same temperature have kinetic energies E_1 and E_2$, respectively. Then,
Options:
A) E_1=E_2
B) E_1> E_2
C) E_1< E_2
D) None of these
61
Medium
An ideal gas goes from state $A to state B via three different processes as indicated in the p-V diagram. If Q_1, Q_2 and Q_3 indicate the heat absorbed by the three processes and \Delta U_1, \Delta U_2 and \Delta U_3$ indicate the change in internal energy along the three processes respectively, then
Options:
A) Q_1 > Q_2 > Q_3 and \Delta U_1=\Delta U_2=\Delta U_3
B) Q_3 > Q_2 > Q_1 and \Delta U_1=\Delta U_2=\Delta U_3
C) Q_1=Q_2=Q_3 and \Delta U_1 > \Delta U_2 > \Delta U_3
D) Q_3 > Q_2 > Q_1 and \Delta U_1 > \Delta U_2 > \Delta U_3
62
Medium
If $150 \mathrm{~J} of heat is added to a system and the work done by the system is 110 \mathrm{~J}$, then change in internal energy will be
Options:
A) 40 J
B) 110 J
C) 150 J
D) 260 J
63
Medium
Two slabs are of the thicknesses $d_1 and d_2. Their thermal conductivities are K_1 and K_2, respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures \theta_1 and \theta_2. Assume \theta_1 > \theta_2. The temperature \theta$ of their common junction is
Options:
A) \frac{K_1 \theta_1+K_2 \theta_2}{\theta_1+\theta_2}
B) \frac{K_1 \theta_1 d_1+K_2 \theta_2 d_2}{K_1 d_2+K_2 d_1}
C) \frac{K_1 \theta_1 d_2+K_2 \theta_2 d_1}{K_1 d_2+K_2 d_1}
D) \frac{K_1 \theta_1+K_2 \theta_2}{K_1+K_2}
64
Medium
A cylinder of radius $r and of thermal conductivity K_1 is surrounded by a cylindrical shell of inner radius r and outer radius 2 r made of a material of thermal conductivity K_2$. The effective thermal conductivity of the system is
Options:
A) \frac{1}{3}\left(K_1+2 K_2\right)
B) \frac{1}{2}\left(2 K_1+3 K_2\right)
C) \frac{1}{3}\left(3 K_2+2 K_1\right)
D) \frac{1}{4}\left(K_1+3 K_2\right)
65
Medium
In an adiabatic expansion of air, the volume is increased by $6.2 \%. The percentage change in pressure is (\gamma=1.4)
Options:
A) 8.68
B) 4.84
C) 6.48
D) 2.24
66
Medium
If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma, the change in internal energy of a mass of a gas when the volume changes from \mathrm{V} to 3 \mathrm{~V}$ at constant pressure is
Options:
A) \frac{R}{(\gamma-1)}
B) 2 P V
C) \frac{2 P V}{\gamma}
D) \frac{2 P V}{(\gamma-1)}
67
Medium
The molecules of a given mass of a gas have root mean square speed of $120 \mathrm{~m} / \mathrm{s} at 88^{\circ} \mathrm{C} and 1 atmospheric pressure. The root mean square speed of the molecules at 127^{\circ} \mathrm{C}$ and 2 atmospheric pressure is
Options:
A) 105.2 m/s
B) 1.443 m/s
C) 126.3 m/s
D) 88/127 m/s
68
Medium
Two black bodies $\mathrm{P} and \mathrm{Q} have equal surface areas and are kept at temperatures 127^{\circ} \mathrm{C} and 27^{\circ} \mathrm{C}$ respectively. The ratio of thermal power radiated by A to that by B is
Options:
A) 81: 256
B) 177: 127
C) 127: 177
D) 256: 81
69
Medium
If heat engine is filled at temperature 27$^\circC and heat of 100 k cal is taken from source at temperature 677^\circ$C. Work done (in J) is
Options:
A) 0.28\times10^6
B) 2.8\times10^6
C) 28\times10^6
D) 0.028\times10^6
70
Medium
From the following p-V diagram, an ideal gas undergoing a change of state from A to B. Four different processes I, II, III and IV as shown in the figure may lead to same change of state.
Options:
A) work done is maximum in case I
B) Change in internal energy is same in all the four cases
C) Change in internal energy is same in IV and III cases, but not in I and II cases
D) Work done is minimum in Case II
71
Medium
An ideal gas is taken through the cycle A $\to B \to C \to A, as shown in the figure. If the net heat supplied to the gas in the cycle is 5 J, the work done by the gas in the process C \to$ A is,
Options:
A) -5$ J
B) -10$ J
C) -15$ J
D) -20$ J
72
Medium
The average kinetic energy of a molecule in air at room temperature of 20$^\circ$C
Options:
A) 6\times10^{-22}$ J
B) 7.06\times10^{-21}$ J
C) 6.07\times10^{-21}$ J
D) 6.70\times10^{-21}$ J
73
Medium
There are two identical containers C$_1 and C_2 containing to identical gases. Gas in C_1 is reduced to half of its original volume adiabatically, while the gas in container C_2 is also reduced to half of its initial volume isothermally. Find the ratio of final pressure in these containers. (\gamma$ be the adiabatic constant).
Options:
A) 2 : 1
B) 1 : 2
C) 2^\gamma : 1
D) 2^{\gamma-1}:1
74
Medium
In which mode of transmission, the heat waves travel along straight line with the speed of light?
Options:
A) Thermal radiation
B) Forced convection
C) Natural convection
D) Thermal conduction
75
Medium
Consider a compound slab consisting of two different materials having equal lengths, thickness and thermal conductivities K and 2K respectively. The equivalent thermal conductivity of the slab is
Options:
A) \sqrt2$K
B) 3$K
C) \frac{4}{3}$K
D) \frac{2}{3}$K
76
Medium
In an adiabatic process with the ratio of two specific heat, $\gamma=\frac{3}{2}, pressure is increased by \frac{2}{3}$%, then decrease in the volume will be
Options:
A) \frac{4}{9}$%
B) \frac{2}{3}$%
C) 4$%
D) \frac{9}{4}$%
77
Medium
For an ideal gas, coefficient of volume expansion is given by
Options:
A) \frac{1}{p}
B) \frac{1}{pV}
C) \frac{1}{R}
D) \frac{1}{T}
78
Medium
Which of the following is not a green house gas?
Options:
A) CH$_4
B) CO$_2
C) O$_3
D) H$_2$O
79
Medium
The collision of the molecules of an ideal gas is taken as
Options:
A) elastic
B) inelastic
C) partially elastic
D) partially inelastic
80
Medium
The average energy associated with a monoatomic molecule is
Options:
A) {K_B}T
B) {1 \over 2}{K_B}T
C) {3 \over 2}{K_B}T
D) 2{K_B}T
81
Medium
Carnot cycle of an engine is given below Total work done by the gas in one cycle is
Options:
A) \mu R{T_2}\log {{{V_2}} \over {{V_1}}} - \mu R{T_1}\log {{{V_3}} \over {{V_4}}}
B) \mu R{T_1}\log {{{V_2}} \over {{V_1}}} - \mu R{T_2}\log {{{V_3}} \over {{V_4}}}
C) \mu R{T_1}\log {{{V_2}} \over {{V_1}}} + \mu R{T_2}\log {{{V_3}} \over {{V_4}}}
D) Zero
82
Medium
A compound slab is made of two parallel plates of copper and brass of the same thickness and having thermal conductivities in the ratio 4 : 1. The free face of copper is at 0$^\circC. The temperature of the interface is 20^\circ$C. What is the temperature of the free face of brass?
Options:
A) 0$^\circ$C
B) 20$^\circ$C
C) 40$^\circ$C
D) 100$^\circ$C
83
Medium
In mm$^3 of a gas is compressed at 1 atmospheric pressure and temperature 27^\circC to 627^\circC. What is the final pressure under adiabatic condition? (\gamma$ for the gas = 1.5)
Options:
A) 27\times10^5 N/m^2
B) 80\times10^5 N/m^2
C) 36\times10^5 N/m^2
D) 56\times10^5 N/m^2
84
Medium
If sink is at a temperature of $-39\UpsilonC and source at 0^\circ$C, then efficiency will be
Options:
A) 39.4%
B) 14.2%
C) 35.2%
D) 45.5%
85
Medium
Equal volumes of two gases, having their densities in the ratio of 1 : 16 exert equal pressures on the walls of two containers. The ratio of their rms velocities $\left(\frac{c_1}{c_2}\right)
Options:
A) 1 : 8
B) 8 : 1
C) 1 : 4
D) 4 : 1
86
Medium
A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $C_p/C_V$ of the mixture is
Options:
A) 1.4
B) 1.54
C) 1.59
D) 1.62
87
Medium
The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4 . It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance 10 . The hot reservoir of the heat pump is at a temperature of 300 K . Which of the following statements is/are correct :
Options:
A) Work extracted from the Carnot engine in one cycle is 60 J.
B) Temperature of the cold reservoir of the Carnot engine is 600 K.
C) Temperature of the cold reservoir of the heat pump is 270 K.
D) Heat supplied to the hot reservoir of the heat pump in one cycle is 540 J.
88
Medium
In the given P-V diagram, a monoatomic gas \left(\gamma=\frac{5}{3}\right) is first compressed adiabatically from state A to state B. Then it expands isothermally from state B to state C. [Given: \left(\frac{1}{3}\right)^{0.6} \simeq 0.5, \ln 2 \simeq 0.7 ]. Which of the following statement(s) is(are) correct?
Options:
A) The magnitude of the total work done in the process A \rightarrow B \rightarrow C is 144 \mathrm{~kJ}.
B) The magnitude of the work done in the process B \rightarrow C is 84 \mathrm{~kJ}.
C) The magnitude of the work done in the process A \rightarrow B is 60 \mathrm{~kJ}.
D) The magnitude of the work done in the process C \rightarrow A is zero.
89
Hard
The filament of a light bulb has surface area 64 mm2 . The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of the eyes of the observer to be circular with radius 3 mm. Then (Take Stefan-Boltzmann constant = 5.67 $ \times 10−8 Wm−2K−4 , Wien’s displacement constant = 2.90 \times 10−3 m-K, Planck’s constant = 6.63 \times 10−34 Js, speed of light in vacuum = 3.00 \times $ 108 ms−1)
Options:
A) power radiated by the filament is in the range 642 W to 645 W
B) radiated power entering into one eye of the observer is in the range 3.15 $ \times 10−8 W to
3.25 \times $ 10−8 W
C) the wavelength corresponding to the maximum intensity of light is 1160 nm
D) taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons
entering per second into one eye of the observer is in the range 2.75 $ \times 1011 to 2.85 \times $ 1011
90
Hard
A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure P0, volume V0, and temperature T0. If the gas mixture is adiabatically compressed to a volume ${{{V_0}} \over 4}$, then the correct statement(s) is/are (Given, 21.2 = 2.3; 23.2 = 9.2; R is a gas constant)
Options:
A) The final pressure of the gas mixture after compression is in between 9P0 and 10P0
B) The average kinetic energy of the gas mixture after compression is in between 18RT0 and 19RT0
C) Adiabatic constant of the gas mixture is 1.6
D) The work |W| done during the process is 13RT0
91
Medium
One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are [R is the gas constant]
Options:
A) Work done in this thermodynamic cycle (1$ \to 2 \to 3 \to 4 \to 1) is \left| W \right| = {1 \over 2}R{T_0}$.
B) The ratio of heat transfer during processes 1$ \to 2 and 2 \to 3 is \left| {{{{Q_{1 \to 2}}} \over {{Q_{2 \to 3}}}}} \right| = {5 \over 3}
C) The above thermodynamic cycle exhibits only isochoric and adiabatic processes.
D) The ratio of heat transfer during processes 1$ \to 2 and 3 \to 4 is \left| {{{{Q_{1 \to 2}}} \over {{Q_{3 \to 4}}}}} \right| = {1 \over 2}
92
Hard
One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V is the volume and T$ is the temperature). Which of the statements below is (are) true?
Options:
A) Process ${\rm I}$ is an isochoric process
B) In process ${\rm II}$, gas absorbs heat
C) In process ${\rm IV}$, gas releases heat
D) Process ${\rm I} and {\rm III}$ are not isobaric
93
Hard
An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T1, pressure P1 and volume V1 and the spring is in its relaxed state. The gas is then heated very slowly to temperature T2, pressure P2 and volume V2. During this process the piston moves out by a distance x.Ignoring the friction between the piston and the cylinder, the correct statements is/are
Options:
A) If V2 = 2V1 and T2 = 3Tl, then the energy stored in the spring is ${1 \over 4}{P_1}{V_1}
B) If V2 = 2V1 and T2 = 3T1, then the change in internal energy is $3{P_1}{V_1}
C) If V2 = 3V1 and T2 = 4T1, then the work done by the gas is ${7 \over 3}{P_1}{V_1}
D) If V2 = 3V1 and T2 = 4T1, then the heat supplied to the gas is ${17 \over 6}{P_1}{V_1}
94
Medium
A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is(are)
Options:
A) The average energy per mole of the gas mixture is 2RT
B) The ratio of speed of sound in the gas mixture to that in helium gas is $\sqrt {{6 \over 5}}
C) The ratio of the rms speed of helium atoms to that of hydrogen molecules is ${1 \over 2}
D) The ratio of the rms speed of helium atoms to that of hydrogen molecules is ${1 \over {\sqrt 2 }}
95
Medium
The figure below shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is(are) correct to a reasonable approximation.
Options:
A) The rate at which heat is absorbed in the range 0-100 K varies linearly with temperature T.
B) Heat absorbed in increasing the temperature from 0-100 K is less than the heat required for increasing the temperature from 400-500 K.
C) There is no change in the rate of heat absorption in the range 400-500 K.
D) The rate of heat absorption increases in the range 200-300 K.
96
Medium
One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P0. Choose the correct option(s) from the following:
Options:
A) Internal energies at A and B are the same.
B) Work done by the gas in process AB is P0V0 ln4.
C) Pressure at C is P0/4.
D) Temperature at C is T0/4.
97
Hard
The figure shows the PV plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semicircle and CDA is half of an ellipse. Then,
Options:
A) the process during the path A $\to$ B is isothermal.
B) heat flows out of the gas during the path B $\to C \to$ D.
C) work done during the path A $\to B \to$ C is zero.
D) positive work is done by the gas in the cycle ABCDA.
98
Easy
C_V and C_P$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then
Options:
A) C_P-C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.
B) C_P+C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.
C) C_P/C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.
D) C_P~.C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.
99
Medium
In a dark room with ambient temperature \mathrm{T}_0, a black body is kept at a temperature T . Keeping the temperature of the black body constant (at T), sunrays are allowed to fall on the black body through a hole in the roof of the dark room. Assuming that there is no change in the ambient temperature of the room, which of the following statement(s) is/are correct?
Options:
A) The quantity of radiation absorbed by the black body in unit time will increase.
B) Since emissivity = absorptivity, hence the quantity of radiation emitted by black body in unit time will increase.
C) Black body radiates more energy in unit time in the visible spectrum.
D) The reflected energy in unit time by the black body remains the same.
100
Medium
An ideal monatomic gas of n moles is taken through a cycle W X Y Z W consisting of consecutive adiabatic and isobaric quasi-static processes, as shown in the schematic V-T diagram. The volume of the gas at W, X and Y points are, 64 \mathrm{~cm}^3, 125 \mathrm{~cm}^3 and 250 \mathrm{~cm}^3, respectively. If the absolute temperature of the gas T_W at the point W is such that n R T_W=1 \mathrm{~J} ( R is the universal gas constant), then the amount of heat absorbed (in J ) by the gas along the path X Y is ___________.
Options:
101
Medium
The left and right compartments of a thermally isolated container of length L are separated by a thermally conducting, movable piston of area A. The left and right compartments are filled with \frac{3}{2} and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant k and natural length \frac{2 L}{5}. In thermodynamic equilibrium, the piston is a distance \frac{L}{2} from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is P=\frac{k L}{A} \alpha, then the value of \alpha is __________.
Options:
102
Medium
Two identical plates P and Q , radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures \mathrm{T}_{\mathrm{P}} and \mathrm{T}_{\mathrm{Q}}, respectively, with \mathrm{T}_{\mathrm{Q}}<\mathrm{T}_{\mathrm{P}}, as shown in Fig. 1. The radiated power transferred per unit area from P to Q is W_0. Subsequently, two more plates, identical to P and Q , are introduced between P and Q, as shown in Fig. 2. Assume that heat transfer takes place only between adjacent plates. If the power transferred per unit area in the direction from P to Q (Fig. 2) in the steady state is W_S, then the ratio \frac{W_0}{W_S} is ________.
Options:
103
Hard
A spherical soap bubble inside an air chamber at pressure P_0=10^5 \mathrm{~Pa} has a certain radius so that the excess pressure inside the bubble is \Delta P=144 \mathrm{~Pa}. Now, the chamber pressure is reduced to 8 P_0 / 27 so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure \Delta P in both the cases to be much smaller than the chamber pressure. The new excess pressure \Delta P in \mathrm{Pa} is ______.
Options:
104
Medium
The specific heat capacity of a substance is temperature dependent and is given by the formula C=k T, where k is a constant of suitable dimensions in SI units, and T is the absolute temperature. If the heat required to raise the temperature of 1 \mathrm{~kg} of the substance from -73^{\circ} \mathrm{C} to 27^{\circ} \mathrm{C} is n k, the value of n is ________. [Given: 0 \mathrm{~K}=-273{ }^{\circ} \mathrm{C}.]
Options:
105
Medium
One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the P-V diagrams below. In cycle I, processes a, b, c and d are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes a^{\prime}, b^{\prime}, c^{\prime} and d^{\prime} are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle \mathrm{I} is W_I and that during cycle II is W_{I I}. The ratio W_I / W_{I I} is ________.
Options:
106
Hard
A cylindrical furnace has height (H) and diameter (D) both 1 \mathrm{~m}. It is maintained at temperature 360 \mathrm{~K}. The air gets heated inside the furnace at constant pressure P_a and its temperature becomes T=360 \mathrm{~K}. The hot air with density \rho rises up a vertical chimney of diameter d=0.1 \mathrm{~m} and height h=9 \mathrm{~m} above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density \rho_a= 1.2 \mathrm{~kg} \mathrm{~m}^{-3}, pressure P_a and temperature T_a=300 \mathrm{~K} enters the furnace. Assume air as an ideal gas, neglect the variations in \rho and T inside the chimney and the furnace. Also ignore the viscous effects. [Given: The acceleration due to gravity g=10 \mathrm{~m} \mathrm{~s}^{-2} and \pi=3.14 ]
Options:
107
Medium
A cylindrical furnace has height (H) and diameter (D) both 1 \mathrm{~m}. It is maintained at temperature 360 \mathrm{~K}. The air gets heated inside the furnace at constant pressure P_a and its temperature becomes T=360 \mathrm{~K}. The hot air with density \rho rises up a vertical chimney of diameter d=0.1 \mathrm{~m} and height h=9 \mathrm{~m} above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density \rho_a= 1.2 \mathrm{~kg} \mathrm{~m}^{-3}, pressure P_a and temperature T_a=300 \mathrm{~K} enters the furnace. Assume air as an ideal gas, neglect the variations in \rho and T inside the chimney and the furnace. Also ignore the viscous effects. [Given: The acceleration due to gravity g=10 \mathrm{~m} \mathrm{~s}^{-2} and \pi=3.14 ]
Options:
108
Medium
A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas (\gamma=5 / 3) and one mole of an ideal diatomic gas (\gamma=7 / 5). Here, \gamma is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of 66 Joule when heated at constant pressure. The change in its internal energy is _______ Joule.
Options:
109
Medium
A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the bottle is sealed at atmosphere pressure p0 = 105 Pa so that the volume of the trapped air is v0 = 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p0 + $\Deltap without changing its orientation. At this pressure, the volume of the trapped air is v0 - \Deltav. Let \Deltav = X cc and \Deltap = Y \times$ 103 Pa.The value of X is _______________.
Options:
110
Medium
A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the bottle is sealed at atmosphere pressure p0 = 105 Pa so that the volume of the trapped air is v0 = 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p0 + $\Deltap without changing its orientation. At this pressure, the volume of the trapped air is v0 - \Deltav. Let \Deltav = X cc and \Deltap = Y \times$ 103 Pa.The value of Y is _______________.
Options:
111
Medium
A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at 0 K. At time t = 0, the temperature of the object is 200 K. The temperature of the object becomes 100 K at t = t1 and 50 K at t = t2. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio (t2/t1) is ____________.
Options:
112
Hard
A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8.3 kg. Thus the partition is held initially at a distance of 4 m from the top, as shown in the schematic figure below. Each of the two parts of the vessel contains 0.1 mole of an ideal gas at temperature 300 K. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached, the distance of the partition from the top (in m) will be _______. (take the acceleration due to gravity = 10 ms−2 and the universal gas constant = 8.3 J mol−1K−1).
Options:
113
Hard
A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R $- a). For a << R the magnitude of the work done in the process in given by (4\pip0Ra2)X, where X is a constant and \gamma$ = Cp/Cv = 41/30. The value of X is ________.
Options:
114
Medium
A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is 700 Wm$-2 and it is absorbed by the water over an effective area of 0.05m2. Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ^\circC) in the temperature of water and the surroundings after a long time will be ___________. (Ignore effect of the container, and take constant for Newton's law of cooling = 0.001 s-1, Heat capacity of water = 4200 J kg-1 K-$1)
Options:
115
Medium
Consider one mole of helium gas enclosed in a container at initial pressure P1 and volume V1. It expands isothermally to volume 4V1. After this, the gas expands adiabatically and its volume becomes 32V1. The work done by the gas during isothermal and adiabatic expansion processes are Wiso and Wadia, respectively. If the ratio ${{{W_{iso}}} \over {{W_{adia}}}}$ = f ln 2, then f is ______.
Options:
116
Medium
One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100\,K and the universal gas constant R=8.0 J\,mo{l^{ - 1}}{K^{ - 1}},$ the decrease in its internal energy, in Joule, is ____________.
Options:
117
Medium
A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays ${\log _2}\left( {{P \over {{P_0}}}} \right)$, where P0 is a constant. When the metal surface is at a temperature of 487oC, the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767oC?
Options:
118
Medium
Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 104 times the power emitted from B. The ratio $\left( {{{{\lambda _A}} \over {{\lambda _B}}}} \right) of their wavelengths {{\lambda _A}} and {{\lambda _B}}$ at which the peaks occur in their respective radiation curves is
Options:
119
Medium
A thermodynamic system is taken from an initial state i with internal energy Ui = 100 J to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and bf are Waf = 200 J, Wib = 50 J and Wbf = 100 J respectively. The heat supplied to the system along the path iaf, ib and bf are Qiaf, Qib and Qbf respectively. If the internal energy of the system in the state b is Ub = 200 J and Qiaf = 500 J, the ratio Qbf / Qib is
Options:
120
Medium
Steel wire of lenght ‘L’ at 40oC is suspended from the ceiling and then a mass ‘m’ is hung from its free end. The wire is cooled down from 40oC to 30oC to regain its original length ‘L’. The coefficient of linear thermal expansion of the steel is 10−5 /oC, Young’s modulus of steel is 1011 N/m2 and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of ‘m’ in kg is nearly
Options:
121
Medium
A piece of ice (heat capacity = 2100 J kg-1 oC-1 and latent heat = 3.36 $ \times $ 105 J kg-1 ) of mass m grams is at - 5 oC at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is
Options:
122
Medium
Two spherical bodies A (radius 6 cm ) and B (radius 18 cm ) are at temperature T1 and T2, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B?
Options:
123
Medium
A diatomic ideal gas is compressed adiabatically ${1 \over {32}} of its initial volume. If the initial temperature of the gas is Ti (in Kelvin) and the final temperature is a Ti, the value of a$ is
Options:
124
Medium
A metal rod AB of length 10x has its one end A in ice at 0$^\circC and the other end B in water at 100^\circC. If a point P on the rod is maintained at 400^\circC, then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of \lambda x from the ice end A, find the value of \lambda$. (Neglect any heat loss to the surrounding.)
Options:
125
Medium
In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Then, find the final temperature of the mixture.
Options:
126
Hard
One mole of a monatomic ideal gas undergoes the cyclic process \mathrm{J} \rightarrow \mathrm{K} \rightarrow \mathrm{L} \rightarrow \mathrm{M} \rightarrow \mathrm{J}, as shown in the P-T diagram. Match the quantities mentioned in List-I with their values in List-II and choose the correct option. [ \mathcal{R} is the gas constant.] List-I List-II (P) Work done in the complete cyclic process (1) RT_0 - 4RT_0 \ln 2 (Q) Change in the internal energy of the gas in the process JK (2) 0 (R) Heat given to the gas in the process KL (3) 3RT_0 (S) Change in the internal energy of the gas in the process MJ (4) -2RT_0 \ln 2 (5) -3RT_0 \ln 2
Options:
A) \mathrm{P} \rightarrow 1 ; \mathrm{Q} \rightarrow 3 ; \mathrm{R} \rightarrow 5 ; \mathrm{S} \rightarrow 4
B) \mathrm{P} \rightarrow 4 ; \mathrm{Q} \rightarrow 3 ; \mathrm{R} \rightarrow 5 ; \mathrm{S} \rightarrow 2
C) \mathrm{P} \rightarrow 4 ; \mathrm{Q} \rightarrow 1 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 2
D) \mathrm{P} \rightarrow 2 ; \mathrm{Q} \rightarrow 5 ; \mathrm{R} \rightarrow 3 ; \mathrm{S} \rightarrow 4
127
Medium
An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n. The internal energy of one mole of the gas is U_n and the speed of sound in the gas is \mathrm{v}_n. At a fixed temperature and pressure, which of the following is the correct option?
Options:
A) v_3 < v_6 and U_3 > U_6
B) v_5 > v_3 and U_3 > U_5
C) v_5 > v_7 and U_5 < U_7
D) v_6 < v_7 and U_6 < U_7
128
Medium
One mole of an ideal gas expands adiabatically from an initial state \left(T_{\mathrm{A}}, V_0\right) to final state \left(T_{\mathrm{f}}, 5 V_0\right). Another mole of the same gas expands isothermally from a different initial state \left(T_{\mathrm{B}}, V_0\right) to the same final state \left(T_{\mathrm{f}}, 5 V_0\right). The ratio of the specific heats at constant pressure and constant volume of this ideal gas is \gamma. What is the ratio T_{\mathrm{A}} / T_{\mathrm{B}} ?
Options:
A) 5^{\gamma-1}
B) 5^{1-\gamma}
C) 5^\gamma
D) 5^{1+\gamma}
129
Medium
Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option. [Given: Wien's constant as 2.9 \times 10^{-3} \mathrm{~m}-\mathrm{K} and \frac{h c}{e}=1.24 \times 10^{-6} \mathrm{~V}-\mathrm{m} ] List - I List - II (P) 2000 \mathrm{~K} (1) The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work function 4 \mathrm{eV}. (Q) 3000 \mathrm{~K} (2) The radiation at peak wavelength is visible to human eye. (R) 5000 \mathrm{~K} (3) The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction. (S) 10000 \mathrm{~K} (4) The power emitted per unit area is 1 / 16 of that emitted by a blackbody at temperature 6000 \mathrm{~K}. (5) The radiation at peak emission wavelength can be used to image human bones.
Options:
A) P \rightarrow 3, Q \rightarrow 5, R \rightarrow 2, S \rightarrow 3
B) P \rightarrow 3, Q \rightarrow 2, R \rightarrow 4, S \rightarrow 1
C) P \rightarrow 3, Q \rightarrow 4, R \rightarrow 2, S \rightarrow 1
D) P \rightarrow 1, Q \rightarrow 2, R \rightarrow 5, S \rightarrow 3
130
Hard
List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process. List-I List-II (I) 10^{-3} \mathrm{~kg} of water at 100^{\circ} \mathrm{C} is converted to steam at the same temperature, at a pressure of 10^{5} \mathrm{~Pa}. The volume of the system changes from 10^{-6} \mathrm{~m}^{3} to 10^{-3} \mathrm{~m}^{3} in the process. Latent heat of water =2250\, \mathrm{~kJ} / \mathrm{kg}. (P) 2 \mathrm{~kJ} (II) 0.2 moles of a rigid diatomic ideal gas with volume V at temperature 500 \mathrm{~K} undergoes an isobaric expansion to volume 3 \mathrm{~V}. Assume R=8.0 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}. (Q) 7 k J (III) One mole of a monatomic ideal gas is compressed adiabatically from volume V=\frac{1}{3} \mathrm{~m}^{3} and pressure 2 \mathrm{kPa} to volume \frac{V}{8}. (R) 4 \mathrm{~kJ} (IV) Three moles of a diatomic ideal gas whose molecules can vibrate, is given 9 \mathrm{~kJ} of heat and undergoes isobaric expansion. (S) 5 \mathrm{~kJ} (T) 3 \mathrm{~kJ} Which one of the following options is correct?
Options:
A) I \rightarrow T, II \rightarrow R, III \rightarrow S, IV \rightarrow Q
B) I \rightarrow S, II \rightarrow P, III \rightarrow T, IV \rightarrow P
C) I \rightarrow P, II \rightarrow R, III \rightarrow T, IV \rightarrow Q
D) I \rightarrow Q, II \rightarrow R, III \rightarrow S, IV \rightarrow T
131
Medium
A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, CV = 2R. Here, R is the gas constant. Initially, each side has a volume V0 and temperature T0. The left side has an electric heater, which is turned on at very low power to transfer heat Q to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to V0/2. Consequently, the gas temperatures on the left and the right sides become TL and TR, respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.
Options:
A) \sqrt 2
B) \sqrt 3
C) 2
D) 3
132
Hard
A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, CV = 2R. Here, R is the gas constant. Initially, each side has a volume V0 and temperature T0. The left side has an electric heater, which is turned on at very low power to transfer heat Q to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to V0/2. Consequently, the gas temperatures on the left and the right sides become TL and TR, respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.
Options:
A) 4(2\sqrt 2 + 1)
B) 4(2\sqrt 2 - 1)
C) (5\sqrt 2 + 1)
D) (5\sqrt 2 - 1)
133
Easy
An ideal gas undergoes a four step cycle as shown in the P-V diagram below. During this cycle, heat is absorbed by the gas in
Options:
A) steps 1 and 2
B) steps 1 and 3
C) steps 1 and 4
D) steps 2 and 4
134
Hard
In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by T$\Delta X where T is temperature of the system and \Delta X is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas, X = {3 \over 2}R\,\ln \left( {{T \over {{T_A}}}} \right) + R\,\ln \left( {{V \over {{V_A}}}} \right)$Here, R is gas constant, V is volume of gas, TA and VA are constants.The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.
Options:
A) I $ \to P, II \to R, III \to T, IV \to $ S
B) I $ \to P, II \to T, III \to Q, IV \to $ T
C) I $ \to S, II \to T, III \to Q, IV \to $ U
D) I $ \to P, II \to R, III \to T, IV \to $ P
135
Hard
In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by T$\Delta X where T is temperature of the system and \Delta X is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas, X = {3 \over 2}R\,\ln \left( {{T \over {{T_A}}}} \right) + R\,\ln \left( {{V \over {{V_A}}}} \right)$Here, R is gas constant, V is volume of gas, TA and VA are constants.The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.
Options:
A) I$ \to S, II \to R, III \to Q, IV \to $ T
B) I $ \to Q, II \to R, III \to P, IV \to $ U
C) I $ \to Q, II \to S, III \to R, IV \to $ U
D) I $ \to Q, II \to R, III \to S, IV \to $ U
136
Medium
One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $PV$-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-I with the corresponding statements in List-II. LIST - I LIST - II P. In process I 1. Work done by the gas is zero Q. In process II 2. Temperature of the gas remainsunchanged R. In process III 3. No heat is exchanged between the gas and its surroundings S. In process IV 4. Work done by the gas is 6P0V0
Options:
A) P \to 4;Q \to 3;R \to 1;S \to 2
B) P \to 1;Q \to 3;R \to 2;S \to 4
C) P \to 3;Q \to 4;R \to 1;S \to 2
D) P \to 3;Q \to 4;R \to 2;S \to
137
Medium
An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P-V diagram in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here Y is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n.
Options:
A) \left( {{\rm I}V} \right)\left( {ii} \right)\left( S \right)
B) \left( {{\rm I}{\rm I}{\rm I}} \right)\left( {ii} \right)\left( S \right)
C) \left( {{\rm I}{\rm I}} \right)\left( {iv} \right)\left( P \right)
D) \left( {{\rm I}{\rm I}} \right)\left( {iv} \right)\left( R \right)
138
Medium
An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P-V diagram in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here Y is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n.
Options:
A) \left( {\rm I} \right)\left( {ii} \right)\left( Q \right)
B) \left( {{\rm I}V} \right)\left( {ii} \right)\left( R \right)
C) \left( {{\rm I}{\rm I}{\rm I}} \right)\left( {iv} \right)\left( R \right)
D) \left( {\rm I} \right)\left( {iv} \right)\left( Q \right)
139
Medium
An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P-V diagram in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here Y is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n.
Options:
A) \left( {{\rm I}{\rm I}} \right)\left( {iv} \right)\left( R \right)
B) \left( {{\rm I}{\rm I}{\rm I}} \right)\left( {iii} \right)\left( P \right)
C) \left( {{\rm I}{\rm I}} \right)\left( {iii} \right)\left( S \right)
D) \left( {{\rm I}{\rm I}} \right)\left( {iii} \right)\left( P \right)
140
Medium
The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 m at 10oC. Now the end P is maintained at 10oC, while the end S is heated and maintained at 400oC. The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2 $ \times $ 10-5 K-1 , the change in length of the wire PQ is
Options:
A) 0.78 mm
B) 0.90 mm
C) 1.56 mm
D) 2.34 mm
141
Medium
A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pi = 105 Pa and volume Vi = 10-3 m3 changes to a final state at Pf = $\left( {{1 \over {32}}} \right) \times {10^5}\,Pa and Vf = 8 \times $ 10-3 m3 in an adiabatic quasi-static process, such that P3V5 = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at Pi followed by an isochoric (isovolumetric) process at volume Vf. The amount of heat supplied to the system in the two-step process is approximately
Options:
A) 112 J
B) 294 J
C) 588 J
D) 813 J
142
Medium
A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30°C and the entire stored 120 litres of water is initially cooled to 10°C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is : (Specific heat of water is 4.2 kJ kg−1 K−1 and the density of water is 1000 kg m−3)
Options:
A) 1600
B) 2067
C) 2533
D) 3933
143
Easy
Parallel rays of light of intensity $I = 912 Wm–2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant \sigma = 5.7 \times $ 10–8 Wm–2K–4 and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to
Options:
A) 330 K
B) 660 K
C) 990 K
D) 1550 K
144
Easy
In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas are ${C_v} = {3 \over 2}R, {C_p} = {5 \over 2}R, and those for an ideal diatomic gas are {C_v} = {5 \over 2}R, {C_p} = {7 \over 2}R$.
Options:
A) 550 K
B) 525 K
C) 513 K
D) 490 K
145
Hard
In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas are ${C_v} = {3 \over 2}R, {C_p} = {5 \over 2}R, and those for an ideal diatomic gas are {C_v} = {5 \over 2}R, {C_p} = {7 \over 2}R$.
Options:
A) 250 R
B) 200 R
C) 100 R
D) -$100 R
146
Medium
One mole of a monatomic ideal gas is taken along two cyclic processes E $\to F \to G \to E and E \to F \to H \to E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic. Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists : List I List II P. G \to E 1. 160{P_0}{V_0}ln2 Q. G \to H 2. 36{P_0}{V_0} R. F \to H 3. 24{P_0}{V_0} S. F \to G 4. 31{P_0}{V_0}
Options:
A) P-4, Q-3, R-2, S-1
B) P-4, Q-3, R-1, S-2
C) P-3, Q-1, R-2, S-4
D) P-1, Q-3, R-2, S-4
147
Medium
Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is
Options:
A) 1 : 4
B) 1 : 2
C) 6 : 9
D) 8 : 9
148
Medium
Two rectangular blocks, having identical dimensions, can be arranged in either configuration-I or configuration-II as shown in the figure. One of the blocks has thermal conductivity $\kappa and the other 2\kappa $. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in configuration-I. The time to transport the same amount of heat in configuration-II is
Options:
A) 2.0 s
B) 3.0 s
C) 4.5 s
D) 6.0 s
149
Medium
Two moles of ideal helium gas are in a rubber balloon at 30oC. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35oC. The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)
Options:
A) 62 J
B) 104 J
C) 124 J
D) 208 J
150
Medium
A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds $\left( {{{{v_{rms}}\left( {helium} \right)} \over {{v_{rms}}\left( {\arg on} \right)}}} \right)$ is
Options:
A) 0.32
B) 0.45
C) 2.24
D) 3.16
151
Medium
Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductively. The first and third plates are maintained at temperatures 2T and 3T, respectively. The temperature of the middle (i.e. second) plate under steady state condition is
Options:
A) {\left( {{{65} \over 2}} \right)^{1/4}}T
B) {\left( {{{97} \over 4}} \right)^{1/4}}T
C) {\left( {{{97} \over 2}} \right)^{1/4}}T
D) {(97)^{1/4}}T
152
Medium
5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T1, the work done in the process is
Options:
A) {9 \over 8}R{T_1}
B) {3 \over 2}R{T_1}
C) {15 \over 8}R{T_1}
D) {9 \over 2}R{T_1}
153
Medium
One mole of a monatomic gas is taken through a cycle ABCDA as shown in the PV diagram. Column II give the characteristics involved in the cycle. Match them with each of the processes given in Column I. Column I Column II (A) Process A$ \to B (P) Internal energy decreases. (B) Process B \to C (Q) Internal energy increase. (C) Process C \to D (R) Heat is lost. (D) Process D \to $A (S) Heat is gained. (T) Work is done on the gas.
Options:
A) (A)$\to(P), (R), (T); (B)\to(P), R; (C)\to(Q), (S); (D)\to$(R), (T)
B) (A)$\to(P), (T); (B)\to(P), (R); (C)\to(Q), (S); (D)\to$(R)
C) (A)$\to(R), (T); (B)\to(P), (R); (C)\to(S); (D)\to$(R), (T)
D) (A)$\to(P), (R), (T); (B)\to(P), (R); (C)\to(Q); (D)\to$(R), (T)
154
Hard
A real gas behaves like an ideal gas if its
Options:
A) pressure and temperature are both high
B) pressure and temperature are both low
C) pressure is high and temperature is low
D) pressure is low and temperature is high
155
Hard
Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II: Column I Column II (A) The energy of the system is increased. (P) System : A capacitor, initially uncharged.Process : It is connected to a battery. (B) Mechanical energy is provided to the system, which is converted into energy of random motion of its parts. (Q) System : A gas in an adiabatic container filled with an adiabatic piston.Process : The gas is compressed by pushing the piston. (C) Internal energy of the system is converted into its mechanical energy. (R) System : A gas in a rigid container.Process : The gas gets cooled due to colder atmosphere surrounding it. (D) Mass of the system is decreased. (S) System : A heavy nucleus, initially at rest.Process : The nucleus fissions into two fragments of nearly equal masses and some neutrons are emitted. (T) System : A resistive wire loop.Process : The loop is placed in a time varying magnetic field perpendicular to its plane.
Options:
A) (A)$\to(P), (S), (T); (B)\to(Q); (C)\to(S); (D)\to$(S), (R)
B) (A)$\to(P), (Q), (T); (B)\to(Q); (C)\to(S); (D)\to$(S)
C) (A)$\to(P), (Q), (T); (B)\to(T); (C)\to(S); (D)\to$(S)
D) (A)$\to(S), (Q), (T); (B)\to(Q); (C)\to(S); (D)\to$(S)
156
Hard
Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 $\times 4 matrix given in the ORS. Column I Column II (A) An insulated container has two chambers separated by a valve. Chamber I contains an ideal gas and the Chamber II has vacuum. The valve is opened. (P) The temperature of the gas decreases (B) An ideal monatomic gas expands to twice its original volume such that its pressure P \propto \frac{1}{\mathrm{V}^2}, where V is the volume of the gas (Q) The temperature of the gas increase or remains constant. (C) An ideal monoatomic gas expands to twice its original volume such that its pressure P \propto \frac{1}{\mathrm{V}^{4/3}}$, where V is its volume (R) The gas loses heat (D) An ideal monoatomic gas expands such that its pressure P and volume V follows the behaviour shown in the graph (S) The gas gains heat
Options:
A) A $\to (P); B \to (P, Q); C \to (R, S); D \to$ (P, R)
B) A $\to (P); B \to (R, S); C \to (P, Q); D \to$ (Q, S)
C) A $\to (Q); B \to (R, S); C \to (P, S); D \to$ (P, R)
D) A $\to (Q); B \to (P, Q); C \to (P, S); D \to$ (Q, S)
157
Medium
An ideal gas is expanding such that PT$^2$ = constant. The coefficient of volume expansion of the gas is
Options:
A) \frac{1}{\mathrm{T}}
B) \frac{2}{\mathrm{T}}
C) \frac{3}{\mathrm{T}}
D) \frac{4}{\mathrm{T}}
158
Medium
STATEMENT 1 The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume. Because STATEMENT 2 The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.
Options:
A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct for Statement-1.
C) Statement-1 is True, Statement-2 is False.
D) Statement-1 is False, Statement-2 is True.
159
Medium
A fixed thermally conducting cylinder has a radius R and height L_0. The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P_0.
Options:
A) P$_0
B) {{{P_0}} \over 2}
C) {{{P_0}} \over 2} + {{Mg} \over {\pi {R^2}}}
D) {{{P_0}} \over 2} - {{Mg} \over {\pi {R^2}}}
160
Medium
A fixed thermally conducting cylinder has a radius R and height L_0. The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P_0.
Options:
A) \rho g{({L_0} - H)^2} + {P_0}({L_0} - H) + {L_0}{P_0} = 0
B) \rho g{({L_0} - H)^2} - {P_0}({L_0} - H) - {L_0}{P_0} = 0
C) \rho g{({L_0} - H)^2} + {P_0}({L_0} - H) - {L_0}{P_0} = 0
D) \rho g{({L_0} - H)^2} - {P_0}({L_0} - H) + {L_0}{P_0} = 0
161
Medium
Heat given to the processes is positive. Match Column I with Column II: Column I Column II (A) JK (P) $\Delta W>0 (B) KL (Q) \Delta \mathrm{Q}<0 (C) LM (R) \Delta \mathrm{W}<0 (D) MJ (S) \Delta Q>0
Options:
A) [\mathrm{A} \rightarrow(\mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{~S}) ; \mathrm{C} \rightarrow(\mathrm{Q}) ; \mathrm{D} \rightarrow( \mathrm{R})]
B) [\mathrm{A} \rightarrow(\mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}) ; \mathrm{C} \rightarrow(\mathrm{~S}) ; \mathrm{D} \rightarrow(\mathrm{Q})]
C) [\mathrm{A} \rightarrow(\mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{~S}) ; \mathrm{C} \rightarrow(\mathrm{~S}) ; \mathrm{D} \rightarrow(\mathrm{Q}, \mathrm{R})]
D) [\mathrm{A} \rightarrow(\mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{S}) ; \mathrm{C} \rightarrow(\mathrm{S}) ; \mathrm{D} \rightarrow( \mathrm{R})]
162
Medium
A cylinder of mass $1 \mathrm{~kg} is given heat of 20000 \mathrm{~J} at atmospheric pressure. If initially temperature of cylinder is 20^{\circ} \mathrm{C}, find (A) The final temperature of the cylinder; (B) The work done by the cylinder; (C) The change in internal energy of the cylinder. Given : The specific heat of cylinder =400 \mathrm{~J} \mathrm{~kg}^{-1 \circ} \mathrm{C}^{-1} Coefficient of volume expansion =9 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1} \text {; } Atmospheric pressure =10^{5} \mathrm{~N} / \mathrm{m}^{2} Density of cylinder =9000 \mathrm{~kg} / \mathrm{m}^{3}$ )
Options:
A) (\mathrm{A}) 70^{\circ} \mathrm{C}, (B) 0.05 \mathrm{~J} (C) \Delta \mathrm{U}=1.9 \times 10^{4} \mathrm{~J}
B) (\mathrm{A}) 70^{\circ} \mathrm{C}, (B) 0.05 \mathrm{~J} (C) \Delta \mathrm{U}=2.9 \times 10^{4} \mathrm{~J}
C) (\mathrm{A}) 60^{\circ} \mathrm{C}, (B) 0.05 \mathrm{~J} (C) \Delta \mathrm{U}=1.9 \times 10^{4} \mathrm{~J}
D) (\mathrm{A}) 70^{\circ} \mathrm{C}, (B) 0.07 \mathrm{~J} (C) \Delta \mathrm{U}=1.9 \times 10^{4} \mathrm{~J}
163
Medium
The mean free path of a molecule of diameter 5 \times 10^{-10} m at the temperature 41^{\circ}C and pressure 1.38 \times 10^5 Pa, is given as ________ m. (Given k_B = 1.38 \times 10^{-23} J/K).
Options:
A) 2\sqrt{2} \times 10^{-10}
B) 10\sqrt{2} \times 10^{-8}
C) 2\sqrt{2} \times 10^{-8}
D) 2 \times 10^{-8}
164
Easy
Which of the following best represents the temperature versus heat supplied graph for water, in the range of -20^{\circ} \mathrm{C} to 120^{\circ} \mathrm{C}?
Options:
A)
B)
C)
D)
165
Medium
10 kg of ice at -10^{\circ} \mathrm{C} is added to 100 kg of water to lower its temperature from 25 { }^{\circ} \mathrm{C}. Consider no heat exchange to surroundings. The decrement to the temperature of water is \_\_\_\_ { }^{\circ} \mathrm{C}. (specific heat of ice =2100 \mathrm{~J} / \mathrm{Kg} .{ }^{\circ} \mathrm{C}, specific heat of water =4200 \mathrm{~J} / \mathrm{Kg} .{ }^{\circ} \mathrm{C}, latent heat of fusion of ice =3.36 \times 10^5 \mathrm{~J} / \mathrm{Kg} )
Options:
A) 15
B) 10
C) 6.67
D) 11.6
166
Medium
In the following p-V diagram the equation of state along the curved path is given by (V-2)^2=4 a p where a is a constant. The total work done in the closed path is
Options:
A) +\frac{1}{3 a}
B) -\frac{1}{a}
C) \frac{1}{2 a}
D) -\frac{1}{3 a}
167
Easy
10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from P_1 to P_2 is \alpha Joule ( P_1=21.7 \mathrm{~Pa} and \left.P_2=30 \mathrm{~Pa}, \mathrm{C}_v=21 \mathrm{~J} / \mathrm{K} . \mathrm{mol}, R=8.3 \mathrm{~J} / \mathrm{mol} . \mathrm{K}\right). The value of \alpha is \_\_\_\_ .
Options:
A) 21
B) 28
C) 24
D) 15
168
Medium
Density of water at 4^{\circ} \mathrm{C} and 20^{\circ} \mathrm{C} are 1000 \mathrm{~kg} / \mathrm{m}^3 and 998 \mathrm{~kg} / \mathrm{m}^3 respectively. The increase in internal energy of 4 kg of water when it is heated from 4^{\circ} \mathrm{C} to 20^{\circ} \mathrm{C} is \_\_\_\_ J. (specific heat capacity of water =4.2 \mathrm{~J} / \mathrm{kg}. and 1 atmospheric pressure =10^5 \mathrm{~Pa} )
Options:
A) 268799.2
B) 315826.2
C) 234699.2
D) 258700.8
169
Medium
One mole of an ideal diatomic gas expands from volume V to 2 V isothermally at a temperature 27^{\circ} \mathrm{C} and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from 27^{\circ} \mathrm{C} doing the same amount of work W, then its final temperature will be (close to) \_\_\_\_ { }^{\circ} \mathrm{C}. $ \left(\log _e 2=0.693\right)
Options:
A) -56
B) -117
C) -30
D) -189
170
Medium
The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of 17 \mathrm{~cm}^2 and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by 4^{\circ} \mathrm{C}, then the piston will move \_\_\_\_ cm. (atmospheric pressure =10^5 \mathrm{~Pa} )
Options:
A) 1.55
B) 14.5
C) 15.5
D) 1.45
171
Medium
An air bubble of volume 2.9 \mathrm{~cm}^3 rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17^{\circ} \mathrm{C}. The volume of the bubble when it reaches the surface, where the water temperature is 27^{\circ} \mathrm{C}, is \_\_\_\_ \mathrm{cm}^3. ( \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, density of water =10^3 \mathrm{~kg} / \mathrm{m}^3, and 1 atm pressure is 10^5 \mathrm{~Pa} )
Options:
A) 2.0
B) 4.2
C) 3.0
D) 4.5
172
Medium
Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is 32 \times 10^{18} / \mathrm{s} then collision frequency in gas A is \_\_\_\_ /s.
Options:
A) 8 \times 10^{18}
B) 2 \times 10^{18}
C) 32 \times 10^{18}
D) 4 \times 10^{18}
173
Medium
Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at 100^{\circ} \mathrm{C} and 40^{\circ} \mathrm{C} respectively. Given the thermal conductivity of \operatorname{rod} x is three times of that of \operatorname{rod} y, the temperature at junction points B and E are (close to):
Options:
A) 60^{\circ} \mathrm{C} and 45^{\circ} \mathrm{C} respectively
B) 80^{\circ} \mathrm{C} and 70^{\circ} \mathrm{C} respectively
C) 89^{\circ} \mathrm{C} and 73^{\circ} \mathrm{C} respectively
D) 80^{\circ} \mathrm{C} and 60^{\circ} \mathrm{C} respectively
174
Medium
The volume of an ideal gas increases 8 times and temperature becomes (1 / 4)^{\text {th }} of initial temperature during a reversible change. If there is no exchange of heat in this process (\Delta \mathrm{Q}=0) then identify the gas from the following options (Assuming the gases given in the options are ideal gases) :
Options:
A) \mathrm{NH}_3
B) \mathrm{O}_2
C) \mathrm{CO}_2
D) He
175
Easy
The r.m.s. speed of oxygen molecules at 47 °C is equal to that of the hydrogen molecules kept at _________ °C. (Mass of oxygen molecule/mass of hydrogen molecule = 32/2)
Options:
A) -100
B) -253
C) -20
D) -235
176
Easy
A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27^{\circ} \mathrm{C} to 87^{\circ} \mathrm{C}. The rate of consumption of the gas is \_\_\_\_ \mathrm{g} / \mathrm{s}. (Take heat of combustion of gas =5.0 \times 10^4 \mathrm{~J} / \mathrm{g} ) specific heat capacity of water =4200 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}
Options:
A) 4.2
B) 2.1
C) 0.21
D) 0.42
177
Easy
A monoatomic gas having \gamma = \frac{5}{3} is stored in a thermally insulated container and the gas is suddenly compressed to \left( \frac{1}{8} \right)^{\text{th}} of its initial volume. The ratio of final pressure and initial pressure is: (\gamma is the ratio of specific heats of the gas at constant pressure and at constant volume)
Options:
A) 16
B) 32
C) 28
D) 40
178
Easy
Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool.(Take g = 10 m/s2, specific heat of water = 4200 J/(kg K))
Options:
A) 0.36 K
B) 0.23 K
C) 0.48 K
D) 0.14 K
179
Easy
The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is: (Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)
Options:
A) 1 : \sqrt{10}
B) 10 : 1
C) 1 : 10
D) 1 : 1
180
Easy
Match List - I with List - II. List - I List - II (A) Isothermal (I) ΔW (work done) = 0 (B) Adiabatic (II) ΔQ (supplied heat) = 0 (C) Isobaric (III) ΔU (change in internal energy) ≠ 0 (D) Isochoric (IV) ΔU = 0 Choose the correct answer from the options given below :
Options:
A) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
B) (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
C) (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
D) (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
181
Easy
Match the List I with List II List - I List - II (A) Triatomic rigid gas (I) \frac{C_p}{C_v}=\frac{5}{3} (B) Diatomic non-rigid gas (II) \frac{C_p}{C_v}=\frac{7}{5} (C) Monoatomic gas (III) \frac{C_p}{C_v}=\frac{4}{3} (D) Diatomic rigid gas (IV) \frac{C_p}{C_v}=\frac{9}{7} Choose the correct answer from the options given below:
Options:
A) A-III, B-IV, C-I, D-II
B) A-II, B-IV, C-I, D-III
C) A-IV, B-II, C-III, D-I
D) A-III, B-II, C-IV, D-I
182
Medium
Consider a rectangular sheet of solid material of length l=9 \mathrm{~cm} and width \mathrm{d}=4 \mathrm{~cm}. The coefficient of linear expansion is \alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1} at room temperature and one atmospheric pressure. The mass of sheet m=0.1 \mathrm{~kg} and the specific heat capacity C_{\mathrm{v}}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}. If the amount of heat supplied to the material is 8.1 \times 10^2 \mathrm{~J} then change in area of the rectangular sheet is :
Options:
A) 2.0 \times 10^{-6} \mathrm{~m}^2
B) 6.0 \times 10^{-7} \mathrm{~m}^2
C) 3.0 \times 10^{-7} \mathrm{~m}^2
D) 4.0 \times 10^{-7} \mathrm{~m}^2
183
Medium
There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K . If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K , at steady state the pressure in the vessels will be (in kPa ).
Options:
A) 24
B) 4.4
C) 18
D) 6
184
Easy
Match List - I with List - II. List - I List - II (A) Isobaric (I) \Delta Q=\Delta W (B) Isochoric (II) \Delta Q=\Delta U (C) Adiabatic (III) \Delta Q= zero (D) Isothermal (IV) \Delta Q=\Delta U+P\Delta V \Delta Q= Heat supplied \Delta W= Work done by the system \Delta \mathrm{U}= Change in internal energy \mathrm{P}= Pressure of the system \Delta \mathrm{V}= Change in volume of the system Choose the correct answer from the options given below :
Options:
A) (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
B) (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
C) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
D) (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
185
Medium
Consider the sound wave travelling in ideal gases of \mathrm{He}, \mathrm{CH}_4, and \mathrm{CO}_2. All the gases have the same ratio \frac{P}{\rho}, where P is the pressure and \rho is the density. The ratio of the speed of sound through the gases \mathrm{V}_{\mathrm{He}}: \mathrm{V}_{\mathrm{CH}_4}: \mathrm{V}_{\mathrm{CO}_2} is given by
Options:
A) \sqrt{\frac{7}{5}}: \sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}
B) \sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}: \sqrt{\frac{4}{3}}
C) \sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}: \sqrt{\frac{7}{5}}
D) \sqrt{\frac{4}{3}}: \sqrt{\frac{5}{3}}: \sqrt{\frac{7}{5}}
186
Medium
The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are 3 \times 10^{-7} \mathrm{~m} and 600 \mathrm{~m} / \mathrm{s}, respectively. Find the frequency of its collisions.
Options:
A) 5 \times 10^8 / \mathrm{s}
B) 9 \times 10^5 / \mathrm{s}
C) 2 \times 10^{10} / \mathrm{s}
D) 2 \times 10^9 / \mathrm{s}
187
Medium
An ideal gas exists in a state with pressure P_0, volume V_0. It is isothermally expanded to 4 times of its initial volume \left(\mathrm{V}_0\right), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is
Options:
A) \mathrm{P}_0 \mathrm{~V}_0(\ln 2-0.75)
B) \mathrm{P}_0 \mathrm{~V}_0(2 \ln 2-0.75)
C) \mathrm{P}_0 \mathrm{~V}_0(2 \ln 2-0.25)
D) \mathrm{P}_0 \mathrm{~V}_0(\ln 2-0.25)
188
Easy
Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4 \% when heated by 1^{\circ} \mathrm{C}. Its initial temperature must be:
Options:
A) 2500 K
B) 25^{\circ} \mathrm{C}
C) 250^{\circ} \mathrm{C}
D) 250 K
189
Medium
A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 \mathrm{~cm}^3 and temperature 27^{\circ} \mathrm{C}. The change in temperature when the gas is adiabatically compressed to 200 \mathrm{~cm}^3 is: (Take \gamma=1.5 ; \gamma is the ratio of specific heats at constant pressure and at constant volume)
Options:
A) 300 K
B) 600 K
C) 327 K
D) 522 K
190
Medium
During the melting of a slab of ice at 273 K at atmospheric pressure :
Options:
A) Internal energy of ice-water system remains unchanged.
B) Positive work is done by the ice-water system on the atmosphere.
C) Positive work is done on the ice-water system by the atmosphere.
D) Internal energy of the ice-water system decreases.
191
Medium
A piston of mass M is hung from a massless spring whose restoring force law goes as F=-k x^3, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' n ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height \mathrm{L}_0 to \mathrm{L}_1, the total energy delivered by the filament is:(Assume spring to be in its natural length before heating)
Options:
A) n R T \ln \left(\frac{L_1}{L_0}\right)+M g\left(L_1-L_0\right)+\frac{3 k}{4}\left(L_1{ }^4-L_0{ }^4\right)
B) n R T \ln \left(\frac{L_1}{L_0}\right)+M g\left(L_1-L_0\right)+\frac{k}{4}\left(L_1^4-L_0{ }^4\right)
C) n R T \ln \left(\frac{L_1^2}{L_0^2}\right)+\frac{M g}{2}\left(L_1-L_0\right)+\frac{k}{4}\left(L_1^4-L_0{ }^4\right)
D) 3 n R T \ln \left(\frac{L_1}{L_0}\right)+2 M g\left(L_1-L_0\right)+\frac{k}{3}\left(L_1{ }^3-L_0{ }^3\right)
192
Easy
\text { Match List - I with List - II. } \begin{array}{lll} & \text { List - I } & {List - II }\\ \text { } \\ \text { (A) } & \text { Heat capacity of body } & \text { (I) } \mathrm{J} \mathrm{~kg}^{-1} \\ \text { (B) } & \text { Specific heat capacity of body } & \text { (II) } \mathrm{J} \mathrm{~K}^{-1} \\ \text { (C) } & \text { Latent heat } & \text { (III) } \mathrm{J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1} \\ \text { (D) } & \text { Thermal conductivity } & \text { (IV) } \mathrm{J} \mathrm{~m}^{-1} \mathrm{~K}^{-1} \mathrm{~s}^{-1} \end{array} \text { Choose the correct answer from the options given below : }
Options:
A) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
B) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
C) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
D) (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
193
Medium
Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from \mathrm{T}_1 to \mathrm{T}_2 is proportional to \left(\mathrm{T}_2-\mathrm{T}_1\right). Choose the correct answer from the options given below :
Options:
A) (B), (D) only
B) (B), (E) only
C) (A), (C), (E) only
D) (A), (C), (D) only
194
Easy
In an adiabatic process, which of the following statements is true?
Options:
A) The internal energy of the gas decreases as the temperature increases
B) The molar heat capacity is zero
C) Work done by the gas equals the increase in internal energy
D) The molar heat capacity is infinite
195
Medium
The equation for real gas is given by \left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}, where \mathrm{P}, \mathrm{V}, \mathrm{T} and R are the pressure, volume, temperature and gas constant, respectively. The dimension of \mathrm{ab}^{-2} is equivalent to that of :
Options:
A) Compressibility
B) Planck's constant
C) Energy density
D) Strain
196
Easy
The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have
Options:
A) low thermal conductivity and high electrical conductivity
B) low thermal conductivity and low electrical conductivity
C) high thermal conductivity and high electrical conductivity
D) high thermal conductivity and low electrical conductivity
197
Medium
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.Reason (R) : In isothermal process, PV = constant, while in adiabatic process PV^{\gamma} = constant. Here \gamma is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.In the light of the above statements, choose the correct answer from the options given below:
Options:
A) (A) is true but (R) is false
B) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
C) (A) is false but (R) is true
D) Both (A) and (R) are true and (R) is the correct explanation of (A)
198
Medium
A cup of coffee cools from 90°C to 80°C in t minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is:
Options:
A) \frac{13}{5}t
B) \frac{10}{13}t
C) \frac{5}{13}t
D) \frac{13}{10}t
199
Medium
A poly-atomic molecule \left(C_V=3 R, C_P=4 R\right., where R is gas constant) goes from phase space point \mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right) to point \mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right) to point \mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right. \mathrm{Pa}, \mathrm{V}_C=8 \times 10^{-6} \mathrm{~m}^3 ). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is :
Options:
A) 500 \mathrm{R}(\ln 3+\ln 4)
B) 450 \mathrm{R}(\ln 4-\ln 3)
C) 500 \mathrm{R} \ln 2
D) 400 \mathrm{R} \ln 4
200
Easy
The work done in an adiabatic change in an ideal gas depends upon only :
Options:
A) change in its pressure
B) change in its temperature
C) change in its specific heat
D) change in its volume
201
Easy
The ratio of vapour densities of two gases at the same temperature is \frac{4}{25} , then the ratio of r.m.s. velocities will be :
Options:
A) \frac{5}{2}
B) \frac{25}{4}
C) \frac{4}{25}
D) \frac{2}{5}
202
Medium
The kinetic energy of translation of the molecules in 50 g of \text{CO}_2 gas at 17°C is :
Options:
A) 4205.5 J
B) 3582.7 J
C) 3986.3 J
D) 4102.8 J
203
Easy
For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?
Options:
A)
B)
C)
D)
204
Medium
A Carnot engine (\mathrm{E}) is working between two temperatures 473 K and 273 K . In a new system two engines - engine E_1 works between 473 K to 373 K and engine E_2 works between 373 K to 273 K . If \eta_{12}, \eta_1 and \eta_2 are the efficiencies of the engines E, E_1 and E_2, respectively, then
Options:
A) \eta_{12}=\eta_1 \eta_2
B) \eta_{12}=\eta_1+\eta_2
C) \eta_{12} \geq \eta_1+\eta_2
D) \eta_{12}<\eta_1+\eta_2
205
Easy
The temperature of a body in air falls from 40^{\circ} \mathrm{C} to 24^{\circ} \mathrm{C} in 4 minutes. The temperature of the air is 16^{\circ} \mathrm{C}. The temperature of the body in the next 4 minutes will be :
Options:
A) \frac{28}{3}{ }^{\circ} \mathrm{C}
B) \frac{56}{3}{ }^{\circ} \mathrm{C}
C) \frac{42}{3}{ }^{\circ} \mathrm{C}
D) \frac{14}{3}{ }^{\circ} \mathrm{C}
206
Medium
The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :
Options:
A) zero
B) 40\pi
C) 5\pi
D) 10\pi
207
Medium
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R) : Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below :
Options:
A) Both (\mathbf{A}) and (\mathbf{R}) are true and (\mathbf{R}) is the correct explanation of (\mathbf{A})
B) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
C) (A) is false but (R) is true
D) (A) is true but (\mathbf{R}) is false
208
Easy
Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?
Options:
A)
B)
C)
D)
209
Medium
An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature. A. The work done by gas during the process is zero. B. The heat added to gas is different from change in its internal energy. C. The volume of the gas is increased. D. The internal energy of the gas is increased. E. The process is isochoric (constant volume process) Choose the correct answer from the options given below:
Options:
A) A, C Only
B) A, D, E Only
C) E Only
D) A, B, C, D Only
210
Easy
Water of mass m gram is slowly heated to increase the temperature from T_1 to T_\gamma. The change in entropy of the water, given specific heat of water is 1 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}, is :
Options:
A) \mathrm{m}\left(\mathrm{T}_2-\mathrm{T}_1\right)
B) zero
C) \mathrm{m} \ln \left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)
D) \mathrm{m} \ln \left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)
211
Easy
Using the given P-V diagram, the work done by an ideal gas along the path A B C D is :
Options:
A) 3 \mathrm{P}_0 \mathrm{~V}_0
B) -3 \mathrm{P}_0 \mathrm{~V}_0
C) -4 \mathrm{P}_0 \mathrm{~V}_0
D) 4 \mathrm{P}_0 \mathrm{~V}_0
212
Easy
Match the List - I with List - II List - I List - II (A) Pressure varies inversely with volume of an ideal gas. (I) Adiabatic process (B) Heat absorbed goes partly to increase internal energy and partly to do work. (II) Isochoric process (C) Heat is neither absorbed nor released by a system. (III) Isothermal process (D) No work is done on or by a gas. (IV) Isobaric process Choose the correct answer from the options given below:
Options:
A) A-I, B-III, C-II, D-IV
B) A-I, B-IV, C-II, D-III
C) A-III, B-I, C-IV, D-II
D) A-III, B-IV, C-I, D-II
213
Easy
A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is _______ grams. (Latent heat of fusion of lead =2.5 \times 10^4 \mathrm{JKg}^{-1} and specific heat capacity of lead =125 \mathrm{JKg}^{-1} \left.\mathrm{K}^{-1}\right)
Options:
A) 20
B) 15
C) 5
D) 10
214
Easy
Given are statements for certain thermodynamic variables, (A) Internal energy, volume (\mathrm{V}) and mass (\mathrm{M}) are extensive variables. (B) Pressure (P), temperature ( T ) and density ( \rho ) are intensive variables. (C) Volume (V), temperature (T) and density ( \rho ) are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the options given below :
Options:
A) (C) and (D) Only
B) (A) and (B) Only
C) (D) and (A) Only
D) (B) and (C) Only
215
Medium
For a diatomic gas, if \gamma_1=\left(\frac{C p}{C v}\right) for rigid molecules and \gamma_2=\left(\frac{C p}{C v}\right) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? (Cp and Cv are specific heats of the gas at constant pressure and volume)
Options:
A) \gamma_2<\gamma_1
B) \gamma_2>\gamma_1
C) \gamma_2=\gamma_1
D) 2 \gamma_2=\gamma_1
216
Medium
Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),
Options:
A) 64 E
B) 16 E
C) E
D) 256 E
217
Medium
An amount of ice of mass 10^{-3} \mathrm{~kg} and temperature -10^{\circ} \mathrm{C} is transformed to vapour of temperature 110^{\circ} \mathrm{C} by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice =2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}, specific heat of water =4180 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}, specific heat of steam =1920 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}, Latent heat of ice =3.35 \times 10^5 \mathrm{Jkg}^{-1} and Latent heat of steam =2.25 \times 10^6 \mathrm{Jkg}^{-1} )
Options:
A) 3022 J
B) 3043 J
C) 3003 J
D) 3024 J
218
Medium
A real gas within a closed chamber at $27^{\circ} \mathrm{C} undergoes the cyclic process as shown in figure. The gas obeys P V^3=R T equation for the path A to B. The net work done in the complete cycle is (assuming R=8 \mathrm{~J} / \mathrm{mol} \mathrm{K}$):
Options:
A) -20$J
B) 205J
C) 225J
D) 20J
219
Easy
The temperature of a gas is $-78^{\circ} \mathrm{C} and the average translational kinetic energy of its molecules is \mathrm{K}. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 \mathrm{~K}$ is :
Options:
A) -78^{\circ} \mathrm{C}
B) 127^{\circ} \mathrm{C}
C) -39^{\circ} \mathrm{C}
D) 117^{\circ} \mathrm{C}
220
Medium
The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is :
Options:
A) \frac{4}{5}
B) \frac{8}{5 \sqrt{5}}
C) \frac{2}{\sqrt{5}}
D) \frac{16}{25}
221
Medium
A sample of 1 mole gas at temperature $T is adiabatically expanded to double its volume. If adiab constant for the gas is \gamma=\frac{3}{2}$, then the work done by the gas in the process is :
Options:
A) \mathrm{R} \mathrm{T}[2+\sqrt{2}]
B) \mathrm{RT}[2-\sqrt{2}]
C) \frac{\mathrm{R}}{\mathrm{T}}[2-\sqrt{2}]
D) \frac{T}{R}[2+\sqrt{2}]
222
Easy
A diatomic gas $(\gamma=1.4) does 100 \mathrm{~J}$ of work in an isobaric expansion. The heat given to the gas is :
Options:
A) 150 J
B) 490 J
C) 350 J
D) 250 J
223
Easy
Given below are two statements : Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from the options given below :
Options:
A) Statement I is false but Statement II is true
B) Both Statement I and Statement II are true
C) Statement I is true but Statement II is false
D) Both Statement I and Statement II are false
224
Easy
A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $(27^{\circ} \mathrm{C})$. The ratio of specific heat of gases at constant volume respectively is:
Options:
A) \frac{3}{2}
B) \frac{3}{5}
C) \frac{7}{5}
D) \frac{5}{3}
225
Medium
Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d} and the ratio \frac{V_b}{V_c}$ is:
Options:
A) \frac{V_a}{V_d} \neq \frac{V_b}{V_c}
B) \frac{V_a}{V_d}=\left(\frac{V_b}{V_c}\right)^{-1}
C) \frac{V_a}{V_d}=\frac{V_b}{V_c}
D) \frac{V_a}{V_d}=\left(\frac{V_b}{V_c}\right)^2
226
Easy
Given below are two statements: Statement (I) : Dimensions of specific heat is $[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}]. Statement (II) : Dimensions of gas constant is [\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}]$. In the light of the above statements, choose the most appropriate answer from the options given below.
Options:
A) Statement (I) is incorrect but statement (II) is correct
B) Both statement (I) and statement (II) are incorrect
C) Both statement (I) and statement (II) are correct
D) Statement (I) is correct but statement (II) is incorrect
227
Medium
Energy of 10 non rigid diatomic molecules at temperature $\mathrm{T}$ is :
Options:
A) 35 RT
B) \frac{7}{2}$ RT
C) 70 KBT
D) 35 KBT
228
Easy
A total of $48 \mathrm{~J} heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by 2^{\circ} \mathrm{C}. The work done by the gas is: Given, \mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$.
Options:
A) 23.1 J
B) 48 J
C) 24.9 J
D) 72.9 J
229
Medium
The specific heat at constant pressure of a real gas obeying $P V^2=R T$ equation is:
Options:
A) R
B) C_V+R
C) C_V+\frac{R}{2 V}
D) \frac{R}{3}+C_V
230
Easy
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :
Options:
A) \frac{1}{2 \sqrt{2}}
B) \frac{1}{4}
C) \frac{2 \sqrt{2}}{1}
D) \frac{1}{32}
231
Medium
During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}$ for the gas is :
Options:
A) \frac{5}{3}
B) \frac{3}{2}
C) \frac{7}{5}
D) \frac{9}{7}
232
Easy
If $\mathrm{n} is the number density and \mathrm{d}$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :
Options:
A) \frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}
B) \frac{1}{\sqrt{2} n^2 \pi^2 d^2}
C) \frac{1}{\sqrt{2 n \pi d^2}}
D) \sqrt{2} \mathrm{n} \pi \mathrm{d}^2
233
Easy
The heat absorbed by a system in going through the given cyclic process is :
Options:
A) 61.6 J
B) 431.2 J
C) 19.6 J
D) 616 J
234
Easy
If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ} \mathrm{C} is \mathrm{Z}, then the collision frequency of the same system at 127^{\circ} \mathrm{C}$ is :
Options:
A) \frac{\sqrt{3}}{2} \mathrm{Z}
B) \frac{2}{\sqrt{3}} \mathrm{Z}
C) \frac{3}{4} \mathrm{Z}
D) \frac{4}{3} \mathrm{Z}
235
Medium
A sample of gas at temperature $T is adiabatically expanded to double its volume. Adiabatic constant for the gas is \gamma=3 / 2. The work done by the gas in the process is: (\mu=1 \text { mole })
Options:
A) R T[2 \sqrt{2}-1]
B) R T[2-\sqrt{2}]
C) R T[1-2 \sqrt{2}]
D) R T[\sqrt{2}-2]
236
Easy
The translational degrees of freedom $\left(f_t\right) and rotational degrees of freedom \left(f_r\right) of \mathrm{CH}_4$ molecule are:
Options:
A) f_t=2 and f_r=2
B) f_t=3 and f_r=3
C) f_t=3 and 4f_r=2$$
D) f_t=2 and f_r=3
237
Medium
P-T diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct :
Options:
A) \rho_1>\rho_2
B) \rho_2<\rho_3
C) \rho_1=\rho_2=\rho_3
D) \rho_1<\rho_2
238
Easy
The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega and 10 \Omega respectively. After inserting in a hot bath of temperature 400^{\circ} \mathrm{C}$, the resistance of platinum wire is :
Options:
A) 10 $\Omega
B) 16 $\Omega
C) 8 $\Omega
D) 2 $\Omega
239
Easy
On celcius scale the temperature of body increases by $40^{\circ} \mathrm{C}$. The increase in temperature on Fahrenheit scale is :
Options:
A) 75^{\circ} \mathrm{F}
B) 70^{\circ} \mathrm{F}
C) 72^{\circ} \mathrm{F}
D) 68^{\circ} \mathrm{F}
240
Easy
A diatomic gas (\gamma=1.4) does 200 \mathrm{~J} of work when it is expanded isobarically. The heat given to the gas in the process is :
Options:
A) 800 \mathrm{~J}
B) 600 \mathrm{~J}
C) 700 \mathrm{~J}
D) 850 \mathrm{~J}
241
Easy
If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 \mathrm{~km} / \mathrm{s}, the root mean square velocity of oxygen at the same condition in \mathrm{km} / \mathrm{s} is :
Options:
A) 1.0
B) 1.5
C) 2.0
D) 0.5
242
Easy
Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :
Options:
A) \frac{3}{2} \mathrm{R}
B) \frac{7}{4} \mathrm{R}
C) \frac{5}{2} \mathrm{R}
D) \frac{9}{4} \mathrm{R}
243
Medium
The pressure and volume of an ideal gas are related as \mathrm{PV}^{\frac{3}{2}}=\mathrm{K} (Constant). The work done when the gas is taken from state A\left(P_1, V_1, T_1\right) to state B\left(P_2, V_2, T_2\right) is :
Options:
A) 2\left(\mathrm{P}_2 \sqrt{\mathrm{V}_2}-\mathrm{P}_1 \sqrt{\mathrm{V}_1}\right)
B) 2\left(\sqrt{\mathrm{P}_1} \mathrm{~V}_1-\sqrt{\mathrm{P}_2} \mathrm{~V}_2\right)
C) 2\left(\mathrm{P}_2 \mathrm{~V}_2-\mathrm{P}_1 \mathrm{~V}_1\right)
D) 2\left(\mathrm{P}_1 \mathrm{~V}_1-\mathrm{P}_2 \mathrm{~V}_2\right)
244
Easy
The speed of sound in oxygen at S.T.P. will be approximately: (given, $R=8.3 \mathrm{~JK}^{-1}, \gamma=1.4$)
Options:
A) 341 m/s
B) 333 m/s
C) 325 m/s
D) 315 m/s
245
Medium
A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:
Options:
A) 29 RT
B) 27 RT
C) 20 RT
D) 21 RT
246
Medium
The given figure represents two isobaric processes for the same mass of an ideal gas, then
Options:
A) P_2>P_1
B) P_1>P_2
C) P_1=P_2
D) P_2 \geq P_1
247
Easy
The parameter that remains the same for molecules of all gases at a given temperature is :
Options:
A) kinetic energy
B) mass
C) momentum
D) speed
248
Easy
A block of ice at $-10^{\circ} \mathrm{C} is slowly heated and converted to steam at 100^{\circ} \mathrm{C}$. Which of the following curves represent the phenomenon qualitatively:
Options:
A)
B)
C)
D)
249
Medium
If three moles of monoatomic gas $\left(\gamma=\frac{5}{3}\right) is mixed with two moles of a diatomic gas \left(\gamma=\frac{7}{5}\right), the value of adiabatic exponent \gamma$ for the mixture is
Options:
A) 1.35
B) 1.52
C) 1.40
D) 1.75
250
Hard
Two thermodynamical processes are shown in the figure. The molar heat capacity for process A and B are $\mathrm{C}_{\mathrm{A}} and \mathrm{C}_{\mathrm{B}}. The molar heat capacity at constant pressure and constant volume are represented by \mathrm{C_P} and \mathrm{C_V}$, respectively. Choose the correct statement.
Options:
A) \mathrm{C_P>C_B>C_A>C_V}
B) \mathrm{C}_{\mathrm{P}}>\mathrm{C}_{\mathrm{V}}>\mathrm{C}_{\mathrm{A}}=\mathrm{C}_{\mathrm{B}}
C) \mathrm{C}_{\mathrm{A}}=0 and \mathrm{C}_{\mathrm{B}}=\infty
D) \mathrm{C_A=\infty, C_B=0}
251
Easy
At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} \mathrm{C}$ ?
Options:
A) 20 K
B) 80 K
C) 4 K
D) -73$ K
252
Easy
The temperature of a gas having $2.0 \times 10^{25} molecules per cubic meter at 1.38 \mathrm{~atm} (Given, \mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}$) is :
Options:
A) 500 K
B) 300 K
C) 200 K
D) 100 K
253
Medium
N moles of a polyatomic gas (f=6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N$ is :
Options:
A) 6
B) 2
C) 4
D) 3
254
Medium
A thermodynamic system is taken from an original state $\mathrm{A} to an intermediate state B by a linear process as shown in the figure. It's volume is then reduced to the original value from \mathrm{B} to \mathrm{C} by an isobaric process. The total work done by the gas from A to B and B to C$ would be :
Options:
A) 800 J
B) 2200 J
C) 33800 J
D) 1200 J
255
Easy
Two vessels $A and B are of the same size and are at same temperature. A contains 1 \mathrm{~g} of hydrogen and B contains 1 \mathrm{~g} of oxygen. \mathrm{P}_{\mathrm{A}} and \mathrm{P}_{\mathrm{B}} are the pressures of the gases in \mathrm{A} and \mathrm{B} respectively, then \frac{P_A}{P_B}$ is:
Options:
A) 4
B) 32
C) 8
D) 16
256
Easy
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{\mathrm{Cp}}{\mathrm{Cv}}$ for the gas is :
Options:
A) \frac{7}{5}
B) \frac{3}{2}
C) \frac{9}{7}
D) \frac{5}{3}
257
Easy
The equation of state of a real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}, where \mathrm{P}, \mathrm{V} and \mathrm{T} are pressure, volume and temperature respectively and \mathrm{R} is the universal gas constant. The dimensions of \frac{\mathrm{a}}{\mathrm{b}^2}$ is similar to that of :
Options:
A) P
B) RT
C) PV
D) R
258
Easy
The total kinetic energy of 1 mole of oxygen at $27^{\circ} \mathrm{C} is : [Use universal gas constant (R)=8.31 \mathrm{~J} /$ mole K]
Options:
A) 6232.5 J
B) 5670.5 J
C) 6845.5 J
D) 5942.0 J
259
Easy
0.08 \mathrm{~kg} air is heated at constant volume through 5^{\circ} \mathrm{C}. The specific heat of air at constant volume is 0.17 \mathrm{~kcal} / \mathrm{kg}^{\circ} \mathrm{C} and \mathrm{J}=4.18 joule/\mathrm{~cal}$. The change in its internal energy is approximately.
Options:
A) 318 J
B) 298 J
C) 284 J
D) 142 J
260
Medium
The average kinetic energy of a monatomic molecule is $0.414 \mathrm{~eV} at temperature : (Use K_B=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{mol}-\mathrm{K}$)
Options:
A) 3000 K
B) 3200 K
C) 1600 K
D) 1500 K
261
Easy
A thermodynamic system is taken through cyclic process. The total work done in the process is :
Options:
A) 100 \mathrm{~J}
B) Zero
C) 300 \mathrm{~J}
D) 200 \mathrm{~J}
262
Easy
A flask contains Hydrogen and Argon in the ratio 2: 1 by mass. The temperature of the mixture is 30^{\circ} \mathrm{C}. The ratio of average kinetic energy per molecule of the two gases ( \mathrm{K} argon/K hydrogen) is : (Given: Atomic Weight of \mathrm{Ar}=39.9 )
Options:
A) \frac{39.9}{2}
B) 2
C) 39.9
D) 1
263
Easy
The initial pressure and volume of an ideal gas are P$_0 and V_0. The final pressure of the gas when the gas is suddenly compressed to volume \frac{V_0}{4} will be : (Given \gamma$ = ratio of specific heats at constant pressure and at constant volume)
Options:
A) P$_0(4)^{\frac{1}{\gamma}}
B) P$_0
C) 4P$_0
D) P$_0(4)^{\gamma}
264
Easy
The mean free path of molecules of a certain gas at STP is $1500 \mathrm{~d}, where \mathrm{d} is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 \mathrm{~K}$ is approximately:
Options:
A) 750 \mathrm{~d}
B) 1500 \mathrm{~d}
C) \mathrm{2049~ d}
D) 1098 \mathrm{~d}
265
Medium
The rms speed of oxygen molecule in a vessel at particular temperature is $\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v, where v is the average speed of the molecule. The value of x will be: \left(\right. Take \left.\pi=\frac{22}{7}\right)
Options:
A) 4
B) 8
C) 28
D) 27
266
Easy
An engine operating between the boiling and freezing points of water will have A. efficiency more than 27%. B. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures. C. efficiency equal to $27 \% D. efficiency less than 27 \%$ Choose the correct answer from the options given below:
Options:
A) B and C only
B) B and D only
C) B, C and D only
D) A and B only
267
Easy
If the r. m.s speed of chlorine molecule is $490 \mathrm{~m} / \mathrm{s} at 27^{\circ} \mathrm{C}, the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon =39.9 \mathrm{u}, molecular mass of chlorine =70.9 \mathrm{u}$ )
Options:
A) 451.7 \mathrm{~m} / \mathrm{s}
B) 751.7 \mathrm{~m} / \mathrm{s}
C) 551.7 \mathrm{~m} / \mathrm{s}
D) 651.7 \mathrm{~m} / \mathrm{s}
268
Easy
The Thermodynamic process, in which internal energy of the system remains constant is
Options:
A) Isobaric
B) Isochoric
C) Adiabatic
D) Isothermal
269
Easy
The root mean square speed of molecules of nitrogen gas at $27^{\circ} \mathrm{C} is approximately : (Given mass of a nitrogen molecule =4.6 \times 10^{-26} \mathrm{~kg} and take Boltzmann constant \mathrm{k}_{\mathrm{B}}=1.4 \times 10^{-23} \mathrm{JK}^{-1}$ )
Options:
A) 91 m/s
B) 1260 m/s
C) 27.4 m/s
D) 523 m/s
270
Medium
1 \mathrm{~kg} of water at 100^{\circ} \mathrm{C} is converted into steam at 100^{\circ} \mathrm{C} by boiling at atmospheric pressure. The volume of water changes from 1.00 \times 10^{-3} \mathrm{~m}^{3} as a liquid to 1.671 \mathrm{~m}^{3} as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisaiton =2257 \mathrm{~kJ} / \mathrm{kg}, Atmospheric pressure = \left.1 \times 10^{5} \mathrm{~Pa}\right)
Options:
A) + 2090 kJ
B) -$ 2426 kJ
C) + 2476 kJ
D) -$ 2090 kJ
271
Easy
On a temperature scale '$\mathrm{X}', the boiling point of water is 65^{\circ} \mathrm{X} and the freezing point is -15^{\circ} \mathrm{X}. Assume that the \mathrm{X} scale is linear. The equivalent temperature corresponding to -95^{\circ} \mathrm{X}$ on the Farenheit scale would be:
Options:
A) -148^{\circ} \mathrm{F}
B) -48^{\circ} \mathrm{F}
C) -63^{\circ} \mathrm{F}
D) -112^{\circ} \mathrm{F}
272
Easy
Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed $\left(v_{\mathrm{rms}}\right)$ and choose the correct answer from the options given below:
Options:
A) \mathrm{v}_{\mathrm{rms}}( mono )=\mathrm{v}_{\mathrm{rms}}( dia )=\mathrm{v}_{\mathrm{rms}}( poly )
B) \mathrm{v}_{\mathrm{rms}} (mono) > \mathrm{v}_{\mathrm{rms}}( dia ) > \mathrm{v}_{\mathrm{rms}}$ (poly)
C) \mathrm{v}_{\mathrm{rms}} (dia) < \mathrm{v}_{\mathrm{rms}} (poly) < \mathrm{v}_{\text {rms }}$ (mono)
D) \mathrm{v}_{\mathrm{rms}} (mono) < \mathrm{v}_{\mathrm{rms}} (dia) < \mathrm{v}_{\mathrm{rms}}$ (poly)
273
Easy
A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,
Options:
A) 4RT
B) 16RT
C) 8RT
D) 11RT
274
Easy
A gas is compressed adiabatically, which one of the following statement is NOT true.
Options:
A) There is no heat supplied to the system
B) The temperature of the gas increases.
C) There is no change in the internal energy
D) The change in the internal energy is equal to the work done on the gas.
275
Medium
Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to $\frac{1}{8} of its original volume while the gas in B is compressed adiabatically to \frac{1}{8}$ of its original volume. The ratio of final pressure of gas in B to that of gas in A is
Options:
A) \frac{1}{8}
B) 8$^\frac{3}{2}
C) 4
D) 8
276
Easy
Match List I with List II : List I List II (A) 3 Translational degrees of freedom (I) Monoatomic gases (B) 3 Translational, 2 rotational degrees of freedoms (II) Polyatomic gases (C) 3 Translational, 2 rotational and 1 vibrational degrees of freedom (III) Rigid diatomic gases (D) 3 Translational, 3 rotational and more than one vibrational degrees of freedom (IV) Nonrigid diatomic gases Choose the correct answer from the options given below:
Options:
A) (A)-(I), (B)-(III), (C)-(IV), (D)-(II)
B) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
C) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
D) (A)-(I), (B)-(IV), (C)-(III), (D)-(II)
277
Easy
The temperature at which the kinetic energy of oxygen molecules becomes double than its value at $27^{\circ} \mathrm{C}$ is
Options:
A) 627^{\circ} \mathrm{C}
B) 927^{\circ} \mathrm{C}
C) 327^{\circ} \mathrm{C}
D) 1227^{\circ} \mathrm{C}
278
Easy
Work done by a Carnot engine operating between temperatures $127^{\circ} \mathrm{C} and 27^{\circ} \mathrm{C} is 2 \mathrm{~kJ}$. The amount of heat transferred to the engine by the reservoir is :
Options:
A) 8 kJ
B) 2 kJ
C) 4 kJ
D) 2.67 kJ
279
Medium
Given below are two statements: Statement I: If heat is added to a system, its temperature must increase. Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the above statements, choose the correct answer from the options given below
Options:
A) Both Statement I and Statement II are true
B) Statement I is false but Statement II is true
C) Statement I is true but Statement II is false
D) Both Statement I and Statement II are false
280
Easy
The temperature of an ideal gas is increased from $200 \mathrm{~K} to 800 \mathrm{~K}. If r.m.s. speed of gas at 200 \mathrm{~K} is v_{0}. Then, r.m.s. speed of the gas at 800 \mathrm{~K}$ will be:
Options:
A) v_{0}
B) 2 v_{0}
C) 4 v_{0}
D) \frac{v_{0}}{4}
281
Easy
A body cools in 7 minutes from $60^{\circ} \mathrm{C} to 40^{\circ} \mathrm{C}. The temperature of the surrounding is 10^{\circ} \mathrm{C}$. The temperature of the body after the next 7 minutes will be:
Options:
A) 34^{\circ} \mathrm{C}
B) 28^{\circ} \mathrm{C}
C) 32^{\circ} \mathrm{C}
D) 30^{\circ} \mathrm{C}
282
Easy
The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:
Options:
A) 1: 1
B) 1: 2
C) 1: 4
D) 4: 1
283
Easy
A source supplies heat to a system at the rate of $1000 \mathrm{~W}. If the system performs work at a rate of 200 \mathrm{~W}$. The rate at which internal energy of the system increases is
Options:
A) 600 W
B) 1200 W
C) 500 W
D) 800 W
284
Easy
The number of air molecules per cm$^3 increased from 3\times10^{19} to 12\times10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is:
Options:
A) 1.25
B) 0.25
C) 0.50
D) 0.75
285
Easy
A Carnot engine operating between two reservoirs has efficiency $\frac{1}{3}. When the temperature of cold reservoir raised by x, its efficiency decreases to \frac{1}{6}. The value of x, if the temperature of hot reservoir is 99^\circ$C, will be :
Options:
A) 66 K
B) 62 K
C) 16.5 K
D) 33 K
286
Easy
For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point '$\mathrm{K}$' is :
Options:
A) -273^{\circ} \mathrm{C}
B) -373^{\circ} \mathrm{C}
C) -100^{\circ} \mathrm{C}
D) -40^{\circ} \mathrm{C}
287
Medium
A sample of gas at temperature $T is adiabatically expanded to double its volume. The work done by the gas in the process is \left(\mathrm{given}, \gamma=\frac{3}{2}\right)$ :
Options:
A) W=T R[\sqrt{2}-2]
B) W=\frac{T}{R}[\sqrt{2}-2]
C) W=\frac{R}{T}[2-\sqrt{2}]
D) W=R T[2-\sqrt{2}]
288
Medium
\left(P+\frac{a}{V^{2}}\right)(V-b)=R T represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of \frac{b^{2}}{a}$, will be:
Options:
A) Energy density
B) Bulk modulus
C) Modulus of rigidity
D) Compressibility
289
Easy
The average kinetic energy of a molecule of the gas is
Options:
A) proportional to volume
B) dependent on the nature of the gas
C) proportional to absolute temperature
D) proportional to pressure
290
Medium
Heat energy of 735 \mathrm{~J} is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be :
Options:
A) 572 \mathrm{~J}
B) 441 \mathrm{~J}
C) 525 \mathrm{~J}
D) 735 \mathrm{~J}
291
Easy
A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is \frac{16}{81}. Then the ratio of \frac{\mathrm{Cp}}{\mathrm{Cv}} will be.
Options:
A) \frac{3}{1}
B) \frac{4}{3}
C) \frac{1}{2}
D) \frac{3}{2}
292
Medium
The pressure of a gas changes linearly with volume from $\mathrm{A} to \mathrm{B}$ as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be
Options:
A) 6 J
B) 4.5 J
C) zero
D) -$4.5 J
293
Easy
The correct relation between $\gamma = {{{c_p}} \over {{c_v}}}$ and temperature T is :
Options:
A) \gamma \propto T
B) \gamma \propto {1 \over {\sqrt T }}
C) \gamma \propto {1 \over T}
D) \gamma \propto T^\circ
294
Easy
Given below are two statements: one is labelled as Assertion \mathbf{A} and the other is labelled as Reason \mathbf{R} Assertion A: Efficiency of a reversible heat engine will be highest at -273^{\circ} \mathrm{C} temperature of cold reservoir. Reason R: The efficiency of Carnot's engine depends not only on the temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as \eta=\left(1-\frac{T_{2}}{T_{1}}\right) In the light of the above statements, choose the correct answer from the options given below
Options:
A) Both \mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}
B) Both \mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}
C) A is false but \mathbf{R} is true
D) A is true but \mathbf{R} is false
295
Easy
A flask contains hydrogen and oxygen in the ratio of 2: 1 by mass at temperature 27^{\circ} \mathrm{C}. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:
Options:
A) 1 : 1
B) 4 : 1
C) 1 : 4
D) 2 : 1
296
Medium
The pressure $(\mathrm{P}) and temperature (\mathrm{T}) relationship of an ideal gas obeys the equation \mathrm{PT}^{2}=$ constant. The volume expansion coefficient of the gas will be :
Options:
A) 3 T^{2}
B) \frac{3}{T^2}
C) \frac{3}{T^3}
D) \frac{3}{T}
297
Easy
Heat is given to an ideal gas in an isothermal process. A. Internal energy of the gas will decrease. B. Internal energy of the gas will increase. C. Internal energy of the gas will not change. D. The gas will do positive work. E. The gas will do negative work. Choose the correct answer from the options given below :
Options:
A) B and D only
B) C and E only
C) A and E only
D) C and D only
298
Medium
Heat energy of 184 kJ is given to ice of mass 600 g at $-12^\circ \mathrm{C}. Specific heat of ice is \mathrm{2222.3~J~kg^{-1^\circ}~C^{-1}} and latent heat of ice in 336 \mathrm{kJ/kg^{-1}} A. Final temperature of system will be 0^\circC. B. Final temperature of the system will be greater than 0^\circ$C. C. The final system will have a mixture of ice and water in the ratio of 5 : 1. D. The final system will have a mixture of ice and water in the ratio of 1 : 5. E. The final system will have water only. Choose the correct answer from the options given below :
Options:
A) A and E only
B) B and D only
C) A and C only
D) A and D only
299
Medium
At 300 K, the rms speed of oxygen molecules is $\sqrt {{{\alpha + 5} \over \alpha }} times to that of its average speed in the gas. Then, the value of \alpha will be (used \pi = {{22} \over 7}$)
Options:
A) 27
B) 28
C) 24
D) 32
300
Easy
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If $d Q and d W represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics d Q=d U-d W$. Reason R: First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the options given below:
Options:
A) Both A and R are correct but R is not the correct explanation of A
B) Both A and R are correct and R is the correct explanation of A
C) A is correct but R is not correct
D) A is not correct but R is correct
301
Easy
Match List I with List II List I List II A. Isothermal Process I. Work done by the gas decreases internal energy B. Adiabatic Process II. No change in internal energy C. Isochoric Process III. The heat absorbed goes partly to increase internal energy and partly to do work D. Isobaric Process IV. No work is done on or by the gas Choose the correct answer from the options given below :
Options:
A) A-I, B-II, C-IV, D-III
B) A-II, B-I, C-III, D-IV
C) A-II, B-I, C-IV, D-III
D) A-I, B-II, C-III, D-IV
302
Easy
The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by :-
Options:
A) {{{t_P}} \over {100}} = {{{t_Q} - 180} \over {150}}
B) {{{t_P}} \over {180}} - {{{t_Q} - 40} \over {100}}
C) {{{t_Q}} \over {150}} = {{{t_P} - 180} \over {100}}
D) {{{t_Q}} \over {100}} = {{{t_P} - 30} \over {150}}
303
Easy
According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-
Options:
A) \frac{9}{2}R
B) \frac{5}{2}R
C) \frac{3}{2}R
D) \frac{7}{2}R
304
Easy
The root mean square velocity of molecules of gas is
Options:
A) Proportional to temperature ($T$)
B) Inversely proportional to square root of temperature $\left( {\sqrt {{1 \over T}} } \right)
C) Proportional to square of temperature ($T^2$)
D) Proportional to square root of temperature ($\sqrt T$)
305
Medium
A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be :
Options:
A) 300 K
B) 1000 K
C) 900 K
D) 360 K
306
Easy
Let $\gamma_1 be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and \gamma_2 be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, \frac{\gamma_1}{\gamma_2}$ is :
Options:
A) \frac{35}{27}
B) \frac{25}{21}
C) \frac{21}{25}
D) \frac{27}{35}
307
Easy
In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; $\mathrm{T_3 > T_2 > T_1}$ as :
Options:
A)
B)
C)
D)
308
Easy
1 g of a liquid is converted to vapour at 3 $\times 10^5 Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm^3$ during this phase change, then the increase in internal energy in the process will be :
Options:
A) 4800 J
B) 4320 J
C) 432000 J
D) 4.32 $\times 10^8$ J
309
Medium
Given below are two statements : Statement I : The temperature of a gas is $-73^\circC. When the gas is heated to 527^\circ$C, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the option given below :
Options:
A) Statement I is true but Statement II is false
B) Both Statement I and Statement II are true
C) Statement I is false but Statement II is true
D) Both Statement I and Statement II are false
310
Medium
A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be
Options:
A) -$450 J
B) 450 J
C) 900 J
D) 1350 J
311
Medium
The root mean square speed of smoke particles of mass $5 \times 10^{-17} \mathrm{~kg} in their Brownian motion in air at NTP is approximately. [Given \mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}$]
Options:
A) 60 \mathrm{~mm} \mathrm{~s}^{-1}
B) 12 \mathrm{~mm} \mathrm{~s}^{-1}
C) 15 \mathrm{~mm} \mathrm{~s}^{-1}
D) 36 \mathrm{~mm} \mathrm{~s}^{-1}
312
Medium
A vessel contains $14 \mathrm{~g} of nitrogen gas at a temperature of 27^{\circ} \mathrm{C}. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be : Take \mathrm{R}=8.32 \mathrm{~J} \mathrm{~mol}^{-1} \,\mathrm{k}^{-1}$.
Options:
A) 2229 J
B) 5616 J
C) 9360 J
D) 13,104 J
313
Medium
A Carnot engine has efficiency of $50 \%. If the temperature of sink is reduced by 40^{\circ} \mathrm{C}, its efficiency increases by 30 \%$. The temperature of the source will be:
Options:
A) 166.7 K
B) 255.1 K
C) 266.7 K
D) 367.7 K
314
Medium
Given below are two statements : Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II : The rms speed of oxygen molecules in a gas is $v. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become 2 v$. In the light of the above statements, choose the correct answer from the options given below :
Options:
A) Both Statement I and Statement II are true
B) Both Statement I and Statement II are false
C) Statement I is true but Statement II is false
D) Statement I is false but Statement II is true
315
Medium
In $1^{\text {st }} case, Carnot engine operates between temperatures 300 \mathrm{~K} and 100 \mathrm{~K}. In 2^{\text {nd }} case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2^{\text {nd }}$ case) will be :
Options:
A) same as the $1^{\text {st }}$ case.
B) always greater than the $1^{\text {st }}$ case.
C) always less than the $1^{\text {st }}$ case.
D) may increase or decrease with respect to the $1^{\text {st }}$ case.
316
Medium
Which statements are correct about degrees of freedom ? (A) A molecule with n degrees of freedom has n$^{2} different ways of storing energy. (B) Each degree of freedom is associated with \frac{1}{2} RT average energy per mole. (C) A monatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom. (D) \mathrm{CH}_{4}$ has a total of 6 degrees of freedom. Choose the correct answer from the options given below :
Options:
A) (B) and (C) only
B) (B) and (D) only
C) (A) and (B) only
D) (C) and (D) only
317
Medium
If $K_{1} and K_{2} are the thermal conductivities, L_{1} and L_{2} are the lengths and A_{1} and A_{2} are the cross sectional areas of steel and copper rods respectively such that \frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2. Then, for the arrangement as shown in the figure, the value of temperature \mathrm{T}$ of the steel - copper junction in the steady state will be:
Options:
A) 18^{\circ} \mathrm{C}
B) 14^{\circ} \mathrm{C}
C) 45^{\circ} \mathrm{C}
D) 150^{\circ} \mathrm{C}
318
Medium
Read the following statements : A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice. B. Two bodies $P and Q having equal surface areas are maintained at temperature 10^{\circ} \mathrm{C} and 20^{\circ} \mathrm{C}. The thermal radiation emitted in a given time by \mathrm{P} and \mathrm{Q} are in the ratio 1: 1.15. C. A Carnot Engine working between 100 \mathrm{~K} and 400 \mathrm{~K} has an efficiency of 75 \%$. D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :
Options:
A) A, B, C only
B) A, B only
C) A, C only
D) B, C, D only
319
Easy
Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1: 4, then A. The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressure in these vessels will be 1: 4. C. The ratio of pressure will be 1: 1. D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of 1: 4$. Choose the correct answer from the options given below :
Options:
A) A and C only
B) B and D only
C) A and B only
D) C and D only
320
Medium
An ice cube of dimensions $60 \mathrm{~cm} \times 50 \mathrm{~cm} \times 20 \mathrm{~cm} is placed in an insulation box of wall thickness 1 \mathrm{~cm}. The box keeping the ice cube at 0^{\circ} \mathrm{C} of temperature is brought to a room of temperature 40^{\circ} \mathrm{C}. The rate of melting of ice is approximately : (Latent heat of fusion of ice is 3.4 \times 10^{5} \mathrm{~J} \mathrm{~kg}^{-1} and thermal conducting of insulation wall is 0.05 \,\mathrm{Wm}^{-1 \circ} \mathrm{C}^{-1}$ )
Options:
A) 61 \times 10^{-3} \mathrm{~kg} \mathrm{~s}^{-1}
B) 61 \times 10^{-5} \mathrm{~kg} \mathrm{~s}^{-1}
C) 208 \mathrm{~kg} \mathrm{~s}^{-1}
D) 30 \times 10^{-5} \mathrm{~kg} \mathrm{~s}^{-1}
321
Easy
A gas has $n$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :
Options:
A) \frac{n}{n+2}
B) \frac{n+2}{n}
C) \frac{n}{2n+2}
D) \frac{n}{n-2}
322
Easy
7 mol of a certain monoatomic ideal gas undergoes a temperature increase of $40 \mathrm{~K} at constant pressure. The increase in the internal energy of the gas in this process is : (Given \mathrm{R}=8.3 \,\mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ )
Options:
A) 5810 J
B) 3486 J
C) 11620 J
D) 6972 J
323
Easy
A monoatomic gas at pressure $\mathrm{P} and volume \mathrm{V}$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :
Options:
A) P
B) 8P
C) 32P
D) 64P
324
Medium
Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt2$ times the speed of sound, then the value of n will be :
Options:
A) 1
B) 2
C) 3
D) 4
325
Easy
Let $\eta_{1} is the efficiency of an engine at T_{1}=447^{\circ} \mathrm{C} and \mathrm{T}_{2}=147^{\circ} \mathrm{C} while \eta_{2} is the efficiency at \mathrm{T}_{1}=947^{\circ} \mathrm{C} and \mathrm{T}_{2}=47^{\circ} \mathrm{C} The ratio \frac{\eta_{1}}{\eta_{2}}$ will be :
Options:
A) 0.41
B) 0.56
C) 0.73
D) 0.70
326
Medium
A certain amount of gas of volume $\mathrm{V} at 27^{\circ} \mathrm{C} temperature and pressure 2 \times 10^{7} \mathrm{Nm}^{-2} expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use \gamma=1.5)$ :
Options:
A) 3.536 \times 10^{5} \mathrm{~Pa}
B) 3.536 \times 10^{6} \mathrm{~Pa}
C) 1.25 \times 10^{6} \mathrm{~Pa}
D) 1.25 \times 10^{5} \mathrm{~Pa}
327
Easy
Following statements are given : (A) The average kinetic energy of a gas molecule decreases when the temperature is reduced. (B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. (C) The average kinetic energy of a gas molecule decreases with increase in volume. (D) Pressure of a gas increases with increase in temperature at constant pressure. (E) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below :
Options:
A) (A) and (D) only
B) (A), (B) and (D) only
C) (B) and (D) only
D) (A), (B) and (E) only
328
Easy
The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid, the pressure becomes 180 cm of mercury. Temperature of the liquid is : (Given 0$^\circ$C = 273 K)
Options:
A) 300 K
B) 400 K
C) 600 K
D) 491 K
329
Medium
A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm3 to 150 cm3 adiabatically. In this process, the value of workdone on the gas will be :
Options:
A) 79 J
B) 405 J
C) 4050 J
D) 9590 J
330
Easy
At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm ? Both the diameters have been measured at room temperature (27$^\circC). (Given : coefficient of linear thermal expansion of gold \alphaL = 1.4 \times 10-5 K-$1)
Options:
A) 125.7$^\circ$C
B) 91.7$^\circ$C
C) 425.7$^\circ$C
D) 152.7$^\circ$C
331
Medium
Starting with the same initial conditions, an ideal gas expands from volume V1 to V2 in three different ways. The work done by the gas is W1 if the process is purely isothermal, W2, if the process is purely adiabatic and W3 if the process is purely isobaric. Then, choose the correct option
Options:
A) W1 < W2 < W3
B) W2 < W3 < W1
C) W3 < W1 < W2
D) W2 < W1 < W3
332
Easy
A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in cm3 is :
Options:
A) 72 $\times$ 105
B) 32 $\times$ 105
C) 27 $\times$ 104
D) 54 $\times$ 104
333
Easy
A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0$^\circC will be : (Given gas constant R = 8.3 JK-1-mol-$1)
Options:
A) 249 J
B) 415 J
C) 498 J
D) 830 J
334
Easy
In van der Waal equation $\left[ {P + {a \over {{V^2}}}} \right] [V - b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants {a \over b}$ is dimensionally equal to :
Options:
A) {P \over V}
B) {V \over P}
C) PV
D) PV3
335
Medium
A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The workdone by the gas during the part CA is :
Options:
A) 20 J
B) 30 J
C) -$30 J
D) -$60 J
336
Easy
What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?
Options:
A) The velocity of atomic oxygen remains same
B) The velocity of atomic oxygen doubles
C) The velocity of atomic oxygen becomes half
D) The velocity of atomic oxygen becomes four times
337
Medium
Given below are two statements : Statement I : When $\mu amount of an ideal gas undergoes adiabatic change from state (P1, V1, T1) to state (P2, V2, T2), then work done is W = {{\mu R({T_2} - {T_1})} \over {1 - \gamma }}, where \gamma = {{{C_p}} \over {{C_v}}}$ and R = universal gas constant. Statement II : In the above case, when work is done on the gas, the temperature of the gas would rise. Choose the correct answer from the options given below :
Options:
A) Both Statement I and Statement II are true.
B) Both Statement I and Statement II are false.
C) Statement I is true but Statement II is false.
D) Statement I is false but Statement II is true.
338
Medium
For a perfect gas, two pressures P1 and P2 are shown in figure. The graph shows :
Options:
A) P1 > P2
B) P1 < P2
C) P1 = P2
D) Insufficient data to draw any conclusion
339
Easy
According to kinetic theory of gases, A. The motion of the gas molecules freezes at 0$^\circC. B. The mean free path of gas molecules decreases if the density of molecules is increased. C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant. D. Average kinetic energy per molecule per degree of freedom is {3 \over 2}{k_B}T$ (for monoatomic gases). Choose the most appropriate answer from the options given below :
Options:
A) A and C only
B) B and C only
C) A and B only
D) C and D only
340
Medium
A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is : (Given : initial temperature of the bullet = 127$^\circC, Melting point of the bullet = 327^\circC, Latent heat of fusion of lead = 2.5 \times 104 J kg-$1, Specific heat capacity of lead = 125 J/kg K)
Options:
A) 125 ms$-$1
B) 500 ms$-$1
C) 250 ms$-$1
D) 600 ms$-$1
341
Medium
A mixture of hydrogen and oxygen has volume 2000 cm3, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be: [Take gas constant R = 8.3 JK$-1mol-$1]
Options:
A) {1 \over 3}
B) {3 \over 1}
C) {1 \over 16}
D) {16 \over 1}
342
Easy
A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27$^\circ$C. The ratio of their average kinetic energy per molecule respectively will be :
Options:
A) 3 : 2
B) 9 : 4
C) 2 : 3
D) 1 : 1
343
Easy
The efficiency of a Carnot's engine, working between steam point and ice point, will be :
Options:
A) 26.81%
B) 37.81%
C) 47.81%
D) 57.81%
344
Medium
A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by : (R = universal gas constant)
Options:
A) {{M{v^2}} \over {7R}}
B) {{M{v^2}} \over {5R}}
C) 2${{M{v^2}} \over {7R}}
D) 7${{M{v^2}} \over {5R}}
345
Easy
A solid metallic cube having total surface area 24 m2 is uniformly heated. If its temperature is increased by 10$^\circC, calculate the increase in volume of the cube. (Given \alpha = 5.0 \times 10-4 ^\circC-$1).
Options:
A) 2.4 $\times$ 106 cm3
B) 1.2 $\times$ 105 cm3
C) 6.0 $\times$ 104 cm3
D) 4.8 $\times$ 105 cm3
346
Easy
A copper block of mass 5.0 kg is heated to a temperature of 500$^\circC and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper : 0.39 J g-1 ^\circC-1 and latent heat of fusion of water : 335 J g-$1]
Options:
A) 1.5 kg
B) 5.8 kg
C) 2.9 kg
D) 3.8 kg
347
Easy
The ratio of specific heats $\left( {{{{C_P}} \over {{C_V}}}} \right)$ in terms of degree of freedom (f) is given by :
Options:
A) \left( {1 + {f \over 3}} \right)
B) \left( {1 + {2 \over f}} \right)
C) \left( {1 + {f \over 2}} \right)
D) \left( {1 + {1 \over f}} \right)
348
Easy
The relation between root mean square speed (vrms) and most probable sped (vp) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :
Options:
A) {v_{rms}} = \sqrt {{2 \over 3}} {v_p}
B) {v_{rms}} = \sqrt {{3 \over 2}} {v_p}
C) {v_{rms}} = {v_p}
D) {v_{rms}} = \sqrt {{1 \over 3}} {v_p}
349
Medium
A Carnot engine takes 5000 kcal of heat from a reservoir at 727$^\circC and gives heat to a sink at 127^\circ$C. The work done by the engine is
Options:
A) 3 $\times$ 106 J
B) Zero
C) 12.6 $\times$ 106 J
D) 8.4 $\times$ 106 J
350
Medium
A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms$-1. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail? [Specific heat capacity of iron = 0.42 Jg-1 ^\circC-$1]
Options:
A) 675$^\circ$C
B) 1600$^\circ$C
C) 16.07$^\circ$C
D) 6.75$^\circ$C
351
Easy
A Carnot engine whose heat sinks at 27$^\circ$C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency?
Options:
A) Increases by 18$^\circ$C
B) Increases by 200$^\circ$C
C) Increases by 120$^\circ$C
D) Increases by 73$^\circ$C
352
Medium
Two metallic blocks M1 and M2 of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M2 is K then the thermal conductivity of M1 will be : [Assume steady state heat conduction]
Options:
A) 10 K
B) 8 K
C) 12.5 K
D) 2 K
353
Medium
Two thin metallic spherical shells of radii r1 and r2 (r1 < r2) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $\theta1 and the outer shell at temperature \theta2(\theta1 < \theta$2). The rate at which heat flows radially through the material is :-
Options:
A) {{4\pi K{r_1}{r_2}({\theta _2} - {\theta _1})} \over {{r_2} - {r_1}}}
B) {{\pi {r_1}{r_2}({\theta _2} - {\theta _1})} \over {{r_2} - {r_1}}}
C) {{K({\theta _2} - {\theta _1})} \over {{r_2} - {r_1}}}
D) {{K({\theta _2} - {\theta _1})({r_2} - {r_1})} \over {4\pi {r_1}{r_2}}}
354
Medium
A mixture of hydrogen and oxygen has volume 500 cm3, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-
Options:
A) 3 : 8
B) 3 : 16
C) 16 : 3
D) 8 : 3
355
Medium
A reversible engine has an efficiency of ${1 \over 4}. If the temperature of the sink is reduced by 58^\circ$C, its efficiency becomes double. Calculate the temperature of the sink :
Options:
A) 174$^\circ$C
B) 280$^\circ$C
C) 180.4$^\circ$C
D) 382$^\circ$C
356
Medium
For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation ${{dp} \over {dv}} = - ap$. If p = p0 at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here R is the gas constant)
Options:
A) {{{p_0}} \over {aeR}}
B) {{a{p_0}} \over {eR}}
C) infinity
D) 0$^\circ$C
357
Easy
if the rms speed of oxygen molecules at 0$^\circC is 160 m/s, find the rms speed of hydrogen molecules at 0^\circ$C.
Options:
A) 640 m/s
B) 40 m/s
C) 80 m/s
D) 332 m/s
358
Easy
The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall?[Given 1 cal = 4.2 J and specific heat of water = 1 cal g$-1 ^\circ0C-$1]
Options:
A) 0.147$^\circ$ C
B) 14.76$^\circ$ C
C) 1.476$^\circ$ C
D) 0.014$^\circ$ C
359
Medium
A balloon carries a total load of 185 kg at normal pressure and temperature of 27$^\circC. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is -7^\circ$C. Assuming the volume constant?
Options:
A) 181.46 kg
B) 214.15 kg
C) 219.07 kg
D) 123.54 kg
360
Medium
An ideal gas is expanding such that PT3 = constant. The coefficient of volume expansion of the gas is :
Options:
A) {1 \over T}
B) {2 \over T}
C) {4 \over T}
D) {3 \over T}
361
Medium
The temperature of equal masses of three different liquids x, y and z are 10$^\circC, 20^\circC and 30^\circC respectively. The temperature of mixture when x is mixed with y is 16^\circC and that when y is mixed with z is 26^\circ$C. The temperature of mixture when x and z are mixed will be :
Options:
A) 28.32$^\circ$C
B) 25.62$^\circ$C
C) 23.84$^\circ$C
D) 20.28$^\circ$C
362
Easy
A cylindrical container of volume 4.0 $\times 10-3 m3 contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is :[Take gas constant as 8.3 J mol-1 K-$1]
Options:
A) 249 $\times$ 101 Pa
B) 24.9 $\times$ 103 Pa
C) 24.9 $\times$ 105 Pa
D) 24.9 Pa
363
Medium
A refrigerator consumes an average 35W power to operate between temperature $-10^\circC to 25^\circ$C. If there is no loss of energy then how much average heat per second does it transfer?
Options:
A) 263 J/s
B) 298 J/s
C) 350 J/s
D) 35 J/s
364
Easy
An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal energy by 2.5 $\times$ 103 J ?
Options:
A) 2.5 $\times$ 102 s
B) 4.1 $\times$ 101 s
C) 2.4 $\times$ 103 s
D) 2.5 $\times$ 101 s
365
Easy
The rms speeds of the molecules of Hydrogen, Oxygen and Carbon dioxide at the same temperature are VH, VO and VC respectively then :
Options:
A) VH > VO > VC
B) VC > VO > VH
C) VH = VO > VC
D) VH = VO = VC
366
Medium
One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27$^\circ C to 37^\circ C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J mol-1 k-$1]
Options:
A) work done by the gas is close to 332 J
B) work done on the gas is close to 582 J
C) work done by the gas is close to 582 J
D) work done on the gas is close to 332 J
367
Medium
Two Carnot engines A and B operate in series such that engine A absorbs heat at T1 and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T3. When workdone in both the cases is equal, to value of T is :
Options:
A) {2 \over 3}{T_1} + {3 \over 2}{T_3}
B) {1 \over 3}{T_1} + {2 \over 3}{T_3}
C) {3 \over 2}{T_1} + {1 \over 3}{T_3}
D) {2 \over 3}{T_1} + {1 \over 3}{T_3}
368
Easy
The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 $\times 10-$9 J per molecules is :
Options:
A) 0.75 $\times$ 1011
B) 3 $\times$ 1011
C) 1.5 $\times$ 1011
D) 6 $\times$ 1011
369
Medium
In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A $\to B and C \to$ D are T1 and T2 (T1 > T2) respectively.Choose the correct option out of the following for work done if processes BC and DA are adiabatic.
Options:
A) WAB = WDC
B) WAD = WBC
C) WBC + WDA > 0
D) WAB < WCD
370
Medium
A heat engine has an efficiency of ${1 \over 6}. When the temperature of sink is reduced by 62^\circ$C, its efficiency get doubled. The temperature of the source is :
Options:
A) 124$^\circ$C
B) 37$^\circ$C
C) 62$^\circ$C
D) 99$^\circ$C
371
Medium
For a gas CP $- CV = R in a state P and CP -$ CV = 1.10 R in a state Q, TP and TQ are the temperatures in two different states P and Q respectively. Then
Options:
A) TP = TQ
B) TP < TQ
C) TP = 0.9 TQ
D) TP > TQ
372
Easy
A monoatomic ideal gas, initially at temperature T1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If l1 and l2 are the lengths of the gas column, before and after the expansion respectively, then the value of ${{{T_1}} \over {{T_2}}}$ will be :
Options:
A) {\left( {{{{l_1}} \over {{l_2}}}} \right)^{{2 \over 3}}}
B) {\left( {{{{l_2}} \over {{l_1}}}} \right)^{{2 \over 3}}}
C) {{{l_2}} \over {{l_1}}}
D) {{{l_1}} \over {{l_2}}}
373
Easy
Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :
Options:
A) {8 \over 3}
B) {3 \over 8}
C) {3 \over 4}
D) {4 \over 3}
374
Easy
What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?
Options:
A) {3 \over 2}{k_B}T
B) {k_B}T
C) {2 \over 3}{k_B}T
D) {1 \over 2}{k_B}T
375
Medium
Which of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning.
Options:
A)
B)
C)
D)
376
Easy
The correct relation between the degrees of freedom f and the ratio of specific heat $\gamma$ is :
Options:
A) f = {2 \over {\gamma - 1}}
B) f = {2 \over {\gamma + 1}}
C) f = {{\gamma + 1} \over 2}
D) f = {1 \over {\gamma + 1}}
377
Easy
Consider a mixture of gas molecule of types A, B and C having masses mA < mB < mC. The ratio of their root mean square speeds at normal temperature and pressure is :
Options:
A) {v_A} = {v_B} \ne {v_C}
B) {1 \over {{v_A}}} > {1 \over {{v_B}}} > {1 \over {{v_C}}}
C) {1 \over {{v_A}}} < {1 \over {{v_B}}} < {1 \over {{v_C}}}
D) {v_A} = {v_B} = {v_C} = 0
378
Easy
The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from 0$^\circ C to 50^\circ$ C when no work is done is ___________. (R is the universal gas constant).
Options:
A) 500 R
B) 250 R
C) 750 R
D) 175 R
379
Medium
The entropy of any system is given by $S = {\alpha ^2}\beta \ln \left[ {{{\mu kR} \over {J{\beta ^2}}} + 3} \right] where \alpha and \beta are the constants. \mu, J, k and R are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively. [Take S = {{dQ} \over T}$] Choose the incorrect option from the following :
Options:
A) \alpha$ and J have the same dimensions.
B) S and $\alpha$ have different dimensions
C) S, $\beta, k and \mu$R have the same dimensions
D) \alpha$ and k have the same dimensions
380
Easy
Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be :(Molecular weight of oxygen is 32g/mol; R = 8.3 J K$-1 mol-$1)
Options:
A) \sqrt {{{3\pi } \over 8}}
B) \sqrt {{3 \over 3}}
C) \sqrt {{8 \over 3}}
D) \sqrt {{{8\pi } \over 3}}
381
Easy
For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats) :
Options:
A) - {1 \over \gamma }{{dV} \over V}
B) - \gamma {V \over {dV}}
C) - \gamma {{dV} \over V}
D) {{dV} \over V}
382
Easy
An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S1 and that of the other part is S2. Given that S1 > S2. If the piston is removed then the total entropy of the system will be :
Options:
A) S1 $-$ S2
B) {{{S_1}} \over {{S_2}}}
C) S1 $\times$ S2
D) S1 + S2
383
Medium
The P-V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process CD is (use $\gamma$ = 1.4) :
Options:
A) -$500 J
B) -$400 J
C) 400 J
D) 200 J
384
Easy
What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T? (kB is Boltzmann constant)
Options:
A) {1 \over 2}{k_B}T
B) {2 \over 3}{k_B}T
C) {3 \over 2}{k_B}T
D) {k_B}T
385
Medium
If one mole of the polyatomic gas is having two vibrational modes and $\beta is the ratio of molar specific heats for polyatomic gas \left( {\beta = {{{C_P}} \over {{C_V}}}} \right) then the value of \beta$ is :
Options:
A) 1.02
B) 1.35
C) 1.2
D) 1.25
386
Medium
Which one is the correct option for the two different thermodynamic processes?
Options:
A) (a) only
B) (c) and (d)
C) (b) and (c)
D) (c) and (a)
387
Medium
A polyatomic ideal gas has 24 vibrational modes. What is the value of $\gamma$?
Options:
A) 1.37
B) 1.30
C) 1.03
D) 10.3
388
Medium
Two ideal polyatomic gases at temperatures T1 and T2 are mixed so that there is no loss of energy. If F1 and F2, m1 and m2, n1 and n2 be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is :
Options:
A) {{{n_1}{F_1}{T_1} + {n_2}{F_2}{T_2}} \over {{F_1} + {F_2}}}
B) {{{n_1}{F_1}{T_1} + {n_2}{F_2}{T_2}} \over {{n_1}{F_1} + {n_2}{F_2}}}
C) {{{n_1}{T_1} + {n_2}{T_2}} \over {{n_1} + {n_2}}}
D) {{{n_1}{F_1}{T_1} + {n_2}{F_2}{T_2}} \over {{n_1} + {n_2}}}
389
Easy
Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of the combination is :
Options:
A) {{2{K_1}{K_2}} \over {{K_1} + {K_2}}}
B) {{{K_1} + {K_2}} \over {{K_1}{K_2}}}
C) {{{K_1} + {K_2}} \over {2{K_1}{K_2}}}
D) {{{K_1}{K_2}} \over {{K_1} + {K_2}}}
390
Easy
A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :
Options:
A) 2400 J
B) 1600 J
C) 1800 J
D) 3200 J
391
Medium
Calculate the value of mean free path ($\lambda) for oxygen molecules at temperature 27^\circC and pressure 1.01 \times 105 Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 \times 10-23 JK-$1)
Options:
A) 32 nm
B) 58 nm
C) 86 nm
D) 102 nm
392
Easy
A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will :
Options:
A) Neither bend nor shrink
B) Bend towards the left
C) Not bend but shrink
D) Bend towards the right
393
Medium
In thermodynamics, heat and work are :
Options:
A) Path functions
B) Point functions
C) Extensive thermodynamics state variables
D) Intensive thermodynamic state variables
394
Easy
The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is :
Options:
A) {{3RT} \over V}
B) {{4RT} \over V}
C) {{88RT} \over V}
D) {5 \over 2}{{RT} \over V}
395
Medium
The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U $=$ 3PV + 4. The gas is :
Options:
A) either monoatomic or diatomic.
B) monoatomic only.
C) polyatomic only.
D) diatomic only.
396
Easy
The temperature $\theta at the junction of two insulating sheets, having thermal resistances R1 and R2 as well as top and bottom temperatures \theta1 and \theta$2 (as shown in figure) is given by :
Options:
A) {{{\theta _1}{R_2} + {\theta _2}{R_1}} \over {{R_1} + {R_2}}}
B) {{{\theta _1}{R_1} + {\theta _2}{R_2}} \over {{R_1} + {R_2}}}
C) {{{\theta _1}{R_2} - {\theta _2}{R_1}} \over {{R_2} - {R_1}}}
D) {{{\theta _2}{R_2} - {\theta _1}{R_1}} \over {{R_2} - {R_1}}}
397
Medium
Given below are two statements :Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.In the light of the above statements, choose the correct answer from the options given below :
Options:
A) Both Statement I and Statement II are true
B) Both Statement I and Statement II are false
C) Statement I is true but Statement II is false.
D) Statement I is false but Statement II is true.
398
Easy
Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V2 = 2V1 then the ratio of temperature T2/T1 is :
Options:
A) \sqrt 2
B) {1 \over {\sqrt 2 }}
C) {1 \over 2}
D) 2
399
Easy
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.Assertion A : When a rod lying freely is heated, no thermal stress is developed in it.Reason R : On heating, the length of the rod increases.In the light of the above statements, choose the correct answer from the options given below :
Options:
A) A is true but R is false
B) A is false but R is true
C) Both A and B are true but R is NOT the correct explanation of A
D) Both A and R are true and R is the correct explanation of A
400
Easy
A diatomic gas, having ${C_p} = {7 \over 2}R and {C_v} = {5 \over 2}R$, is heated at constant pressure. The ratio dU : dQ : dW :
Options:
A) 5 : 7 : 3
B) 3 : 7 : 2
C) 5 : 7 : 2
D) 3 : 5 : 2
401
Medium
If one mole of an ideal gas at (P1, V1) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B $ \to $ C). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net workdone by the gas is equal to :
Options:
A) - {{RT} \over {2(\gamma - 1)}}
B) RT\left( {\ln 2 - {1 \over {2(\gamma - 1)}}} \right)
C) RT\ln 2
D) 0
402
Easy
On the basis of kinetic theory of gases, the gas exerts pressure because its molecules :
Options:
A) continuously lose their energy till it reaches wall.
B) are attracted by the walls of container.
C) suffer change in momentum when impinge on the walls of container.
D) continuously stick to the walls of container.
403
Easy
Match List I with List II. List I List II (a) Isothermal (i) Pressure constant (b) Isochoric (ii) Temperature constant (c) Adiabatic (iii) Volume constant (d) Isobaric (iv) Heat content is constant Choose the correct answer from the options given below :
Options:
A) (a) - (ii), (b) - (iii), (c) - (iv), (d) - (i)
B) (a) - (ii), (b) - (iv), (c) - (iii), (d) - (i)
C) (a) - (iii), (b) - (ii), (c) - (i), (d) - (iv)
D) (a) - (i), (b) - (iii), (c) - (ii), (d) - (iv)
404
Medium
n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.A $ \to B : Isothermal expansion at temperature T so that the volume is doubled from V1 to V2 = 2V1 and pressure charges from P1 to P2B \to C : Isobaric compression at pressure P2 to initial volume V1.C \to $ A : Isochoric change leading to change of pressure from P2 to P1.Total workdone in the complete cycle ABCA is :
Options:
A) nRTln 2
B) 0
C) nRT\left( {\ln 2 - {1 \over 2}} \right)
D) nRT\left( {\ln 2 + {1 \over 2}} \right)
405
Easy
Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is '$\alpha'. The metal sheet is heated uniformly, by a small temperature \DeltaT, so that its new temperature is T + \Delta$T. Calculate the increase in the volume of the metal box.
Options:
A) 3a3$\alpha\Delta$T
B) 4$\pia3\alpha\Delta$T
C) {{4 \over 3}}\pia3\alpha\Delta$T
D) 4a3$\alpha\Delta$T
406
Medium
In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as :
Options:
A) \sqrt T
B) T
C) {1 \over T}
D) {1 \over {\sqrt T }}
407
Medium
Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity K1 , K2 and K3 , respecrtively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100oC and the other at 0oC (see figure). If the joints of the rod are at 70oC and 20oC in steady state and there is no loss of energy from the surface of the rod, the correct relationship between K1 , K2 and K3 is :
Options:
A) K1 : K3 = 2 : 3,
K2 : K3 = 2 : 5
B) K1 < K2 < K3
C) K1 : K2 = 5 : 2,
K1 : K3 = 3 : 5
D) K1 > K2 > K3
408
Medium
Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom.The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of $\gamma \left( { = {{{C_p}} \over {{C_v}}}} \right)$ are given, respectively by:
Options:
A) U = ${5 \over 2}RT and \gamma = {7 \over 5}
B) U = 5RT and $\gamma = {6 \over 5}
C) U = 5RT and $\gamma = {7 \over 5}
D) U = ${5 \over 2}RT and \gamma = {6 \over 5}
409
Medium
Two different wires having lengths L1 and L2, and respective temperature coefficient of linear expansion $\alpha 1 and \alpha $2, are joined end-to-end. Then the effective temperature coefficient of linear expansion is :
Options:
A) 2\sqrt {{\alpha _1}{\alpha _2}}
B) 4{{{\alpha _1}{\alpha _2}} \over {{\alpha _1} + {\alpha _2}}}{{{L_2}{L_1}} \over {{{\left( {{L_2} + {L_1}} \right)}^2}}}
C) {{{\alpha _1} + {\alpha _2}} \over 2}
D) {{{\alpha _1}{L_1} + {\alpha _2}{L_2}} \over {{L_1} + {L_2}}}
410
Medium
In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is :
Options:
A) 128
B) 32
C) 326
D) {1 \over {32}}
411
Medium
A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030 cal/(g – oC) (1 cal = 4.2 × 107 ergs) close to :
Options:
A) 87.5 oC
B) 83.3 oC
C) 38.4 oC
D) 119.2 oC
412
Medium
Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are labelled as A $ \to B, A \to C and A \to $ D. The change in internal energies during these process are taken as EAB, EAC and EAD and the work done as WAB, WAC and WAD. The correct relation between these parameters are :
Options:
A) EAB < EAC < EAD, WAB > 0, WAC > WAD
B) EAB = EAC = EAD, WAB > 0, WAC = 0, WAD < 0
C) EAB > EAC > EAD, WAB < WAC < WAD
D) EAB = EAC < EAD, WAB > 0, WAC = 0, WAD < 0
413
Medium
Number of molecules in a volume of 4 cm3 of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is 4 $ \times $ 10–14 erg, g = 980 cm/s2, density of mercury = 13.6 g/cm3)
Options:
A) 5.8 $ \times $ 1018
B) 4.0 $ \times $ 1016
C) 5.8 $ \times $ 1016
D) 4.0 $ \times $ 1018
414
Medium
Match the thermodynamic processes taking place in a system with the correct conditions. In the table : $\Delta Q is the heat supplied, \Delta W is the work done and \Delta U is change in internal energy of the system. Process Condition (I) Adiabatic (1) \Delta W = 0 (II) Isothermal (2) \Delta Q = 0 (III) Isochoric (3) \Delta U \ne 0, \Delta W \ne 0, \Delta Q \ne 0 (IV) Isobaric (4) \Delta $U = 0
Options:
A) (I) - (1), (II) - (1), (III) - (2), (IV) - (3)
B) (I) - (2), (II) - (4), (III) - (1), (IV) - (3)
C) (I) - (1), (II) - (2), (III) - (4), (IV) - (4)
D) (I) - (2), (II) - (1), (III) - (4), (IV) - (3)
415
Medium
The specific heat of water = 4200 J kg-1K-1 and the latent heat of ice = 3.4 $ \times $ 105 J kg–1. 100 grams of ice at 0oC is placed in 200 g of water at 25oC. The amount of ice that will melt as the temperature of water reaches 0oC is close to (in grams) :
Options:
A) 63.8
B) 61.7
C) 69.3
D) 64.6
416
Medium
Match the ${{{C_P}} \over {{C_V}}}$ ratio for ideal gases with different type of molecules : Molecule Type CP/CV (A) Monatomic (I) 7/5 (B) Diatomic rigid molecules (II) 9/7 (C) Diatomic non-rigid molecules (III) 4/3 (D) Triatomic rigid molecules (IV) 5/3
Options:
A) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
B) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
C) (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
D) (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
417
Medium
A calorimeter of water equivalent 20 g contains 180 g of water at 25oC. ‘m’ grams of steam at 100oC is mixed in it till the temperature of the mixure is 31oC. The value of ‘m’ is close to :(Latent heat of water = 540 cal g–1, specific heat of water = 1 cal g–1 oC–1)
Options:
A) 2.6
B) 2
C) 4
D) 3.2
418
Medium
To raise the temperature of a certain mass of gas by 50oC at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100oC at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?
Options:
A) 6
B) 7
C) 5
D) 3
419
Medium
A balloon filled with helium (32oC and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as
Options:
A) Irreversible adiabatic
B) Reversible adiabatic
C) Irreversible isothermal
D) Reversible isothermal
420
Medium
Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is :
Options:
A) {3 \over 2}RT
B) {9 \over 2}RT
C) {5 \over 2}RT
D) 3RT
421
Medium
A heat engine is involved with exchange of heat of 1915 J, – 40J, + 125 J and –Q J, during one cycle achieving an efficiency of 50.0%. The value of Q is
Options:
A) 980 J
B) 40 J
C) 400 J
D) 640 J
422
Medium
An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true? (A) the mean free path of the molecules decreases. (B) the mean collision time between the molecules decreases. (C) the mean free path remains unchanged. (D) the mean collision time remains unchanged.
Options:
A) (C) and (D)
B) (A) and (D)
C) (B) and (C)
D) (A) and (B)
423
Medium
When the temperature of a metal wire is increased from 0oC to 10oC, its length increases by 0.02%. The percentage change in its mass density will be closest to :
Options:
A) 0.008
B) 0.06
C) 0.8
D) 2.3
424
Medium
A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is :
Options:
A) 11
B) 20
C) 15
D) 13
425
Medium
Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The raito of their respective mean free times is closest to :
Options:
A) 2.3
B) 1.83
C) 4.67
D) 3.67
426
Medium
Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure ? where, 1 $ \to $ 2 is adiabatic. (Graphs are schematic and are not to scale)
Options:
A)
B)
C)
D)
427
Medium
Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass ${m \over 4} . The ratio of the specific heats (C_V^A and C_V^B$ ) of gas A and B, respectively is :
Options:
A) 7 : 9
B) 5 : 7
C) 3 : 5
D) 5 : 9
428
Medium
A carnot engine having an efficiency of ${1 \over {10}}$ is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at lower temperature is :
Options:
A) 90 J
B) 99 J
C) 1 J
D) 100 J
429
Medium
Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its CP/CV value will be :
Options:
A) 23/15
B) 67/45
C) 40/27
D) 19/13
430
Medium
The plot that depicts the behavior of the mean free time t (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)
Options:
A)
B)
C)
D)
431
Medium
A thermodynamic cycle xyzx is shown on a V-T diagram. The P-V diagram that best describes this cycle is : (Diagrams are schematic and not to scale)
Options:
A)
B)
C)
D)
432
Medium
Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperature, T1 and T2 . The temperature of the hot reservoir of the first engine is T1 and the temperature of the cold reservoir of the second engine is T2 . T is temperature of the sink of first engine which is also the source for the second which is also the source for the second engine. How is T related to T1 and T2 . If both engines perform equal amount of work?
Options:
A) T = {{2{T_1}{T_2}} \over {{T_1} + {T_2}}}
B) T = \sqrt {{T_1}{T_2}}
C) T = {{{T_1} + {T_2}} \over 2}
D) T = 0
433
Medium
Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from ${\tau _1} to {\tau _2} . If {{{C_p}} \over {{C_v}}} = \gamma for this gas then a good estimate for {{{\tau _2}} \over {{\tau _1}}}$ is given by :
Options:
A) {\left( 2 \right)^{{{1 + \gamma } \over 2}}}
B) 2
C) {\left( {{1 \over 2}} \right)^{{{1 + \gamma } \over 2}}}
D) {\left( {{1 \over 2}} \right)^\gamma }
434
Medium
Two moles of an ideal gas with ${{{C_P}} \over {{C_V}}} = {5 \over 3} are mixed with 3 moles of another ideal gas with {{{C_P}} \over {{C_V}}} = {4 \over 3}. The value of {{{C_P}} \over {{C_V}}}$ for the mixture is :
Options:
A) 1.50
B) 1.45
C) 1.47
D) 1.42
435
Medium
A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $\gamma $ = 1.40, the work done by air is : (31.4 = 4.6555) [Take air to be an ideal gas]
Options:
A) 60.7 J
B) 100.8 J
C) 90.5 J
D) 48 J
436
Medium
One kg of water, at 20oC, heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 $\Omega $. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to : [Specific heat of water = 4200 J/(kg oC), Latent heat of water = 2260 kJ/kg]
Options:
A) 10 minutes
B) 22 minutes
C) 3 minutes
D) 16 minutes
437
Medium
A Carnot engine has an efficiency of ${1 \over 6}$. When the temperature of the sink is reduced by 62ºC, its efficiency is doubled. The temperatures of the source and the sink are, respectively
Options:
A) 99oC, 37oC
B) 124oC, 62oC
C) 37oC, 99oC
D) 62oC, 124oC
438
Medium
A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process ?
Options:
A) 35 J
B) 30 J
C) 25 J
D) 40 J
439
Medium
Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ? (R = 8.3 J/mol K)
Options:
A) 21.6 J/mol K
B) 17.4 J/mol K
C) 15.7 J/mol K
D) 19.7 J/mol K
440
Medium
When M1 gram of ice at –10oC (specific heat = 0.5 cal g–1 oC–1 ) is added to M2 gram of water at 50C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g–1 is :
Options:
A) {{50{M_2}} \over {{M_1}}} - 5
B) {{50{M_2}} \over {{M_1}}}
C) {{5{M_2}} \over {{M_1}}} - 5
D) {{5{M_1}} \over {{M_2}}} - 50
441
Medium
A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is –180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is:
Options:
A) 120 J
B) 130 J
C) 100 J
D) 140 J
442
Medium
At 40o C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40oC to 20oC it regains its original length of 0.2 m. The value of M is close to : (Coefficient of linear expansion and Young’s modulus of brass are 10–5 /oC and 1011 N/m 2 , respectively; g= 10 ms–2 )
Options:
A) 1.5 kg
B) 0.5 kg
C) 9 kg
D) 0.9 kg
443
Medium
When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by $\Delta $T. the heat required to produce the same change in temperature, at a constant pressure is :
Options:
A) {7 \over 5}Q
B) {3 \over 2}Q
C) {2 \over 3}Q
D) {5 \over 3}Q
444
Medium
One mole of ideal gas passes through a process where pressure and volume obey the relation $P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]$. Here P0 and V0 are constants. Calculate the change in the temperature of the gas if its volume changes form V0 to 2V0
Options:
A) {3 \over 4}{{{P_0}{V_0}} \over R}
B) {1 \over 2}{{{P_0}{V_0}} \over R}
C) {5 \over 4}{{{P_0}{V_0}} \over R}
D) {1 \over 4}{{{P_0}{V_0}} \over R}
445
Medium
A 25 × 10–3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300K). The molecular diameter of O2, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an O2 molecule ?
Options:
A) ~1013
B) ~1012
C) ~1011
D) ~1010
446
Medium
A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is : [Given that R = 8.31 J mol–1 K–1]
Options:
A) 374 J
B) 700 J
C) 748 J
D) 350 J
447
Medium
n moles of an ideal gas with constant volume heat capcity CV undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is :
Options:
A) {{nR} \over {{C_V} - nR}}
B) {{4nR} \over {{C_V} - nR}}
C) {{4nR} \over {{C_V} + nR}}
D) {{nR} \over {{C_V} + nR}}
448
Medium
A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely ? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K)
Options:
A) 10–3 K
B) 10–1 K
C) 10–5K
D) 10–4 K
449
Medium
The specific heats, CP and CV of a gas of diatomic molecules, A, are given (in units of J mol–1 K–1) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :-
Options:
A) A is rigid but B has a vibrational mode
B) A has a vibrational mode but B has none
C) A has one vibrational mode and B has two
D) Both A and B have a vibrational mode each
450
Medium
Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are '$\theta 2' and '\theta 1' respectively, (\theta 2 > \theta $1). The temperature at the interface is :-
Options:
A) {{{\theta _1}} \over {10}} + {{9{\theta _2}} \over {10}}
B) {{{\theta _2} + {\theta _1}} \over 2}
C) {{{\theta _1}} \over {6}} + {{5{\theta _2}} \over {6}}
D) {{{\theta _1}} \over {3}} + {{2{\theta _2}} \over {3}}
451
Medium
An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $\overline v $ , m is its mass and kB is Boltzmann constant, then its temperature will be :
Options:
A) {{m{{\overline v }^2}} \over {5{k_B}}}
B) {{m{{\overline v }^2}} \over {6{k_B}}}
C) {{m{{\overline v }^2}} \over {7{k_B}}}
D) {{m{{\overline v }^2}} \over {3{k_B}}}
452
Medium
Following figure shows two processes A and B for a gas. If $\Delta QA and \Delta QB are the amount of heat absorbed by the system in two cases, and \Delta UA and \Delta $UB are changes in internal energies, respectively, then :
Options:
A) \Delta QA > \Delta QB ; \Delta UA > \Delta $UB
B) \Delta QA < \Delta QB ; \Delta UA < \Delta $UB
C) \Delta QA > \Delta QB ; \Delta UA = \Delta $UB
D) \Delta QA = \Delta QB ; \Delta UA = \Delta $UB
453
Medium
For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be :
Options:
A) 100 m/s
B) 100 $\sqrt 5 $ m/s
C) 80 $\sqrt 5 $ m/s
D) 80 m/s
454
Medium
The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to : [Boltzmann Constant kB = 1.38 × 10–23 J/K Avogadro Number NA = 6.02 × 1026 /kg Radius of Earth : 6.4 × 106 m Gravitational acceleration on Earth = 10ms–2]
Options:
A) 3 × 105 K
B) 104 K
C) 650 K
D) 800 K
455
Medium
The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by :-
Options:
A) d a b c
B) a d b c
C) d a c b
D) a d c b
456
Medium
Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 × 102 kg/m3 and specific heat of 2000 J kg–1 K–1 while liquid in B has density of 103 kg m–3 and specific heat of 4000 J kg–1 K–1. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)
Options:
A)
B)
C)
D)
457
Medium
A thermally insulated vessel contains 150g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to : (Latent heat of vaporization of water = 2.10 × 106 J kg–1 and Latent heat of Fusion of water = 3.36 × 105 J kg–1)
Options:
A) 35 g
B) 130 g
C) 20 g
D) 150 g
458
Medium
A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $\ell 1, and that below the piston is \ell 2, such that \ell 1 > \ell $2. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by : (R is universal gas constant and g is the acceleration due to gravity)
Options:
A) {{nRT} \over g}\left[ {{{{\ell _1} - {\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]
B) {{RT} \over g}\left[ {{{2{\ell _1} + {\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]
C) {{nRT} \over g}\left[ {{1 \over {{\ell _2}}} + {1 \over {{\ell _1}}}} \right]
D) {{RT} \over {ng}}\left[ {{{{\ell _1} - 3{\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]
459
Medium
An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 $ \times $ 10–8 s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to
Options:
A) 0.5 $ \times 10-$8 s
B) 4 $ \times 10-$8 s
C) 3 $ \times 10-$6 s
D) 2 $ \times 10-$7 s
460
Medium
For the given cyclic process CAB as shown for a gas, the work done is :
Options:
A) 1 J
B) 10 J
C) 5 J
D) 30 J
461
Medium
A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and the of the outer cylinder is K2. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :
Options:
A) K1 + K2
B) {{{K_1} + 3{K_2}} \over 4}
C) {{{K_1} + {K_2}} \over 2}
D) {{2{K_1} + 3{K_2}} \over 5}
462
Medium
An ideal gas occupies a volume of 2m3 at a pressure of 3 $ \times $ 106 Pa. The energy of the gas is :
Options:
A) 6 $ \times $ 104 J
B) 9$ \times $ 106 J
C) 3 $ \times $ 102 J
D) 108 J
463
Medium
Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180oC and B upto ToC, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is
Options:
A) 200oC
B) 270oC
C) 230oC
D) 250oC
464
Medium
A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and x0/3 when in contact with ice. What is the temperature of an object in oC, if this thermometer in the contact with the object reads x0/2 ?
Options:
A) 60
B) 35
C) 25
D) 40
465
Medium
When 100 g of a liquid A at 100oC is added to 50 g of a liquid B at temperature 75oC, the temperature of the mixture becomes 90oC. The temperature of the mixture, if 100 g of liquid A at 100oC is added to 50 g of liquid B at 50oC, will be :
Options:
A) 60oC
B) 70oC
C) 85oC
D) 80oC
466
Medium
In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is increased by $\Delta $T. The amount of heat absorbed by gas is (R is gas constant) :
Options:
A) {1 \over 2} KR\Delta $T
B) {1 \over 2} R\Delta $T
C) {3 \over 2} R\Delta $T
D) {2K \over 3} \Delta $T
467
Medium
A metal ball of mass 0.1 kg is heated upto 500oC and dropped into a vessel of heat capacity 800 JK–1 and containing 0.5 kg water. The initial temperature of water and vessel is 30oC. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg–1 and 400 Jkg–1 K–1
Options:
A) 20%
B) 25%
C) 15%
D) 30%
468
Medium
Ice at –20oC is added to 50 g of water at 40oC. When the temperature of the mixture reaches 0oC, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2J/g/oC Specific heat of Ice = 2.1J/g/oC Heat of fusion of water at 0oC= 334J/g)
Options:
A) 100 g
B) 60 g
C) 50 g
D) 40 g
469
Medium
A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TVx = constant, then x is :
Options:
A) {5 \over 3}
B) {2 \over 5}
C) {3 \over 5}
D) {2 \over 3}
470
Medium
A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. considering only translational and rotational modes, the total internal energy of the system is :
Options:
A) 12 RT
B) 20 RT
C) 4 RT
D) 15 RT
471
Medium
Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20oC to 90oC. Work done by gas is close to – (Gas constant R = 8.31 J/mol.K)
Options:
A) 581 J
B) 73 J
C) 146 J
D) 291 J
472
Medium
Two kg of a monoatomic gas is at a pressure of 4 $ \times $ 104 N/m2. The density of the gas is 8 kg/m3. What is the order of energy of the gas due to its thermal motion ?
Options:
A) 104 J
B) 103 J
C) 105 J
D) 106 J
473
Medium
An unknown metal of mass 192 g heated to a temperature of 100oC was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4oC. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5oC. (Specific heat of brass is 394 J kg–1 K–1)
Options:
A) 458 J kg–1 K–1
B) 1232 J kg–1 K–1
C) 654 J kg–1 K–1
D) 916 J kg–1 K–1
474
Medium
A heat source at T = 103 K is connected to another heat reservoir at T = 102 K by a copper slab which is 1 mthick. Given that the thermal conductivity of copper is 0.1 WK–1m–1, the energy flux through it in the steady state is -
Options:
A) 200 Wm$-$2
B) 65 Wm$-$2
C) 120 Wm$-$2
D) 90 Wm$-$2
475
Medium
Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2 and T3, as shown, with T1 > T2 > T3 > T4. The three engines are equally efficient if -
Options:
A) T2 = (T13T4)1/4; T3 = (T1T43)1/4
B) T2 = (T1T4)1/2; T3 = (T12T4)1/3
C) T2 = (T1T42)1/3; T3 = (T12T4)1/3
D) T2 = (T12T4)1/3; T3 = (T1T42)1/3
476
Medium
Two Carnot engines A and B are operated in series. The first one, A, receives heat at T1 (= 600 K) and rejects to a reservoir at temperature T2. The second engine B receives heat rejected by the first engine and, in tum, rejects to a heat reservoir at T3 (=400 K). Calculate the temperature T2 if the work outputs of the two engines are equal :
Options:
A) 600 K
B) 400 K
C) 300 K
D) 500 K
477
Medium
A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27oC. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/K mole]
Options:
A) 0.9 kJ
B) 6 kJ
C) 10 kJ
D) 14 kJ
478
Medium
A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds $\left[ {{{{V_{rms}}\,(helium)} \over {{V_{rms}}\,(\arg on)}}} \right],$ is close to :
Options:
A) 3.16
B) 0.32
C) 0.45
D) 2.24
479
Medium
A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat Flow into the system in path ADB is :
Options:
A) 40 J
B) 80 J
C) 100 J
D) 20 J
480
Medium
A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion $\alpha /oC. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by \Delta $TK. Young's modulus, Y, for this metal is :
Options:
A) {F \over {A\alpha \Delta T}}
B) {F \over {A\alpha (\Delta T - 273)}}
C) {F \over {2A\alpha \Delta T}}
D) {{2F} \over {A\alpha \Delta T}}
481
Medium
Temperature difference of 120oC is maintained between ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length ${{3L} \over 2},$ is connected across AB (see figure). In steady state, temperature difference between P and Q will be close to :
Options:
A) 45oC
B) 75oC
C) 60oC
D) 35oC
482
Medium
Two moles of helium are mixed with n moles of hydrogen. If ${{Cp} \over {Cv}} = {3 \over 2}$ for the mixture, then the value of n is :
Options:
A) 1
B) 3
C) 2
D) 3 / 2
483
Medium
One mole of an ideal monoatomic gas is taken along the path ABCA as show in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :
Options:
A) {{25} \over {16}}\,{{{P_o}{V_o}} \over R}
B) {{25} \over {8}}\,{{{P_o}{V_o}} \over R}
C) {{25} \over {4}}\,{{{P_o}{V_o}} \over R}
D) {{5} \over {8}}\,{{{P_o}{V_o}} \over R}
484
Medium
Two moles of an ideal monatomic gas occupies a volume V at 27oC. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.
Options:
A) (a) 195 K (b) 2.7 kJ
B) (a) 189 K (b) 2.7 kJ
C) (a) 195 K (b) –2.7 kJ
D) (a) 189 K (b) – 2.7 kJ
485
Medium
The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms-1 is : [kB =1.4 $ \times 10-23 J/K; mHe = 7 \times $ 10 -27 kg ]
Options:
A) 1.3 $ \times $ 104
B) 1.3 $ \times $ 103
C) 1.3 $ \times $ 105
D) 1.3 $ \times $ 102
486
Medium
Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K. If the efficiencies of the two energies A and B are represented by ${\eta _A} and {\eta _B}, respectively, then what is the value of {{{\eta _B}} \over {{\eta _A}}}$ ?
Options:
A) {{12} \over 7}
B) {{7} \over 12}
C) {{12} \over 5}
D) {{5} \over 12}
487
Medium
One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, ${27^ \circ }C.$ The work done on the gas will be :
Options:
A) 300 R
B) 300 R ln 6
C) 300 R ln 2
D) 300 R ln 7
488
Medium
A Carnot's engine works as a refrigerator between $250 K and 300 K. It receives 500$ cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is :
Options:
A) 420 J
B) 772 J
C) 2100 J
D) 2520 J
489
Medium
A steel rail of length 5 m and area of cross section 40cm2 is prevented from expanding along its length while the temperature rises by 10oC. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10−5 K−1 and 2×1011 Nm−2 respectively, the force developed in the rail is approximately :
Options:
A) 2 $ \times $ 107 N
B) 1 $ \times $ 105 N
C) 2 $ \times $ 109 N
D) 3 $ \times 10-$5 N
490
Medium
For the P-V diagram given for an ideal gas, out of the following which one correctly represents the T-P diagram ?
Options:
A)
B)
C)
D)
491
Medium
N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas ?
Options:
A) {1 \over 2}$ nRT
B) 0
C) {3 \over 2}$ nRT
D) {5 \over 2}$ nRT
492
Medium
In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto 150oC. Immediately, it is put into water of volume 150 cc at 27oC kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40oC. The specific heat of aluminium is : (take 4.2 Joule = 1 calorie)
Options:
A) 378 J/kg $-$oC
B) 315 J/kg $-$oC
C) 476 J/kg $-$oC
D) 434 J/kg $-$oC
493
Medium
A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T. The net change in its length is zero. Let \ell be the length of the rod, A its area of cross-section,Y its Young’s modulus, and \alpha $ its coefficient of linear expansion. Then, F is equal to :
Options:
A) \ell 2 Y\alpha \Delta $T
B) \ell A Y\alpha \Delta $T
C) A Y$\alpha \Delta $T
D) {{AY} \over {\alpha \,\Delta T}}
494
Medium
An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp ) and at constant volume (Cv) is :
Options:
A) 6
B) {7 \over 2}
C) {5 \over 2}
D) {7 \over 5}
495
Medium
An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is : (Take Cv = 1.5 R, where R is gas constant)
Options:
A) 0.24
B) 0.15
C) 0.32
D) 0.08
496
Medium
The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 $ \times $ 105 Pa. If Ni and Nf are the number of molecules in the room before and after heating, then Nf – Ni will be :
Options:
A) - 1.61 $ \times $ 1023
B) 1.38 $ \times $ 1023
C) 2.5 $ \times $ 1025
D) - 2.5 $ \times $ 1025
497
Medium
An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:
Options:
A) {P \over {3\alpha K}}
B) {P \over {\alpha K}}
C) {3 \alpha \over {P K}}
D) 3PK$\alpha
498
Medium
A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75oC. T is given by: (Given : room temperature = 30oC, specific heat of copper = 0.1 cal/gmoC)
Options:
A) 825oC
B) 800oC
C) 885oC
D) 1250oC
499
Medium
CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for hydrogen gas CP – Cv = b for nitrogen gas The correct relation between a and b is
Options:
A) a = 28 b
B) a = 1/14 b
C) a = b
D) a = 14 b
500
Medium
A Carnot freezer takes heat from water at 0oC inside it and rejects it to the room at a temperature of 27oC. The latent heat of ice is 336×103 J kg−1. If 5 kg of water at 0oC is converted into ice at 0oC by the freezer, then the energy consumed by the freezer is close to :
Options:
A) 1.67 $ \times $ 105 J
B) 1.68 $ \times $ 106 J
C) 1.51 $ \times $ 105 J
D) 1.71 $ \times $ 107 J
501
Medium
Which of the following shows the correct relationship between the pressure ‘P’ and density $\rho $ of an ideal gas at constant temperature ?
Options:
A)
B)
C)
D)
502
Medium
The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :
Options:
A) {3 \over 5}
B) {2 \over 3}
C) {3 \over 2}
D) {2 \over 5}
503
Medium
A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0oC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is $\alpha $ then the value of S is :
Options:
A) \alpha
B) {\alpha \over 2}
C) 2$\alpha
D) {1 \over \alpha }
504
Medium
200 g water is heated from 40oC to 60oC. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J/kg/K) :
Options:
A) 8.4 kJ
B) 4.2 kJ
C) 16.7 kJ
D) 167.4 kJ
505
Medium
'n' moles of an ideal gas undergoes a process A \to B$ as shown in the figure. The maximum temperature of the gas during the process will be :
Options:
A) {{9{P_0}{V_0}} \over {2nR}}
B) {{9{P_0}{V_0}} \over {nR}}
C) {{9{P_0}{V_0}} \over {4nR}}
D) {{3{P_0}{V_0}} \over {2nR}}
506
Medium
A pendulum clock loses $12 s a day if the temperature is {40^ \circ }C and gains 4 s a day if the temperature is {20^ \circ }C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion \left( \alpha \right)$ of the metal of the pendulum shaft are respectively :
Options:
A) {30^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 3}}/{}^ \circ C
B) {55^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 2}}/{}^ \circ C
C) {25^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 5}}/{}^ \circ C
D) {60^ \circ }C;\,\,\alpha = 1.85 \times {10^{ - 4}}/{}^ \circ C
507
Medium
An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $C remains constant. If during this process the relation of pressure P and volume V is given by P{V^n} = constant, then n is given by (Here {C_p} and {C_v}$ are molar specific heat at constant pressure and constant volume, respectively:
Options:
A) n = {{{C_p} - C} \over {C - {C_v}}}
B) n = {{C - {C_v}} \over {C - {C_p}}}
C) n = {{{C_p}} \over {{C_v}}}
D) n = {{C - {C_p}} \over {C - {C_v}}}
508
Medium
Consider a spherical shell of radius $R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = {U \over V}\, \propto \,{T^4} and pressure p = {1 \over 3}\left( {{U \over V}} \right) . If the shell now undergoes an adiabatic expansion the relation between T and R$ is:
Options:
A) T\, \propto {1 \over R}
B) T\, \propto {1 \over {{R^3}}}
C) T\, \propto \,{e^{ - R}}
D) T\, \propto \,{e^{ - 3R}}
509
Medium
A solid body of constant heat capacity $1 J/{}^ \circ C is being heated by keeping it in contact with reservoirs in two ways: (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir \,\,\,\,\,\,\,\,supplies same amount of heat. (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir \,\,\,\,\,\,\,\,\,\,supplies same amount of heat. In both the cases body is brought from initial temperature {100^ \circ }C to final temperature {200^ \circ }C$. Entropy change of the body in the two cases respectively is :
Options:
A) ln2, 2ln2
B) 2ln2, 8ln2
C) ln2, 4ln2
D) ln2, ln2
510
Medium
Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as ${V^q}, where V is the volume of the gas. The value of q is: \left( {\gamma = {{{C_p}} \over {{C_v}}}} \right)
Options:
A) {{\gamma + 1} \over 2}
B) {{\gamma - 1} \over 2}
C) {{3\gamma + 5} \over 6}
D) {{3\gamma - 5} \over 6}
511
Medium
One mole of a diatomic ideal gas undergoes a cyclic process $ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K$ respectively. Choose the correct statement :
Options:
A) The change in internal energy in whole cyclic process is $250 R.
B) The change in internal energy in the process $CA is 700 R$.
C) The change in internal energy in the process $AB is - 350 R.
D) The change in internal energy in the process $BC is - 500 R.
512
Medium
Three rods of Copper, Brass and Steel are welded together to form a $Y shaped structure. Area of cross - section of each rod = 4c{m^2}. End of copper rod is maintained at {100^ \circ }C where as ends of brass and steel are kept at {0^ \circ }C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS$ units respectively. Rate of heat flow through copper rod is:
Options:
A) 1.2 cal/s
B) 2.4 cal/s
C) 4.8 cal/s
D) 6.0 cal/s
513
Medium
The above $p-v$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is
Options:
A) {p_0}{v_0}
B) \left( {{{13} \over 2}} \right){p_0}{v_0}
C) \left( {{{11} \over 2}} \right){p_0}{v_0}
D) 4{p_0}{v_0}
514
Medium
Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is $T, density of liquid is \rho and L$ is its latent heat of vaporization.
Options:
A) \rho L/T
B) \sqrt {T/\rho L}
C) T/\rho L
D) 2T/\rho L
515
Medium
A wooden wheel of radius $R is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2\pi R. To fit the ring on the wheel, it is heated so that its temperature rises by \Delta T and it just steps over the wheel. As it cools down to surrounding temperature, it process the semicircular parts together. If the coefficient of linear expansion of the metal is \alpha , and its Young's modulus is Y,$ the force that one part of the wheel applies on the other part is :
Options:
A) 2\pi SY\alpha \Delta T
B) SY\alpha \Delta T
C) \pi SY\alpha \Delta T
D) 2SY\alpha \Delta T
516
Medium
Helium gas goes through a cycle $ABCD$ (consisting of two isochoric and isobaric lines) as shown in figure efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)
Options:
A) 15.4\%
B) 9.1\%
C) 10.5\%
D) 12.5\%
517
Medium
A Carnot engine, whose efficiency is $40\% , takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60\% .$ Then, the intake temperature for the same exhaust (sink) temperature must be :
Options:
A) efficiency of Carnot engine cannot be made larger than $50\%
B) 1200 K
C) 750 K
D) 600 K
518
Medium
100g of water is heated from {30^ \circ }C to {50^ \circ }C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/kg/K$):
Options:
A) 8.4 kJ
B) 84 kJ
C) 2.1 kJ
D) 4.2 kJ
519
Medium
A thermally insulated vessel contains an ideal gas of molecular mass $M and ratio of specific heats \gamma . It is moving with speed v$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:
Options:
A) {{\left( {\gamma - 1} \right)} \over {2\gamma R}}M{v^2}K
B) {{\gamma {M^2}v} \over {2R}}K
C) {{\left( {\gamma - 1} \right)} \over {2R}}M{v^2}K
D) {{\left( {\gamma - 1} \right)} \over {2\left( {\gamma + 1} \right)R}}M{v^2}K
520
Medium
Three perfect gases at absolute temperatures ${T_1},\,{T_2} and {T_3} are mixed. The masses of molecules are {m_1},{m_2} and {m_3} and the number of molecules are {n_1}, {n_2} and {n_3}$ respectively. Assuming no loss of energy, the final temperature of the mixture is:
Options:
A) {{{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}} \over {{n_1} + {n_2} + {n_3}}}
B) {{{n_1}T_1^2 + {n_2}T_2^2 + {n_3}T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}
C) {{n_1^2T_1^2 + n_2^2T_2^2 + n_3^2T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}
D) {{\left( {{T_1} + {T_2} + {T_3}} \right)} \over 3}
521
Medium
A Carnot engine operating between temperatures ${{T_1}} and {{T_2}} has efficiency {1 \over 6}. When {T_2} is lowered by 62 K its efficiency increases to {1 \over 3}. Then {T_1} and {T_2}$ are, respectively:
Options:
A) 372 K and 330 K
B) 330 K and 268 K
C) 310 K and 248 K
D) 372 K and 310 K
522
Medium
A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V to 32 V$, the efficiency of the engine is
Options:
A) 0.5
B) 0.75
C) 0.99
D) 0.25
523
Medium
A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta along the length x$ of the bar from its hot end is best described by which of the following figures?
Options:
A)
B)
C)
D)
524
Medium
Two moles of helium gas are taken over the cycle $ABCD, as shown in the P-T diagram. The work done on the gas in taking it from D to A$ is :
Options:
A) +414 R
B) -690 R
C) +690 R
D) -414 R
525
Medium
Two moles of helium gas are taken over the cycle $ABCD, as shown in the P-T diagram. The net work done on the gas in the cycle ABCDA$ is:
Options:
A) 276 R
B) 1076 R
C) 1904 R
D) zero
526
Medium
Statement - 1: The temperature dependence of resistance is usually given as $R = {R_0}\left( {1 + \alpha \,\Delta t} \right). The resistance of wire changes from 100\Omega to 150\Omega when its temperature is increased from {27^ \circ }C to {227^ \circ }C. This implies that \alpha = 2.5 \times {10^{ - 3}}/C. Statement - 2: R = {R_0}\left( {1 + \alpha \,\Delta t} \right) is valid only when the change in the temperature \Delta T is small and \Delta T = \left( {R - {R_0}} \right) < < {R_0}.
Options:
A) Statement - 1 is true, Statement - 2 is true; Statement - 2 is the correct explanation of Statement - 1
B) Statement - 1 is true, Statement - 2 is true; Statement - 2 is not the correct explanation of Statement - 1
C) Statement - 1 is false, Statement - 2 is true
D) Statement - 1 is true, Statement - 2 is false
527
Medium
One $kg of a diatomic gas is at a pressure of 8 \times {10^4}\,N/{m^2}. The density of the gas is 4kg/{m^3}$. What is the energy of the gas due to its thermal motion ?
Options:
A) 5 \times {10^4}\,J
B) 6 \times {10^4}\,J
C) 7 \times {10^4}\,J
D) 3 \times {10^4}\,J
528
Medium
Two moles of helium gas are taken over the cycle $ABCD, as shown in the P-T diagram. Assuming the gas to be ideal the work done on the gas in taking it from A to B$ is :
Options:
A) 300 R
B) 400 R
C) 500 R
D) 200 R
529
Medium
An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume ${V_1} and contains ideal gas at pressure {P_1} and temperature {T_1}. The other chamber has volume {V_2} and contains ideal gas at pressure {P_2} and temperature {T_2}$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be
Options:
A) {{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)} \over {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}}}
B) {{{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \over {{P_1}{V_1} + {P_2}{V_2}}}
C) {{{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \over {{P_1}{V_1} + {P_2}{V_2}}}
D) {{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)} \over {{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}}}
530
Medium
The speed of sound in oxygen $\left( {{O_2}} \right) at a certain temperature is 460\,\,m{s^{ - 1}}. The speed of sound in helium (He)$ at the same temperature will be (assume both gases to be ideal)
Options:
A) 1421\,\,m{s^{ - 1}}
B) 500\,\,m{s^{ - 1}}
C) 650\,\,m{s^{ - 1}}
D) 300\,\,m{s^{ - 1}}
531
Medium
One end of a thermally insulated rod is kept at a temperature ${T_1} and the other at {T_2}. The rod is composed of two sections of length {L_1} and {L_2} and thermal conductivities {K_1} and {K_2}$ respectively. The temperature at the interface of the two section is
Options:
A) {{\left( {{K_1}{L_1}{T_1} + {K_2}{L_2}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}
B) {{\left( {{K_2}{L_2}{T_1} + {K_1}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}
C) {{\left( {{K_2}{L_1}{T_1} + {K_1}{L_2}{T_2}} \right)} \over {\left( {{K_2}{L_1} + {K_1}{L_2}} \right)}}
D) {{\left( {{K_1}{L_2}{T_1} + {K_2}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_2} + {K_2}{L_1}} \right)}}
532
Medium
When a system is taken from state $i to state f along the path iaf, it is found that Q=50 cal and W=20 cal. Along the path ibf Q=36 cal. W along the path ibf$ is
Options:
A) 14 cal
B) 6 cal
C) 16 cal
D) 66 cal
533
Medium
If ${C_p} and {C_v}$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then
Options:
A) {C_p} - {C_v} = 28R
B) {C_p} - {C_v} = R/28
C) {C_p} - {C_v} = R/14
D) {C_p} - {C_v} = R
534
Medium
A Carnot engine, having an efficiency of $\eta = 1/10 as heat engine, is used as a refrigerator . If the work done on the system is 10 J$, the amount of energy absorbed from the reservoir at lower temperature is
Options:
A) 100 J
B) 99 J
C) 90 J
D) 1 J
535
Medium
The work of $146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by {7^ \circ }C. The gas is \left( {R = 8.3J\,\,mo{l^{ - 1}}\,{K^{ - 1}}} \right)
Options:
A) diatomic
B) triatomic
C) a mixture of monoatomic and diatomic
D) monoatomic
536
Medium
Assuming the Sun to be a spherical body of radius $R at a temperature of TK, evaluate the total radiant powered incident of Earth at a distance r from the Sun Where r0 is the radius of the Earth and \sigma $ is Stefan's constant.
Options:
A) 4\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}
B) \pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}
C) r_0^2{R^2}\sigma {{{T^4}} \over {4\pi {r^2}}}
D) {R^2}\sigma {{{T^4}} \over {{r^2}}}
537
Medium
Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature ${T_0}, while Box contains one mole of helium at temperature \left( {{7 \over 3}} \right){T_0}. The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, {T_f} in terms of {T_0}$ is
Options:
A) {T_f} = {3 \over 7}{T_0}
B) {T_f} = {7 \over 3}{T_0}
C) {T_f} = {3 \over 2}{T_0}
D) {T_f} = {5 \over 2}{T_0}
538
Medium
The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is
Options:
A) {1 \over 4}
B) {1 \over 2}
C) {2 \over 3}
D) {1 \over 3}
539
Medium
The figure shows a system of two concentric spheres of radii ${r_1} and {r_2} are kept at temperatures {T_1} and {T_2}$, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to
Options:
A) In\left( {{{{r_2}} \over {{r_1}}}} \right)
B) {{\left( {{r_2} - {r_1}} \right)} \over {\left( {{r_1}{r_2}} \right)}}
C) {\left( {{r_2} - {r_1}} \right)}
D) {{{r_1}{r_2}} \over {\left( {{r_2} - {r_1}} \right)}}
540
Medium
A gaseous mixture consists of $16 g of helium and 16 g of oxygen. The ratio {{Cp} \over {{C_v}}}$ of the mixture is
Options:
A) 1.62
B) 1.59
C) 1.54
D) 1.4
541
Medium
A system goes from $A to B via two processes I and II as shown in figure. If \Delta {U_1} and \Delta {U_2} are the changes in internal energies in the processes I and II$ respectively, then
Options:
A) relation between $\Delta {U_1} and \Delta {U_2}$ can not be determined
B) \Delta {U_1} = \Delta {U_2}
C) \Delta {U_2} < \Delta {U_1}
D) \Delta {U_2} > \Delta {U_1}
542
Medium
Two thermally insulated vessels $1 and 2 are filled with air at temperatures \left( {{T_1},{T_2}} \right), volume \left( {{V_1},{V_2}} \right) and pressure \left( {{P_1},{P_2}} \right)$ respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
Options:
A) {T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)/\left( {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \right)
B) \left( {{T_1} + {T_2}} \right)/2
C) {{T_1} + {T_2}}
D) {T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)/\left( {{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \right)
543
Medium
One mole of ideal monatomic gas $\left( {\gamma = 5/3} \right) is mixed with one mole of diatomic gas \left( {\gamma = 7/5} \right). What is \gamma for the mixture? \gamma $ Denotes the ratio of specific heat at constant pressure, to that at constant volume
Options:
A) 35/23
B) 23/15
C) 3/2
D) 4/3
544
Medium
If the temperature of the sun were to increase from $T to 2T and its radius from R to 2R$, then the ratio of the radiant energy received on earth to what it was previously will be
Options:
A) 32
B) 16
C) 4
D) 64
545
Medium
The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K and 2K and thickness x and 4x, respectively, are {T_2} and {T_1}\left( {{T_2} > {T_1}} \right). The rate of heat transfer through the slab, in a steady state is \left( {{{A\left( {{T_2} - {T_1}} \right)K} \over x}} \right)f, with f$ equal to
Options:
A) {2 \over 3}
B) {1 \over 2}
C) 1
D) {1 \over 3}
546
Medium
Time taken by a $836 W heater to heat one litre of water from 10{}^ \circ C to 40{}^ \circ C$ is
Options:
A) 150 s
B) 100 s
C) 50 s
D) 200 s
547
Medium
Which of the following statements is correct for any thermodynamic system ?
Options:
A) The change in entropy can never be zero
B) Internal energy and entropy and state functions
C) The internal energy changes in all processes
D) The work done in an adiabatic process is always zero,
548
Medium
The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by
Options:
A) Rayleigh Jeans law
B) Planck's law of radiation
C) Stefan's law of radiation
D) Wien's law
549
Medium
Which of the following parameters does not characterize the thermodynamic state of mattter?
Options:
A) Temperature
B) Pressure
C) Work
D) Volume
550
Medium
A carnot engine takes $3 \times {10^6} cal. of heat from a reservoir at {627^ \circ }C, and gives it to a sink at {27^ \circ }C$. The work done by the engine is
Options:
A) 4.2 \times {10^6}J
B) 8.4 \times {10^6}J
C) 16.8 \times {10^6}J
D) zero
551
Medium
''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or consequence of :
Options:
A) second law of thermodynamics
B) conservation of momentum
C) conservation of mass
D) first law of thermodynamics
552
Medium
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio ${C_p}/{C_V}$ for the gas is
Options:
A) {4 \over 3}
B) 2
C) {5 \over 3}
D) {3 \over 2}
553
Medium
Two spheres of the same material have radii $1 m and 4 m and temperatures 4000 K and 2000 K$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second is
Options:
A) 1:1
B) 16:1
C) 4:1
D) 1:9
554
Medium
Even Carnot engine cannot give $100\% $ efficiency because we cannot
Options:
A) prevent radiation
B) find ideal sources
C) reach absolute zero temperature
D) eliminate friction.
555
Medium
Infrared radiation is detected by
Options:
A) spectrometer
B) pyrometer
C) nanometer
D) photometer
556
Medium
Which statement is incorrect?
Options:
A) all reversible cycles have same efficiency
B) reversible cycle has more efficiency than an irreversible one
C) Cannot cycle is a reversible one
D) Cannot cycle has the maximum efficiency in all cycles.
557
Medium
Which of the following is more close to a black body?
Options:
A) black board paint
B) green leaves
C) black holes
D) red roses
558
Medium
Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will
Options:
A) increase
B) decrease
C) remain same
D) decrease for some, while increase for others
559
Medium
Heat given to a body which raises its temperature by ${1^ \circ }C$ is
Options:
A) water equivalent
B) thermal capacity
C) specific heat
D) temperature gradient
560
Medium
If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should
Options:
A) increase
B) remain unchanged
C) decrease
D) first increase then decrease
561
Medium
At what temperature is the $r.m.s velocity of a hydrogen molecule equal to that of an oxygen molecule at {47^ \circ }C?
Options:
A) 80K
B) -73 K
C) 3 K
D) 20 K
562
Medium
1 mole of a gas with $\gamma = 7/5 is mixed with 1 mole of a gas with \gamma = 5/3, then the value of \gamma $ for the resulting mixture is
Options:
A) 7/5
B) 2/5
C) 3/2
D) 12/7
563
Easy
A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ______ J.
Options:
564
Medium
When 300 J of heat given to an ideal gas with C_p=\frac{7}{2} R its temperature raises from 20^{\circ} \mathrm{C} to 50^{\circ} \mathrm{C} keeping its volume constant. The mass of the gas is (approximately) \_\_\_\_ g. (\mathrm{R}=8.314 \mathrm{~J} / \mathrm{mol} . \mathrm{K})
Options:
565
Easy
A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50^{\circ} \mathrm{C}. The gas is now heated to double its temperature. The modified pressure is \_\_\_\_ Pa .
Options:
566
Easy
An insulated cylinder of volume 60 \mathrm{~cm}^3 is filled with a gas at 27^{\circ} \mathrm{C} and 2 atmospheric pressure. Then the gas is compressed making the final volume as 20 \mathrm{~cm}^3 while allowing the temperature to rise to 77^{\circ} \mathrm{C}. The final pressure is \_\_\_\_ atmospheric pressure.
Options:
567
Easy
A diatomic gas (\gamma=1.4) does 100 J of work when it is expanded isobarically. Then the heat given to the gas \_\_\_\_ J.
Options:
568
Easy
10 mole of oxygen is heated at constant volume from 30^{\circ} \mathrm{C} to 40^{\circ} \mathrm{C}. The change in the internal energy of the gas is \_\_\_\_ cal. (The molecular specific heat of oxygen at constant pressure, C_P=7 \mathrm{cal} / \mathrm{mol} .{ }^{\circ} \mathrm{C} and \left.\mathrm{R}=2 \mathrm{cal} . / \mathrm{mol} .{ }^{\circ} \mathrm{C}.\right)
Options:
569
Medium
Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal conductivites of these rods are: \frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{1}{2}, \frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=2 and \frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{1}{2}. The free ends of rods A and B are maintained at 400 K , 200 K , respectively. The temperature of rods interface is ______________ K, when equilibrium is established.
Options:
570
Medium
A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727^{\circ} \mathrm{C} and power radiated by the wire is 94.2 W . Its emissivity is \frac{x}{8} where x= _________. (Given \sigma=6.0 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}, \pi=3.14 and assume that the emissivity of wire material is same at all wavelength.)
Options:
571
Easy
An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ________ \times 10^{-1} \mathrm{~J}. (Take \pi=3.14 )
Options:
572
Easy
The internal energy of air in 4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m} sized room at 1 atmospheric pressure will be___________________\times 10^6 \mathrm{~J} (Consider air as diatomic molecule)
Options:
573
Medium
\gamma_{\mathrm{A}} is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. \gamma_B is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If \frac{\gamma_A}{\gamma_B}=\left(1+\frac{1}{n}\right), then the value of n is ________ .
Options:
574
Easy
A container of fixed volume contains a gas at 27°C. To double the pressure of the gas, the temperature of gas should be raised to _____ °C.
Options:
575
Easy
The temperature of 1 mole of an ideal monoatomic gas is increased by 50^{\circ} \mathrm{C} at constant pressure. The total heat added and change in internal energy are E_1 and E_2, respectively. If \frac{E_1}{E_2}=\frac{x}{9} then the value of x is _________.
Options:
576
Medium
An ideal gas initially at 0^{\circ} \mathrm{C} temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3 / 2, the change in temperature due to the thermodynamic process is _________ K.
Options:
577
Medium
Three conductors of same length having thermal conductivity k_1, k_2 and k_3 are connected as shown in figure. Area of cross sections of 1^{\text {st }} and 2^{\text {nd }} conductor are same and for 3^{\text {rd }} conductor it is double of the 1^{\text {st }} conductor. The temperatures are given in the figure. In steady state condition, the value of \theta is _________ { }^{\circ} \mathrm{C}. (Given : \mathrm{k}_1=60 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_2=120 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_3=135 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1} )
Options:
578
Easy
Two plates $\mathrm{A} and \mathrm{B} have thermal conductivities 84 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1} and 126 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1} respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of \mathrm{A} and \mathrm{B} are kept at 100^{\circ} \mathrm{C} and 0{ }^{\circ} \mathrm{C} respectively, then the temperature of the surface of contact in steady state is _____________ { }^{\circ} \mathrm{C}$.
Options:
579
Easy
A steel rod of length $1 \mathrm{~m} and cross sectional area 10^{-4} \mathrm{~m}^{2} is heated from 0^{\circ} \mathrm{C} to 200^{\circ} \mathrm{C} without being allowed to extend or bend. The compressive tension produced in the rod is ___________ \times 10^{4} \mathrm{~N}. (Given Young's modulus of steel =2 \times 10^{11} \mathrm{Nm}^{-2}, coefficient of linear expansion =10^{-5} \mathrm{~K}^{-1}$ )
Options:
580
Easy
A water heater of power 2000 \mathrm{~W} is used to heat water. The specific heat capacity of water is 4200 \mathrm{~J} \mathrm{kg}^{-1} \mathrm{~K}^{-1}. The efficiency of heater is 70 \%. Time required to heat 2 \mathrm{~kg} of water from 10^{\circ} \mathrm{C} to 60^{\circ} \mathrm{C} is _________ s. (Assume that the specific heat capacity of water remains constant over the temperature range of the water).
Options:
581
Easy
A faulty thermometer reads 5^{\circ} \mathrm{C} in melting ice and 95^{\circ} \mathrm{C} in stream. The correct temperature on absolute scale will be __________ \mathrm{K} when the faulty thermometer reads 41^{\circ} \mathrm{C}.
Options:
582
Easy
A hole is drilled in a metal sheet. At $\mathrm{27^\circ C}, the diameter of hole is 5 cm. When the sheet is heated to \mathrm{177^\circ C}, the change in the diameter of hole is \mathrm{d\times10^{-3}} cm. The value of d will be __________ if coefficient of linear expansion of the metal is 1.6\times10^{-5}/^\circ$C.
Options:
583
Medium
The pressure $\mathrm{P}_{1} and density \mathrm{d}_{1} of diatomic gas \left(\gamma=\frac{7}{5}\right) changes suddenly to \mathrm{P}_{2}\left(>\mathrm{P}_{1}\right) and \mathrm{d}_{2} respectively during an adiabatic process. The temperature of the gas increases and becomes ________ times of its initial temperature. (given \frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}=32$)
Options:
584
Medium
One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{\alpha^{2}}{4} \mathrm{R} \,\mathrm{J} / \mathrm{mol} \,\mathrm{K}; then the value of \alpha$ will be _________. (Assume that the given diatomic gas has no vibrational mode).
Options:
585
Medium
At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _________ J.
Options:
586
Easy
A block of ice of mass 120 g at temperature 0$^\circC is put in 300 g of water at 25^\circC. The x g of ice melts as the temperature of the water reaches 0^\circC. The value of x is _____________. [Use specific heat capacity of water = 4200 Jkg-1K-1, Latent heat of ice = 3.5 \times 105 Jkg-$1]
Options:
587
Medium
A unit scale is to be prepared whose length does not change with temperature and remains $20 \mathrm{~cm}, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is 40 \mathrm{~cm} and length of iron will be __________ \mathrm{cm}. \left(\alpha_{\text {iron }}=1.2 \times 10^{-5} \mathrm{~K}^{-1}\right. and \left.\alpha_{\text {brass }}=1.8 \times 10^{-5} \mathrm{~K}^{-1}\right)$.
Options:
588
Medium
Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be ___________ min.
Options:
589
Medium
As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm2 for each plate. The equivalent thermal conductivity of the compound plate is $\left( {1 + {5 \over \alpha }} \right) K, then the value of \alpha$ will be ______________.
Options:
590
Medium
300 cal. of heat is given to a heat engine and it rejects 225 cal. If source temperature is 227$^\circC, then the temperature of sink will be ______________ ^\circ$C.
Options:
591
Easy
The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _____________ J. (Given R = 8.31 J/mol.K)
Options:
592
Easy
A diatomic gas ($\gamma$ = 1.4) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is __________ J.
Options:
593
Easy
In a carnot engine, the temperature of reservoir is 527$^\circC and that of sink is 200 K. If the work done by the engine when it transfers heat from reservoir to sink is 12000 kJ, the quantity of heat absorbed by the engine from reservoir is ______________ \times$ 106 J.
Options:
594
Easy
A geyser heats water flowing at a rate of 2.0 kg per minute from 30$^\circC to 70^\circC. If geyser operates on a gas burner, the rate of combustion of fuel will be ___________ g min-1. [Heat of combustion = 8 \times 103 Jg-1, Specific heat of water = 4.2 Jg-1 ^\circC-$1]
Options:
595
Easy
A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is ____________ K.
Options:
596
Easy
When a gas filled in a closed vessel is heated by raising the temperature by 1$^\circ$C, its pressure increases by 0.4%. The initial temperature of the gas is ___________ K.
Options:
597
Easy
A steam engine intakes 50 g of steam at 100$^\circC per minute and cools it down to 20^\circC. If latent heat of vaporization of steam is 540 cal g-1, then the heat rejected by the steam engine per minute is __________ \times 103 cal. (Given : specific heat capacity of water : 1 cal g-1 ^\circC-$1)
Options:
598
Medium
A monoatomic gas performs a work of ${Q \over {4}}$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ______________ R during this transformation. Where R is the gas constant.
Options:
599
Medium
0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127$^\circC. Th amount of heat required to double the speed of its molecules is ____________ k cal. Take R = 2 cal mole-1 K-$1)
Options:
600
Medium
The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0$^\circC without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is {x \over {10}}. Then the value of x (round off to the nearest integer) is ___________. (Given R = 8.31 J mol-1 K-$1)
Options:
601
Medium
The average translational kinetic energy of N2 gas molecules at .............$^\circC becomes equal to the K.E. of an electron accelerated from rest through a potential difference of 0.1 volt. (Given kB = 1.38 \times 10-$23 J/K) (Fill the nearest integer).
Options:
602
Medium
A sample of gas with $\gamma$ = 1.5 is taken through an adiabatic process in which the volume is compressed from 1200 cm3 to 300 cm3. If the initial pressure is 200 kPa. The absolute value of the workdone by the gas in the process = _____________ J.
Options:
603
Easy
A heat engine operates between a cold reservoir at temperature T2 = 400 K and a hot reservoir at temperature T1. It takes 300 J of heat from the hot reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be ______________ K.
Options:
604
Medium
A rod CD of thermal resistance 10.0 KW$-1 is joined at the middle of an identical rod AB as shown in figure. The end A, B and D are maintained at 200^\circC, 100^\circC and 125^\circ$C respectively. The heat current in CD is P watt. The value of P is ................. .
Options:
605
Medium
A system consists of two types of gas molecules A and B having same number density 2 $\times 1025/m3. The diameter of A and B are 10 \mathop A\limits^o and 5 \mathop A\limits^o respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is ____________ \times 10-$2
Options:
606
Medium
The area of cross-section of a railway track is 0.01 m2. The temperature variation is 10$^\circC. Coefficient of liner expansion of material of track is 10-5/^\circC. The energy stored per meter in the track is ____________ J/m.(Young's modulus of material of track is 1011 Nm-$2)
Options:
607
Easy
One mole of an ideal gas at 27$^\circ is taken from A to B as shown in the given PV indicator diagram. The work done by the system will be _________ \times 10-$1 J. [Given : R = 8.3 J/mole K, ln2 = 0.6931] (Round off to the nearest integer)
Options:
608
Medium
In the reported figure, heat energy absorbed by a system in going through a cyclic process is ___________ $\pi$J.
Options:
609
Easy
For an ideal heat engine, the temperature of the source is 127$^\circC. In order to have 60% efficiency the temperature of the sink should be ___________^\circ$C. (Round off to the Nearest Integer)
Options:
610
Medium
1 mole of rigid diatomic gas performs a work of ${Q \over 5} when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is {xR \over 8}$. The value of x is _________. [R = universal gas constant]
Options:
611
Medium
The volume V of a given mass of monoatomic gas changes with temperature T according to the relation $V = K{T^{{2 \over 3}}}$. The workdone when temperature changes by 90K will be xR. The value of x is _________. [R = universal gas constant]
Options:
612
Easy
A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 atm. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is x $\times 10-$1 atm. Value of x is ________.
Options:
613
Medium
A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52K, its efficiency is doubled. The temperature in Kelvin of the source will be __________.
Options:
614
Medium
A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R = gas constant) is ${x \over {3R}}$. Value of x is ___________.
Options:
615
Medium
In a certain thermodynamical process, the pressure of a gas depends on its volume as kV3. The work done when the temperature changes from 100$^\circC to 300^\circ$C will be ___________ nR, where n denotes number of moles of a gas.
Options:
616
Easy
The root mean square speed of molecules of a given mass of a gas at 27$^\circC and 1 atmosphere pressure is 200 ms-1. The root mean square speed of molecules of the gas at 127^\circC and 2 atmosphere pressure is {{x \over {\sqrt 3 }}} ms-$1. The value of x will be _________.
Options:
617
Medium
An engine operates by taking a monoatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to __________.
Options:
618
Medium
Initially a gas of diatomic molecules is contained in a cylinder of volume V1 at a pressure P1 and temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a volume 2V1 is given by P2 . The ratio ${{{P_2}} \over {{P_1}}}$ is ________.
Options:
619
Medium
Nitrogen gas is at 300oC temperature. The temperature (in K) at which the rms speed of a H2 molecule would be equal to the rms speed of a nitrogen molecule, is _______. (Molar mass of N2 gas 28 g).
Options:
620
Medium
The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta P is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity \Delta T at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm. respectively. If |\Delta T| = C|\Delta $P| then value of C in (K/atm.) is _________.
Options:
621
Medium
A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to _______.
Options:
622
Medium
If minimum possible work is done by a refrigerator in converting 100 grams of water at 0oC to ice, how much heat (in calories) is released to the surroundings at temperature 27oC (Latent heat of ice = 80 Cal/gram) to the nearest integer ?
Options:
623
Medium
A bakelite beaker has volume capacity of 500 cc at 30oC. When it is partially filled with Vm volume (at 30oC) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If $\gamma (beaker) = 6 × 10–6 oC–1 and \gamma (mercury) = 1.5 × 10–4 oC–1, where \gamma $ is the coefficient of volume expansion, then Vm (in cc) is close to ____.
Options:
624
Medium
An engine takes in 5 moles of air at 20oC and 1 atm, and compresses it adiabatically to 1/10th of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is________.
Options:
625
Medium
Starting at temperature 300 K, one mole of an ideal diatomic gas ($\gamma = 1.4) is first compressed adiabatically from volume V1 to V2 = {{{V_1}} \over {16}}$. It is then allowed to expand isobarically to volume 2V2. If all the processes are the quasi-static then the final temperature of the gas (in oK) is (to the nearest integer) _____.
Options:
626
Medium
Three containers C1, C2 and C3 have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) The value of $\theta $ (in °C to the nearest integer) is ..........
Options:
627
Medium
M grams of steam at 100oC is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produced liquid water at 40oC [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g] the value of M is ____
Options:
628
Medium
A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine performs 1200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle, is _______.
Options:
629
Medium
A non-isotropic solid metal cube has coefficients of linear expansion as : 5 $ \times 10-5/oC along the x-axis and 5 \times 10-6/oC along the y and the z-axis. If the coefficient of volume expansion of the solid is C \times $ 10-6/oC then the value of C is
Options:
630
Medium
Choose the correct statement for processes A & B shown in figure.
Options:
A) P V=k for process B and A$.
B) \frac{P^{\gamma-1}}{T^\gamma}=k for process B and T=k for process A$.
C) \frac{T^\gamma}{P^{\gamma-1}}=k for process A and P V=k for process B$.
D) P V^{\prime}=k for process B and P V=k for process A$.
631
Medium
Which of the following is incorrect regarding the first law of thermodynamics?
Options:
A) It is a restatement of the principle of conservation of energy
B) It is not applicable to any cyclic process
C) It introduces the concept of the entropy
D) It introduces the concept of the internal energy
632
Medium
A black body has maximum wavelength ' \lambda_{\mathrm{m}} ' at temperature 2000 K . Its maximum wavelength at 3000 K will be
Options:
A) \frac{3}{2} \lambda_{\mathrm{m}}
B) \frac{16}{81} \lambda_m
C) \frac{81}{16} \lambda_m
D) \frac{2}{3} \lambda_m
633
Medium
The relation between efficiency (\eta) of Carnot engine and coefficient of performance \left(\eta_1\right) of refrigerator is
Options:
A) \eta=\frac{1}{1+\eta_1}
B) \eta=\frac{1}{1-\eta_1}
C) \quad \eta=\frac{\eta_1}{1-\eta_1}
D) \eta=\frac{1+\eta_1}{\eta_1}
634
Medium
500 gram of a diatomic gas is enclosed at a pressure of 10^5 \mathrm{Nm}^{-2}. The density of the gas is 5 \mathrm{kgm}^{-3}. The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator]
Options:
A) 1.5 \times 10^4 \mathrm{~J}
B) 2.5 \times 10^4 \mathrm{~J}
C) 1.5 \times 10^7 \mathrm{~J}
D) 2.5 \times 10^7 \mathrm{~J}
635
Medium
The outer surface of star in the form of a sphere radiates heat as a black body at temperature ' T '. The total radiant energy per unit area, normal to the direction of incidence, received at a distance ' R ' from the centre of a star of radius ' r ' is (R>r)(\sigma= Stefan's constant )
Options:
A) \frac{\sigma \mathrm{r}^2 \mathrm{~T}^4}{\mathrm{R}^2}
B) \frac{\sigma r^2 T^4}{4 \pi R^2}
C) \frac{\sigma \mathrm{r}^2 \mathrm{~T}^4}{\mathrm{R}^4}
D) \frac{4 \pi \sigma r^2 T^4}{R^2}
636
Medium
A gas having \gamma=\frac{5}{2} and volume 360 c.c. is suddenly compressed to 90 c.c. If the initial pressure of the gas is P , then the final pressure will be
Options:
A) \frac{\mathrm{P}}{4}
B) 8 P
C) 16 P
D) 32 P
637
Medium
The length of steel rod is 5 cm longer than the copper rod at all temperatures. The length of the steel and copper rod is respectively (Coefficient of linear expansion for steel and copper is respectively 1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C} and 1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C} )
Options:
A) nearly 15 cm and 10 cm
B) nearly 14 cm and 9 cm
C) nearly 12 cm and 7 cm
D) nearly 13 cm and 8 cm
638
Medium
Two spherical black bodies have radii ' R_1 ' and ' \mathrm{R}_2 '. Their surface temperatures are ' \mathrm{T}_1 ' and ' T_2 '. If they radiate same power, then \frac{R_2}{R_1} is
Options:
A) \frac{T_2}{T_1}
B) \frac{T_1}{T_2}
C) \left(\frac{T_2}{T_1}\right)^2
D) \left(\frac{T_1}{T_2}\right)^2
639
Medium
An ideal gas taken through a process ABCA as shown in figure. If the net heat supplied to gas in the cycle is 5 J , then the work done by the gas in process from C to A is
Options:
A) -5 J
B) -10 J
C) -15 J
D) -20 J
640
Medium
A calorimeter contains 10 g of water at 20^{\circ} \mathrm{C}. The temperature fall to 15^{\circ} \mathrm{C} in 10 min . When calorimeter contains 20 g of water at 20^{\circ} \mathrm{C}, it takes 15 min . for the temperature to become 15^{\circ} \mathrm{C}. The water equivalent at the calorimeter is
Options:
A) 50 g
B) 25 g
C) 10 g
D) 5 g
641
Medium
Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic gas at temperature T K. The piston of cylinder A is free to move while that of cylinder B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise of temperature of the gas in A is \mathrm{dT}_{\mathrm{A}}, then the rise in temperature of the gas in B is \left(\gamma=\frac{C_p}{C_v}\right)
Options:
A) \frac{\mathrm{dT}_{\mathrm{A}}}{2}
B) \frac{\mathrm{dT}_{\mathrm{A}}}{\gamma}
C) \quad \gamma d T_A
D) \quad 2 \mathrm{dT}_{\mathrm{A}}
642
Medium
A black sphere has radius R whose rate of radiation is E at temperature T . If radius is made R / 2 and temperature 3T, the rate of radiation will be
Options:
A) \frac{3 \mathrm{E}}{2}
B) \frac{27 \mathrm{E}}{8}
C) \frac{81 \mathrm{E}}{4}
D) \frac{9 \mathrm{E}}{4}
643
Medium
In the thermodynamic processes, which of the following statements is NOT true?
Options:
A) In an isothermal process, the temperature remains constant.
B) In an adiabatic process, the system is insulated from surroundings.
C) In an isochoric process, pressure remains constant.
D) In an adiabatic process, \mathrm{PV}^\gamma= constant.
644
Medium
In case of free expansion, which one of the following statements is WRONG?
Options:
A) It is an instantaneous change.
B) The system is not in thermodynamic equilibrium.
C) Free expansion can be plotted on a P-V diagram.
D) It is an uncontrolled change.
645
Medium
An ideal gas expands adiabatically, (\gamma=1.5). To reduce the r.m.s. velocity of the molecules 4 times, the gas has to be expanded
Options:
A) 256 times
B) 128 times
C) 64 times
D) 8 times
646
Medium
The temperature at which oxygen molecules will have same r.m.s. speed as helium molecules at 57^{\circ} \mathrm{C} is (molecular masses of oxygen and helium are 32 and 4 respectively.)
Options:
A) 1320 K
B) 2240 K
C) 2640 K
D) 3230 K
647
Medium
Two black spheres \mathrm{P} \& \mathrm{Q} have radii in the ratio 4: 3. The wavelength of maximum intensity of radiation are in the ratio 4: 5 respectively. The ratio of radiated power by P to Q is
Options:
A) \frac{625}{144}
B) \frac{125}{81}
C) \frac{25}{9}
D) \frac{5}{3}
648
Medium
The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by 48^{\circ} \mathrm{C} at constant pressure is (Molecular weight of nitrogen =28, R= gas constant, \mathrm{C}_{\mathrm{p}}=\frac{7}{2} \mathrm{R} for diatomic gas)
Options:
A) 76 R
B) 84 R
C) 90 R
D) 96 R
649
Medium
The difference in length between two rods A and B is 60 cm at all temperatures. If \alpha_{\mathrm{A}}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C} and \alpha_{\mathrm{B}}=27 \times 10^{-6} /{ }^{\circ} \mathrm{C}, then the length of \operatorname{rod} \mathrm{A} and \operatorname{rod} \mathrm{B} at 0^{\circ} \mathrm{C} is respectively
Options:
A) l_{\mathrm{A}}=120 \mathrm{~cm}, l_{\mathrm{B}}=60 \mathrm{~cm}.
B) l_{\mathrm{A}}=180 \mathrm{~cm}, l_{\mathrm{B}}=120 \mathrm{~cm}.
C) l_{\mathrm{A}}=240 \mathrm{~cm}, l_{\mathrm{B}}=180 \mathrm{~cm}.
D) l_{\mathrm{A}}=270 \mathrm{~cm}, l_{\mathrm{B}}=210 \mathrm{~cm}.
650
Medium
The initial average kinetic energy of the molecules was E , when a gas sample is at 27^{\circ} \mathrm{C}. When the gas is heated to 327^{\circ} \mathrm{C}, then the final average kinetic energy will be
Options:
A) \quad \sqrt{2} \mathrm{E}
B) 2 E
C) 300 E
D) 327 E
651
Medium
A sample of an ideal gas \left(\gamma=\frac{5}{3}\right) is heated at constant pressure. If 100 J of heat is supplied to the gas, the work done by the gas is
Options:
A) 150 J
B) 60 J
C) 40 J
D) 250 J
652
Medium
A balloon is filled at 27^{\circ} \mathrm{C} and 1 atmospheric pressure by volume 500 \mathrm{~m}^3 helium gas. At -3^{\circ} \mathrm{C} and 0.5 atmospheric pressure, the volume of helium gas will be
Options:
A) 500 \mathrm{~m}^3
B) 700 \mathrm{~m}^3
C) 900 \mathrm{~m}^3
D) 1000 \mathrm{~m}^3
653
Medium
The volume of a metal sphere increases by 0.33 \% when its temperature is raised by 50^{\circ} \mathrm{C}. The coefficient of linear expansion of the metal is
Options:
A) 2.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}
B) 6.6 \times 10^{-5} /{ }^{\circ} \mathrm{C}
C) 13.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}
D) 19.8 \times 10^{-5} /{ }^{\circ} \mathrm{C}
654
Medium
Heat supplied d Q= increased in internal energy dU is true for
Options:
A) isothermal process.
B) adiabatic process.
C) isobaric process.
D) isochoric process.
655
Medium
A black body emits radiation of maximum intensity at wavelength ' \lambda ' at temperature T K. Its corresponding wavelength at temperature 1.5 T K will be
Options:
A) \frac{2 \lambda}{3}
B) \frac{4 \lambda}{3}
C) \frac{16 \lambda}{81}
D) \frac{81 \lambda}{16}
656
Medium
A rectangular black body of temperature 127^{\circ} \mathrm{C} has surface area 4 \mathrm{~cm} \times 2 \mathrm{~cm} and rate of radiation is E . If its temperature is increased by 400^{\circ} \mathrm{C} and surface area is reduced to half of the initial value then the rate of radiation is
Options:
A) 4 E
B) E
C) 2 E
D) 16 E
657
Medium
The temperature of an ideal gas is increased from 100 K to 400 K . If ' x ' is the root mean square velocity of its molecules at 100 K , r.m.s. velocity becomes
Options:
A) \frac{x}{4}
B) 2 x
C) 3 x
D) 4 x
658
Medium
According to the kinetic theory of gases, when two molecules of a gas collide with each other then
Options:
A) both kinetic energy and momentum are conserved.
B) neither kinetic energy nor momentum is conserved.
C) momentum is conserved but kinetic energy is not conserved.
D) kinetic energy is conserved but momentum is not conserved.
659
Medium
During the isothermal expansion, a confined ideal gas does (-150) \mathrm{J} of work against its surroundings. This means that
Options:
A) 150 J of heat has been added to the gas
B) 150 J of heat has been removed from the gas
C) 300 J of heat has been added to the gas
D) no heat is transferred because the process is isothermal
660
Medium
A body cools from 80^{\circ} \mathrm{C} to 50^{\circ} \mathrm{C} in 5 min . In the next time of ' t ' in, the body continues to cool from 50^{\circ} \mathrm{C} to 30^{\circ} \mathrm{C}. The total time taken by the body to cool from 80^{\circ} \mathrm{C} to 30^{\circ} \mathrm{C} is [The temperature of the surroundings is 20^{\circ} \mathrm{C}.]
Options:
A) 10 min
B) 7.5 min
C) 15.0 min
D) 12.5 min
661
Medium
The volume of given mass of a gas is increased by 7 \% at constant temperature. The pressure should be increased by
Options:
A) 7 \%
B) 14 \%
C) 7.52 \%
D) 14.52 \%
662
Medium
A monoatomic ideal gas is compressed adiabatically to \left(\frac{1}{27}\right) of its initial volume. If initial temperature of the gas is ' T ' K and final temperature is ' xT ' K , the value of ' x ' is
Options:
A) 7
B) 9
C) 11
D) 13
663
Medium
Select the correct statement.
Options:
A) The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
B) The temperature of gas is -73^{\circ} \mathrm{C}. When the gas is heated to 527^{\circ} \mathrm{C}, the r.m.s. speed of the molecules is doubled.
C) The temperature of gas is -100^{\circ} \mathrm{C}. When the gas is heated to +627^{\circ} \mathrm{C}, the r.m.s. speed of the molecules is four times.
D) The product of pressure and volume of an ideal gas will be equal to half the translational kinetic energy.
664
Medium
A polyatomic gas at pressure P , having volume ' V ' expands isothermally to a volume ' 3 V ' and then adiabatically to a volume ' 24 V '. The final pressure of gas is (for moderate temperature changes)
Options:
A) 16 P
B) 24 P
C) P / 36
D) P / 48
665
Medium
A stationary object at 4^{\circ} \mathrm{C} and weighing 3.5 kg falls from a height of 2000 m on snow mountain at 0^{\circ} \mathrm{C}. If the temperature of the object just before hitting the snow is 0^{\circ} \mathrm{C} and the object comes to rest immediately then the quantity of ice that melts is (Acceleration due to gravity =10 \mathrm{~m} / \mathrm{s}^2, Latent heat of ice =3.5 \times 10^5 \mathrm{~J} / \mathrm{kg} )
Options:
A) 2 gram
B) 20 gram
C) 200 gram
D) 2 kg
666
Medium
Six molecules of a gas in container have speeds 2 \mathrm{~m} / \mathrm{s}, 5 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}, 6 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}, and 5 \mathrm{~m} / \mathrm{s}. The r.m.s. speed is
Options:
A) 4 \mathrm{~m} / \mathrm{s}
B) 1.7 \mathrm{~m} / \mathrm{s}
C) 4.24 \mathrm{~m} / \mathrm{s}
D) 5 \mathrm{~m} / \mathrm{s}
667
Medium
During thermodynamic process, the increase in internal energy of a system is equal to the \mathrm{w}_{0 r k} done on the system. Which process does the system undergo?
Options:
A) Isothermal
B) Adiabatic
C) Isochoric
D) Isobaric
668
Medium
How much should the pressure be increased in order to reduce the volume of a given mass of gas by 5 \% at the constant temperature?
Options:
A) 5 \%
B) 10 \%
C) 5.26 \%
D) 4 \%
669
Medium
A polyatomic gas is compressed to \left(\frac{1}{8}\right)^{\text {th }} of its volume adiabatically. If its initial pressure is \mathrm{P}_0, its new pressure will be [Given, \frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{4}{3} ]
Options:
A) \quad 6 \mathrm{P}_0
B) \quad 2 \mathrm{P}_0
C) \quad 8 \mathrm{P}_0
D) 16 \mathrm{P}_0
670
Medium
The pressure ' P ', volume ' V ' and temperature ' T ' of a gas in a jar ' A ' and the gas in other jar ' B ' is at pressure ' 2 P ', volume ' V ' and temperature ' \frac{T}{4} '. Then the ratio of the number of molecules in jar A and jar B will be
Options:
A) 1: 1
B) 1: 2
C) 2: 1
D) 4: 1
671
Medium
Two moles of an ideal monoatomic gas undergo a cyclic process as shown in figure. The temperatures in different states are given as 6 \mathrm{~T}_1=3 \mathrm{~T}_2=2 \mathrm{~T}_4=\mathrm{T}_3=2400 \mathrm{~K}. The work done by the gas during the complete cycle is ( \mathrm{R}= Universal gas constant)
Options:
A) -1600 R
B) 1600 R
C) -1200 R
D) 800 R
672
Medium
Two spherical black bodies have radii ' R_1 ' and ' R_2 '. Their surface temperatures are T_1 K and T_2 K respectively. If they radiate the same power, the ratio \frac{R_1}{R_2} is
Options:
A) \left(\frac{T_1}{T_2}\right)^4
B) \left(\frac{T_1}{T_2}\right)^2
C) \left(\frac{T_2}{T_1}\right)^4
D) \left(\frac{T_2}{T_1}\right)^2
673
Medium
A thermometer bulb has volume 10^{-6} \mathrm{~m}^3 and cross-section of the stem is 0.002 \mathrm{~cm}^2. The bulb is filled with mercury at 0^{\circ} \mathrm{C}. If the thermometer reads temperature as 100^{\circ} \mathrm{C}, then the length of mercury column is (coefficient of cubical expansion of mercury =18 \times 10^{-5} /{ }^{\circ} \mathrm{C} )
Options:
A) 90 cm
B) 9 mm
C) 9 cm
D) 0.9 mm
674
Medium
The two ends of a rod of length ' x ' and uniform cross-sectional area ' A ' are kept at temperatures ' \mathrm{T}_1 ' and ' \mathrm{T}_2 ' respectively ( \mathrm{T}_1>\mathrm{T}_2 ). If the rate of heat transfer is ' \mathrm{Q} / \mathrm{t} ', through the rod in steady state, then the coefficient of thermal conductivity ' K ' is
Options:
A) \frac{A Q}{\operatorname{tx}\left(T_1-T_2\right)}
B) \frac{x Q}{t A\left(T_1-T_2\right)}
C) \frac{x A Q}{t\left(T_1-T_2\right)}
D) \frac{Q}{\operatorname{txA}\left(T_1-T_2\right)}
675
Medium
When the pressure of the gas contained in a closed vessel is increased by 2.3 \%, the temperature of the gas increases by 4 K . The initial temperature of the gas is
Options:
A) 80 K
B) 150 K
C) 160 K
D) 320 K
676
Medium
Black bodies A and B radiate maximum energy with wavelength difference 4 \mu \mathrm{~m}. The absolute temperature of body A is 3 times that of B. The wavelength at which body B radiates maximum energy is
Options:
A) 4 \mu \mathrm{~m}
B) 6 \mu \mathrm{~m}
C) 2 \mu \mathrm{~m}
D) 8 \mu \mathrm{~m}
677
Medium
A monoatomic ideal gas, initially at temperature \mathrm{T}_1 is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature \mathrm{T}_2. If \mathrm{L}_1 and \mathrm{L}_2 are the lengths of the gas columns before and after expansion respectively, then \left(T_2 / T_1\right) is given by
Options:
A) \frac{\mathrm{L}_1}{\mathrm{~L}_2}
B) \frac{\mathrm{L}_2}{\mathrm{~L}_1}
C) \left(\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right)^{2 / 3}
D) \left(\frac{L_2}{L_1}\right)^{2 / 3}
678
Medium
Two bodies A and B at temperatures ' \mathrm{T}_1 ' K and ' \mathrm{T}_2 ' K respectively have the same dimensions. Their emissivities are in the ratio 16: 1. At \mathrm{T}_1=\mathrm{xT}_2, they radiate the same amount of heat per unit area per unit time. The value of x is
Options:
A) 8
B) 4
C) 2
D) 0.5
679
Medium
In an isobaric process of an ideal gas, the ratio of heat supplied and work done by the system \left(\frac{\mathrm{Q}}{\mathrm{W}}\right) is \left[\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\gamma\right].
Options:
A) 1
B) \gamma
C) \frac{\gamma}{\gamma-1}
D) \frac{\gamma-1}{\gamma}
680
Medium
The temperature of a body on Kelvin scale is ' x ' K. When it is measured by a Fahrenheit thermometer, it is found to be ' x ' { }^{\circ} \mathrm{F}. The value of ' x ' is (nearly)
Options:
A) 40
B) 313
C) 574
D) 301
681
Medium
For a gas at a particular temperature on an average, the quantity which remains same for all molecules is
Options:
A) velocity
B) momentum
C) kinetic energy
D) angular momentum
682
Medium
If 120 J of thermal energy is incident on area 3 \mathrm{~m}^2, the amount of heat transmitted is 12 J , coefficient of absorption is 0.6 , then the amount of heat reflected is
Options:
A) 24 J
B) 30 J
C) 36 J
D) 40 J
683
Medium
When an ideal gas \left(\gamma=\frac{5}{3}\right) is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work?
Options:
A) 60 \%
B) 20 \%
C) 30 \%
D) 40 \%
684
Medium
The mean kinetic energy of the molecules of an ideal gas at 399^{\circ} \mathrm{C} is ' E '. The temperature at which the mean kinetic energy of its molecules will be ' \mathrm{E} / 2 ', is
Options:
A) 336^{\circ} \mathrm{C}
B) 276^{\circ} \mathrm{C}
C) 123^{\circ} \mathrm{C}
D) 63^{\circ} \mathrm{C}
685
Medium
A gas undergoes a change in which its pressure ' P ' and volume ' V ' are related as \mathrm{PV}^{\mathrm{n}}= constant, where n is a constant. If the specific heat of the gas in this change is zero, then the value of n is ( \gamma= adiabatic ratio)
Options:
A) 1-\gamma
B) \gamma+1
C) \quad \gamma-1
D) \gamma
686
Medium
Hot water cools from 80^{\circ} \mathrm{C} to 60^{\circ} \mathrm{C} in 1 minutes. In cooling from 60^{\circ} \mathrm{C} to 50^{\circ} \mathrm{C} it will take (room temperature =30^{\circ} \mathrm{C} )
Options:
A) 48 s
B) 42 s
C) 50 s
D) 45 s
687
Medium
A Carnot engine has efficiency \frac{1}{6}. It becomes \frac{1}{3}, when the temperature of \operatorname{sink} is lowered by 57 K . The temperature of the source is
Options:
A) 171 K
B) 399 K
C) 342 K
D) 285 K
688
Medium
The r.m.s. speed of gas molecules at 800 K will be
Options:
A) same as at 200 K
B) twice the value at 200 K
C) four times the value at 200 K
D) half the value at 200 K
689
Medium
If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling ' \mathrm{R}_0 ', the same body at 900 K , surrounded by same atmosphere, will have rate of cooling nearly
Options:
A) 4 \mathrm{R}_0
B) 16 \mathrm{R}_0
C) 36 \mathrm{R}_0
D) \frac{81 R_0}{16}
690
Medium
The temperature of an ideal gas is increased from 100 K to 400 K . If ' x ' is the R.M.S. velocity of its molecules at 100 K , it becomes
Options:
A) \frac{x}{4}
B) 2 x
C) 3 x
D) 4 x
691
Medium
Heat is given to an ideal gas in an isothermal process. Then A. internal energy of the gas will decrease. B. internal energy of the gas will increase. C. internal energy of the gas will not change. D. the gas will do negative work.
Options:
A) B
B) C
C) D
D) A
692
Medium
A rectangular block of surface area A emits energy E per second at 27^{\circ} \mathrm{C}. If length and breadth is reduced to half of initial value and temperature is raised to 327^{\circ} \mathrm{C} then energy emitted per second becomes
Options:
A) 2 E
B) 4 E
C) E
D) 8 E
693
Medium
When a diatomic gas (rigid) undergoes adiabatic change, its pressure (\mathrm{P}) and temperature (\mathrm{T}) are related as P \propto T^c. The value of c is
Options:
A) 2.5
B) 3.5
C) 1.5
D) 5.2
694
Medium
For an ideal gas, the density of the gas is \rho_0 when temperature and pressure of the gas are \mathrm{T}_0 and P_0 respectively. when the temperature of the gas is 2 \mathrm{~T}_0, its pressure becomes 3 \mathrm{P}_0. The new density will be
Options:
A) \frac{2}{3} \rho_0
B) \frac{3}{4} \rho_0
C) \frac{4}{3} \rho_0
D) \frac{3}{2} \rho_0
695
Medium
A centigrade and Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit temperature observed is 140^{\circ} \mathrm{F}. At that time the temperature registered by the centigrade thermometer is
Options:
A) 80^{\circ} \mathrm{C}
B) 60^{\circ} \mathrm{C}
C) 40^{\circ} \mathrm{C}
D) 20^{\circ} \mathrm{C}
696
Medium
An engine operating between temperatures T_1 and T_2 has efficiency \frac{1}{5}. When T_2 is lowered by 45 K , its efficiency becomes \frac{1}{2}. Temperatures T_1 and T_2 are respectively
Options:
A) 100 \mathrm{~K}, 70 \mathrm{~K}
B) 160 \mathrm{~K}, 120 \mathrm{~K}
C) 140 \mathrm{~K}, 110 \mathrm{~K}
D) 150 \mathrm{~K}, 120 \mathrm{~K}
697
Medium
Two cylinders A and B fitted with pistons contain equal amount of an ideal rigid diatomic gas at 303 K . The piston of cylinder A is free to move and that of cylinder B is held fixed. The same amount heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 49 K , then the rise in temperature of the gas in A is
Options:
A) 30 K
B) 35 K
C) 70 K
D) 75 K
698
Medium
If a gas is compressed isothermally then the r.m.s. velocity of its molecules
Options:
A) increases.
B) decreases.
C) remains the same.
D) first increases and then decreases.
699
Medium
The following graph represents the radiant power versus wavelength of the black body. The area under the curve represents
Options:
A) the maximum wavelength emitted by the object.
B) the minimum wavelength emitted by the object.
C) the total energy emitted per unit time by the black body at some particular wavelength
D) the total energy emitted per unit time per unit area by the black body at all wavelengths.
700
Medium
In a cyclic process, work done by the system is
Options:
A) more than the heat given to the system.
B) equal to the heat given to the system.
C) zero.
D) independent of the heat given to the system.
701
Medium
A metal sphere cools at a rate of 1.5^{\circ} \mathrm{C} / \mathrm{min} when its temperature is 80^{\circ} \mathrm{C}. When the temperature of the sphere is 40^{\circ} \mathrm{C}, its rate of cooling is 0.3^{\circ} \mathrm{C} / \mathrm{min}. The temperature of the surrounding \left(\theta_0\right) is
Options:
A) 30^{\circ} \mathrm{C}
B) 35^{\circ} \mathrm{C}
C) 25^{\circ} \mathrm{C}
D) 27^{\circ} \mathrm{C}
702
Medium
The change in the internal energy of the mass of gas, when the volume changes from V to 2 V at constant pressure P is \left(\gamma=\frac{\mathrm{Cp}}{\mathrm{Cv}}\right)
Options:
A) \frac{\mathrm{V}}{\mathrm{P}(\gamma-1)}
B) \frac{\mathrm{P}}{\mathrm{V}(\gamma-1)}
C) \frac{\mathrm{PV}}{\gamma+1}
D) \frac{\mathrm{PV}}{\gamma-1}
703
Medium
For a perfectly black body, coefficient of emission is
Options:
A) zero.
B) unity.
C) less than one (non-zero).
D) infinity.
704
Medium
A body cools from 60^{\circ} \mathrm{C} to 40^{\circ} \mathrm{C} in 6 minutes. After next 6 minutes its temperature will be (Temperature of the surroundings is 10^{\circ} \mathrm{C} )
Options:
A) 24^{\circ} \mathrm{C}
B) 28^{\circ} \mathrm{C}
C) 18^{\circ} \mathrm{C}
D) 32^{\circ} \mathrm{C}
705
Medium
A tyre of a vehicle is filled with air having pressure 270 kPa at 27^{\circ} \mathrm{C}. The air pressure in the tyre when the temperature increases to 37^{\circ} \mathrm{C} is
Options:
A) 282 kPa
B) 270 kPa
C) 265 kPa
D) 279 kPa
706
Medium
The average force applied on the walls of a closed container depends as \mathrm{T}^{\mathrm{x}} where T is the temperature of an ideal gas. The value of x is
Options:
A) 1
B) 2
C) 3
D) 4
707
Medium
A diatomic gas \left(\gamma=\frac{7}{5}\right) is compressed adiabatically to volume \frac{\mathrm{V}_0}{32}, where \mathrm{V}_0 is its initial volume. The initial temperature of the gas is \mathrm{T}_{\mathrm{i}} in kelvin and the final temperature is \mathrm{xT}_{\mathrm{i}} in kelvin. The value of x is
Options:
A) 5
B) 4
C) 3
D) 2
708
Medium
The work done by a gas as it is taken in a cyclic process (shown in graph) is
Options:
A) 2 pv
B) -2 pv
C) 3 pv
D) -3 pv
709
Medium
Two gases A and B are at absolute temperatures 350 K and 420 K respectively. The ratio of average kinetic energy of the molecules of gas B to that of gas A is
Options:
A) 6: 5
B) \sqrt{6}: \sqrt{5}
C) 36: 25
D) 5: 6
710
Medium
A composite slab consists of two materials having coefficients of thermal conductivity K and 2 K, thickness x and 4 x respectively. The temperatures of two outer surfaces of a composite slab are \mathrm{T}_2 and \mathrm{T}_1 respectively \left(\mathrm{T}_2>\mathrm{T}_1\right). The rate of heat transfer through the slab in a steady state is \left[\frac{A\left(T_2-T_1\right) K}{x}\right] f, where f is equal to
Options:
A) 1
B) \frac{2}{3}
C) \frac{1}{2}
D) \frac{1}{3}
711
Medium
The co-efficient of absorption and the coefficient of reflection of a thin uniform plate are 0.77 and 0.17 respectively. If 250 kcal of heat is incident on the surface of the plate, the quantity of heat transmitted is
Options:
A) 7 kcal
B) 12 kcal
C) 15 kcal
D) 22 kcal
712
Medium
An ideal gas at pressure ' P ' and temperature ' T ' is enclosed in a vessel of volume ' V '. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to ' P '. Assuming that the temperature ture of the gas remains constant during the leakage , the number of moles of the gas that have leaked is
Options:
A) \frac{2 \mathrm{~V}}{\mathrm{RT}}\left(\mathrm{P}-\mathrm{P}^{\prime}\right)
B) \frac{\mathrm{V}}{\mathrm{RT}}\left(\mathrm{P}-\mathrm{P}^{\prime}\right)
C) \frac{\mathrm{V}}{\mathrm{RT}}\left(\mathrm{P}+\mathrm{P}^{\prime}\right)
D) \frac{\mathrm{V}}{2 \mathrm{RT}}\left(\mathrm{P}+\mathrm{P}^{\prime}\right)
713
Medium
If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen molecule at 47^{\circ} \mathrm{C}, the temperature of hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are 2 and 32 respectively)
Options:
A) 23^{\circ} \mathrm{C}
B) 47^{\circ} \mathrm{C}
C) 80^{\circ} \mathrm{C}
D) 114^{\circ} \mathrm{C}
714
Medium
A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in increasing the internal energy and that used for doing external work is A and B respectively. Then the ratio, \mathrm{A}: \mathrm{B} is
Options:
A) 5: 3
B) 2: 3
C) 3: 2
D) 2: 5
715
Medium
Black sphere of radius R radiates power P at certain temperature T. If the temperature is doubled, the radius gets doubled. Now the power radiated would be
Options:
A) 4 P
B) 8 P
C) 16 P
D) 64 P
716
Medium
Three samples X, Y, and Z of same gas have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for X , adiabatic for Y and isobaric for Z . If the final pressures are equal for the three samples, the ratio of the initial pressures is ( \gamma=3 / 2)
Options:
A) 1: \sqrt{2}: 2 \sqrt{3}
B) 2: 2 \sqrt{2}: 1
C) 3: 3 \sqrt{3}: 1
D) 5: 5 \sqrt{5}: 1
717
Medium
Two rods of different materials have lengths ' l ' and ' l_2 ' whose coefficient of linear expansions are ' \alpha_1 ' and ' \alpha_2 ' respectively. If the difference between the two lengths is independent of temperature then
Options:
A) \alpha_1^2 l_1=\alpha_2^2 l_2
B) \frac{l_1}{l_2}=\frac{\alpha_2}{\alpha_1}
C) \frac{l_1}{l_2}=\frac{\alpha_1}{\alpha_2}
D) l_1^2 \alpha_2=l_2^2 \alpha_1
718
Medium
The molar specific heat of an ideal gas at constant pressure and constant volume is ' \mathrm{C}_{\mathrm{p}} ' and ' \mathrm{C}_{\mathrm{v}} ' respectively. If ' R ' is a universal gas constant and the ratio of ' \mathrm{C}_{\mathrm{p}} ' to ' \mathrm{C}_{\mathrm{v}} ' is \gamma, then ' \mathrm{C}_{\mathrm{p}} ' is equal to
Options:
A) \left(\frac{\gamma-1}{\gamma+1}\right) \mathrm{R}
B) \frac{(\gamma-1) R}{\gamma}
C) \frac{\mathrm{R} \gamma}{(\gamma-1)}
D) \frac{\mathrm{R} \gamma}{(\gamma+1)}
719
Medium
For ideal non-rigid diatomic gas, the value of \frac{\mathrm{R}}{\mathrm{C}_{\mathrm{V}}} is nearly \left(\gamma=\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{9}{7}\right)
Options:
A) 0.4
B) 0.66
C) 0.28
D) 1.28
720
Medium
When the heat is given to a gas in an Isothermal process, then there will be
Options:
A) external work done.
B) rise in temperature.
C) increase in internal energy.
D) external work done and also rise in temperature.
721
Medium
During an experiment, an ideal gas is found to obey an additional law \mathrm{VP}^2= constant. The gas is initially at temperature ' T ' and volume ' V '. What will be the temperature of the gas when it expands to a volume 2 V ?
Options:
A) \sqrt{3} \mathrm{~T}
B) \sqrt{\frac{1}{2 T}}
C) \sqrt{2} \mathrm{~T}
D) \sqrt{3 \mathrm{~T}}
722
Medium
The first operation involved in a Carnot cycle is
Options:
A) isothermal expansion.
B) adiabatic expansion.
C) isothermal compression.
D) adiabatic compression.
723
Medium
Temperature remaining constant, the pressure of gas is decreased by 20 \%. The percentage change in volume
Options:
A) increases by 29 \%
B) decreases by 20 \%
C) increases by 25 \%
D) decreases by 25 \%
724
Medium
At certain temperature, \operatorname{rod} \mathrm{A} and \operatorname{rod} \mathrm{B} of different materials have lengths \mathrm{L}_{\mathrm{A}} and \mathrm{L}_B respectively. Their co-efficients of linear expansion are \alpha_A and \alpha_B respectively. It is observed that the difference between their lengths remain constant at all temperatures. The ratio L_A / L_B is given by
Options:
A) \frac{\alpha_A}{\alpha_B}
B) \frac{\alpha_B}{\alpha_A}
C) \frac{\alpha_A+\alpha_B}{\alpha_A}
D) \frac{\alpha_A+\alpha_B}{\alpha_B}
725
Medium
A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in changing the internal energy is
Options:
A) 30 \%
B) 40 \%
C) 50 \%
D) 60 \%
726
Medium
The ratio of the specific heats \frac{C_p}{C_v}=\gamma, in terms of degrees of freedom ( n ) is
Options:
A) \left(1+\frac{1}{n}\right)
B) \left(1+\frac{2}{n}\right)
C) \left(1+\frac{\mathrm{n}}{3}\right)
D) \left(1+\frac{\mathrm{n}}{2}\right)
727
Medium
Assuming the expression for the pressure exerted by the gas, it can be shown that pressure is
Options:
A) \left(\frac{3}{4}\right)^{\text {th }} of kinetic energy per unit volume of a gas.
B) \left(\frac{2}{3}\right)^{\text {rd }} of kinetic energy per unit volume of a gas.
C) \left(\frac{1}{3}\right)^{\mathrm{rd}} of kinetic energy per unit volume of a gas.
D) \left(\frac{3}{2}\right)^{\text {rd }} of kinetic energy per unit volume of a gas.
728
Medium
If heat energy \Delta \mathrm{Q} is supplied to an ideal diatomic gas, the increase in internal energy is \Delta U and the amount of work done by the gas is \Delta \mathrm{W}. The ratio \Delta \mathrm{W}: \Delta \mathrm{U}: \Delta \mathrm{Q} is
Options:
A) 2: 3: 5
B) 2: 5: 7
C) 7: 5: 9
D) 1: 2: 5
729
Medium
The power radiated by a black body is P and it radiates maximum energy around the wavelength \lambda_0. Now the temperature of the black body is changed so that it radiates maximum energy around wavelength \left(\frac{\lambda_0}{2}\right). The power radiated by it will now increase by a factor of
Options:
A) 2
B) 8
C) 16
D) 32
730
Medium
A bucket full of hot water is kept in a room. If it cools from 75^{\circ} \mathrm{C} to 70^{\circ} \mathrm{C} in t_1 minutes, from 70^{\circ} \mathrm{C} to 65^{\circ} \mathrm{C} in \mathrm{t}_2 minutes and 65^{\circ} \mathrm{C} to 60^{\circ} \mathrm{C} in t_3 minutes, then
Options:
A) \mathrm{t}_1<\mathrm{t}_2<\mathrm{t}_3
B) \mathrm{t_1>t_2>t_3}
C) \mathrm{t}_1=\mathrm{t}_2=\mathrm{t}_3
D) \mathrm{t}_1<\mathrm{t}_2=\mathrm{t}_3
731
Medium
An ideal diatomic gas is heated at constant pressure. What is the fraction of total energy applied, which increases the internal energy for the gas?
Options:
A) \frac{2}{5}
B) \frac{5}{7}
C) \frac{3}{7}
D) \frac{3}{5}
732
Medium
In ideal gas of 27^{\circ} \mathrm{C} is compressed adiabatically to (8 / 27) of its original volume. If \gamma=\frac{5}{3}, the rise in temperature of a gas is
Options:
A) 300 K
B) 375 K
C) 400 K
D) 450 K
733
Medium
A cylindrical rod is having temperatures \theta_1 and \theta_2 at its ends. The rate of heat flow is \mathrm{Q} J / \mathrm{S}. All the linear dimensions of the rod are doubled by keeping the temperature constant. The new rate of flow of heat is
Options:
A) \mathrm{4Q}
B) \mathrm{2 Q}
C) \frac{\mathrm{Q}}{2}
D) \mathrm{\frac{Q}{4}}
734
Medium
A monoatomic ideal gas, initially at temperature T_1 is enclosed in a cylinder fitted with frictionless piston. The gas is allowed to expand adiabatically to a temperature T_2 by releasing the piston suddenly. L_1 and L_2 are the lengths of the gas columns before and after the expansion respectively. The ratio T_2 / T_1 is
Options:
A) \left[\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right]^{2 / 3}
B) \left[\frac{\mathrm{L}_2}{\mathrm{~L}_1}\right]^{2 / 3}
C) \left[\frac{L_2}{L_1}\right]^{1 / 2}
D) \left[\frac{L_1}{L_2}\right]^{1 / 2}
735
Medium
In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as \mathrm{T}^{\mathrm{x}}. The value of x is
Options:
A) 0.25
B) 2
C) 0.5
D) 1
736
Medium
Heat engine operating between temperature T_1 and T_2 has efficiency \frac{1}{6}. When T_2 is lowered by 62 K , its efficiency increases to \frac{1}{3}. Then T_1 and T_2 respectively are
Options:
A) 372 \mathrm{~K}, 310 \mathrm{~K}
B) 372 \mathrm{~K}, 330 \mathrm{~K}
C) 330 \mathrm{~K}, 268 \mathrm{~K}
D) 310 \mathrm{~K}, 248 \mathrm{~K}
737
Medium
The absolute temperature of a gas is determined by
Options:
A) the average momentum of the molecule.
B) the velocity of sound in the gas.
C) the number of molecules in the gas.
D) the mean square velocity of the molecules.
738
Medium
When a system is taken from state ' a ' to state ' c ' along a path abc, it is found that \mathrm{Q}=80 \mathrm{cal} and \mathrm{W}=35 \mathrm{cal}. Along path adc \mathrm{Q}=65 \mathrm{cal} the work done W along path adc is
Options:
A) 20 cal.
B) 35 cal.
C) 45 cal.
D) 65 cal.
739
Medium
The ratio of work done by an ideal rigid diatomic gas to the heat supplied by the gas in an isobaric process is
Options:
A) \frac{3}{7}
B) \frac{2}{7}
C) \frac{4}{7}
D) \frac{5}{7}
740
Medium
The internal energy of an ideal diatomic gas corresponding to volume ' V ' and pressure ' P ' is 2.5 PV. The gas expands from 1 litre to 2 litre at a constant pressure of 10^5 \mathrm{~N} / \mathrm{m}^2. The heat supplied to a gas is
Options:
A) 350 J
B) 300 J
C) 250 J
D) 200 J
741
Medium
Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. \left[C_{\mathrm{v}}\right. for hydrogen =\frac{5}{2} R, C_v for helium =\frac{3}{2} R, \quad C_{\mathrm{v}} for water vapour \left.=3 \mathrm{R}\right] What is the molar specific heat at constant pressure of the mixture?
Options:
A) \frac{11}{3} \mathrm{R}
B) \frac{23}{7} R
C) \frac{16}{7} R
D) \frac{23}{3} R
742
Medium
A sheet of steel is 40 cm long and 5 cm broad at 0^{\circ} \mathrm{C}. The surface area of the sheet increases by 1.4 \mathrm{~cm}^2 at 100^{\circ} \mathrm{C}. Coefficient of linear expansion of steel is
Options:
A) 1.9 \times 10^{-5} /{ }^{\circ} \mathrm{C}
B) 2.4 \times 10^{-5} /^{\circ} \mathrm{C}
C) 3.5 \times 10^{-5} /^{\circ} \mathrm{C}
D) 7 \times 10^{-5} / \mathrm{C}
743
Medium
A quantity of heat ' Q ' is supplied to monoatomic ideal gas which expands at constant pressure. The fraction of heat converted into work is \left[\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{5}{3}\right]
Options:
A) 3: 5
B) 5: 3
C) 2: 5
D) 3: 2
744
Medium
What is the pressure of hydrogen in a cylinder of volume 10 litre if its total energy of translation is 7.5 \times 10^3 \mathrm{~J} ?
Options:
A) 5 \times 10^5 \mathrm{Nm}^{-2}
B) 10^6 \mathrm{Nm}^{-2}
C) 0.5 \times 10^5 \mathrm{Nm}^{-2}
D) 5 \times 10^6 \mathrm{Nm}^{-2}
745
Medium
' N ' molecules of gas A, each having mass ' m ' and ' 2 N ' molecules of gas B , each of mass ' 2 m ' are contained in the same vessel which is at constant temperature ' T '. The mean square velocity of B is V^2 and mean square of x -component of A is \omega^2. The value of \frac{\omega^2}{\mathrm{~V}^2} is
Options:
A) 3: 2
B) 2: 3
C) 1: 2
D) 2: 1
746
Medium
The \mathrm{p}-\mathrm{V} diagram for a fixed mass of an ideal gas undergoing cyclic process is as shown in figure. AB represents isothermal process and CA represents adiabatic process. Which one of the following graphs represents the p-T diagram of this cyclic process?
Options:
A) (G)
B) (F)
C) (H)
D) (E)
747
Medium
Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic as at temperature ' T ' K . The piston of cylinder A is free to move while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise temperature of the gas in A is ' \mathrm{dT}_{\mathrm{A}} ', then the rise in temperature of the gas in cylinder B is \left(\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\right)
Options:
A) 2 \mathrm{dt}_{\mathrm{A}}
B) \frac{\mathrm{dT}_{\mathrm{A}}}{2}
C) \mathrm{\gamma d T_A}
D) \frac{\mathrm{dT}_A}{\gamma}
748
Medium
A metal rod having coefficient of linear expansion 2 \times 10^{-5} /^{\circ} \mathrm{C} is 0.75 m long at 45^{\circ} \mathrm{C}. When the temperature rises to 65^{\circ} \mathrm{C}, the increase in length of the rod will be
Options:
A) 3.0 mm
B) 0.75 mm
C) 0.30 mm
D) 0.15 mm
749
Medium
The ratio of the velocity of sound in hydrogen gas \left(\gamma=\frac{7}{5}\right) to that in helium gas \left(\gamma=\frac{5}{3}\right) at the same temperature is
Options:
A) 1: 1
B) 7: 3
C) 21: 25
D) \sqrt{42}: 5
750
Medium
Two spheres S_1 and S_2 have same radii but temperatures T_1 and T_2 respectively. Their emissive power is same and emissivity in the ratio 1:4. Then the ratio T_1: T_2 is
Options:
A) 2: 1
B) \sqrt{2}: 1
C) 1: \sqrt{2}
D) 1: 2
751
Medium
Two gases A and B having same initial state ( \mathrm{P}, \mathrm{V}, \mathrm{n}, \mathrm{T} ). Now gas A is compressed to \frac{\mathrm{V}}{8} by isothermal process and other gas B is compressed to \frac{\mathrm{V}}{8} by adiabatic process. The ratio of final pressure of gas A and B is (Both gases are monoatomic, \gamma=5 / 3)
Options:
A) \frac{1}{8}
B) \frac{1}{4}
C) \frac{1}{64}
D) \frac{1}{12}
752
Medium
Two vessels separately contain two ideal gases A and B at the same temperature, pressure of A being twice that of B . Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weights of A and B is
Options:
A) 1: 2
B) 2: 3
C) 3: 4
D) 2: 1
753
Medium
An insulated container contains a diatomic gas of molar mass ' m '. The container is moving with velocity ' V ', if it is stopped suddenly, the change in temperature is ( R= gas constant)
Options:
A) \frac{\mathrm{mV}^2}{3 \mathrm{R}}
B) \frac{\mathrm{mV}^2}{5 \mathrm{R}}
C) \frac{\mathrm{mV}}{7 \mathrm{R}}
D) \frac{5 m V}{3 R}
754
Medium
Rails of material of steel are laid with gaps to allow for thermal expansion. Each track is 10 m long, when laid at temperature 17^{\circ} \mathrm{C}. The maximum temperature that can be reached is 45^{\circ} \mathrm{C}. The gap to be kept between the two segments of railway track is $\left(\alpha_{\text {steel }}=1.3 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)
Options:
A) 1.68 mm
B) 2.06 mm
C) 3.64 mm
D) 4.32 mm
755
Medium
In an adiabatic process for an ideal gas, the relation between the universal gas constant ' R ' and specific heat at constant volume ' \mathrm{C}_{\mathrm{v}} ' is R=0.4 C_v. The pressure ' P ' of the gas is proportional to the temperature ' T ', of the gas as T^k. The value of constant ' K ' is
Options:
A) \frac{7}{2}
B) \frac{7}{3}
C) 5
D) 5
756
Medium
The black discs \mathrm{x}, \mathrm{y} and z have radii 1 \mathrm{~m}, 2 \mathrm{~m} and 3 m respectively. The wavelengths corresponding to maximum intensity are 200 \mathrm{~nm}, 300 \mathrm{~nm} and 400 nm respectively. The relation between emissive power E_x, E_y and E_z is
Options:
A) \mathrm{E}_{\mathrm{x}}>\mathrm{E}_{\mathrm{y}}>\mathrm{E}_{\mathrm{z}}
B) \mathrm{E}_{\mathrm{x}}<\mathrm{E}_{\mathrm{y}}<\mathrm{E}_{\mathrm{z}}
C) \mathrm{E}_{\mathrm{x}}=\mathrm{E}_{\mathrm{y}}=\mathrm{E}_{\mathrm{z}}
D) \mathrm{E}_{\mathrm{y}}>\mathrm{E}_{\mathrm{x}}<\mathrm{E}_{\mathrm{z}}
757
Medium
For a gas, \frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}=0.4 where R is the universal gas constant and ' \mathrm{C}_{\mathrm{V}} ' is molar specific heat at constant volume. The gas is made up of molecules which are
Options:
A) rigid diatomic.
B) monoatomic.
C) non-rigid diatomic.
D) polyatomic.
758
Medium
In a thermodynamic system ' \Delta \mathrm{U} ' represents the increase in internal energy and ' W ' the work done by the system. Which of the following statement is true?
Options:
A) \Delta \mathrm{U}=-\mathrm{W} in an adiabatic process.
B) \Delta \mathrm{U}=\mathrm{W} in an isothermal process.
C) \Delta \mathrm{U}=-\mathrm{W} in an isothermal process.
D) \Delta \mathrm{U}=\mathrm{W} in an adiabatic process.
759
Medium
Rate of radiation by a black body is ' R ' at temperature 'T'. Another body has same area but emissivity is 0.2 and temperature 3T. Its rate of radiation is
Options:
A) (162) R
B) (81) \mathrm{R}
C) (16.2) R
D) (8.1) \mathrm{R}
760
Medium
A Carnot's cycle operating between T_H=600 \mathrm{~K} and T_c=300 \mathrm{~K} produces 1.5 kJ of mechanical work per cycle. The heat transferred to the engine by the reservoir is
Options:
A) 2.5 kJ
B) 3.0 kJ
C) 3.5 kJ
D) 4.0 kJ
761
Medium
An ordinary body cools from ' 4 \theta^{\prime} ' to ' 3 \theta^{\prime} ' in ' t ' minutes. The temperature of that body after next 't' minutes is (Assume Newton's law of cooling and room temperature is \theta)
Options:
A) \frac{9 \theta}{4}
B) \frac{2 \theta}{5}
C) \frac{5 \theta}{3}
D) \frac{7 \theta}{3}
762
Medium
A black sphere has radius R whose rate of radiation is E at temperature T . If radius is made half and temperature 4 T , the rate of radiation will be
Options:
A) 64 E
B) 32 E
C) 16 E
D) 8 E
763
Medium
Ordinary bodies P and Q radiate maximum energy with wavelength difference 3 \mu \mathrm{~m}. The absolute temperature of body P is four times that of Q. The wavelength at which body Q radiates maximum energy is
Options:
A) 2 \mum
B) 4 \mum
C) 6 \mum
D) 8 \mum
764
Medium
The average force applied on the wall of a closed container depends as \mathrm{T}^{\mathrm{x}} where T is the temperature of an ideal gas. The value of x is
Options:
A) 0.5
B) 1
C) 2
D) 1.5
765
Medium
Which of the following graphs between pressure and volume correctly show isochoric process?
Options:
A) D
B) A
C) C
D) B
766
Medium
Initial pressure and volume of a gas are ' P ' and ' V ' respectively. First its volume is expanded to ' 4 V ' by isothermal process and then again its volume is reduced to ' V ' by adiabatic process then its final pressure if \left(\gamma=\frac{3}{2}\right)
Options:
A) P
B) 2P
C) 3P
D) 4P
767
Medium
The P-V diagrams for particular gas of different thermodynamic processes are given by
Options:
A) Figure (a) and (b) show isobaric curve and isothermal curve respectively.
B) Figure (a) and (c) show isothermal curve and isochoric curve respectively.
C) Figure (b) and (c) show isobaric curve and isochoric curve respectively.
D) Figure (a) and (c) show isothermal curve and isobaric curve respectively.
768
Medium
An ideal gas (\gamma=1.5) is expanded adiabatically. To reduce root mean square velocity of molecules two times, the gas should be expanded
Options:
A) 20 times
B) 16 times
C) 12 times
D) 8 times
769
Medium
A black body radiates power ' P ' and maximum energy is radiated by it at a wavelength \lambda_0. The temperature of the black body is now so changed that it radiates maximum energy at the wavelength \frac{\lambda_0}{4}. The power radiated by it at new temperature is
Options:
A) 64 P
B) 256 P
C) 4 P
D) 16 P
770
Medium
The temperature of a liquid falls from 365 K to 359 K in 3 minutes. The time during which temperature of this liquid falls from 342 K to 338 K is [Let the room temperature be 296 K ]
Options:
A) 6 min
B) 4 min
C) 3 min
D) 2 min
771
Medium
In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat exchanged (\mathrm{Q}) is \left(\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\right)
Options:
A) \gamma
B) \gamma-1
C) \frac{\gamma}{\gamma-1}
D) \frac{\gamma-1}{\gamma}
772
Medium
Three identical metal spheres (of same surface area) have red, black and white colors and they are heated up to same temperature. They are allowed to cool. Arrange them from maximum rate of cooling to minimum rate of cooling
Options:
A) black, red, white
B) white, red, black,
C) red, black, white
D) red, white, black
773
Medium
At certain temperature, \operatorname{rod} \mathrm{A} and \operatorname{rod} \mathrm{B} of different materials have lengths \mathrm{L}_{\mathrm{A}} and \mathrm{L}_{\mathrm{B}} respectively. Their coefficients of linear expansion are \alpha_A and \alpha_B respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio \mathrm{L}_{\mathrm{A}}: \mathrm{L}_{\mathrm{B}} is given by
Options:
A) \frac{\alpha_A}{\alpha_B}
B) \frac{\alpha_B}{\alpha_A}
C) \frac{\alpha_A+\alpha_B}{\alpha_A}
D) \frac{\alpha_A+\alpha_B}{\alpha_B}
774
Medium
The internal energy of a gas will increase when it
Options:
A) expands adiabatically.
B) is compressed adiabatically.
C) expands isothermally.
D) is compressed isothermally.
775
Medium
A gas is contained in closed vessel. The initial temperature of the gas is 100^{\circ} \mathrm{C}. If the pressure of the gas is increased by 4 \%, the increase in the temperature of the gas is
Options:
A) 2^{\circ} \mathrm{C}
B) 3^{\circ} \mathrm{C}
C) 4^{\circ} \mathrm{C}
D) 5^{\circ} \mathrm{C}
776
Medium
For an ideal gas, in an isobaric process, the ratio of heat supplied ' Q ' to the work done ' w ' by the system is ( \gamma= ratio of specific heat at constant pressure to that at constant volume)
Options:
A) \frac{1}{\gamma}
B) \frac{1}{\gamma-1}
C) \frac{\gamma}{\gamma-1}
D) \frac{\gamma-1}{\gamma}
777
Medium
The temperature of a gas is -80^{\circ} \mathrm{C}. To what temperature the gas should be heated so that the r.m.s. speed is increased by 2 times?
Options:
A) 499^{\circ} \mathrm{C}
B) 772^{\circ} \mathrm{C}
C) 1464^{\circ} \mathrm{C}
D) 1737^{\circ} \mathrm{C}
778
Medium
Two bodies ' X ' and ' Y ' at temperatures ' \mathrm{T}_1 ' K and ' T_2 ' K respectively have the same dimensions. If their emissive powers are same, the relation between their temperatures is
Options:
A) \frac{T_1}{T_2}=\frac{1}{3}
B) \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{81}{1}
C) \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{3^{\frac{1}{4}}}{1}
D) \frac{T_1}{T_2}=\frac{9^{\frac{1}{4}}}{1}
779
Medium
A lead bullet moving with velocity ' v ' strikes a wall and stops. If 50 \% of its energy is converted into heat, then the increase in temperature is ( s= specific heat of lead)
Options:
A) \frac{\mathrm{v}^2 \mathrm{~s}}{2 \mathrm{~J}}
B) \frac{v^2}{4 \mathrm{Js}}
C) \frac{\mathrm{v}^2 \mathrm{~s}}{\mathrm{~J}}
D) \frac{2 v^2}{\mathrm{Js}}
780
Medium
If C_p and C_v are molar specific heats of an ideal gas at constant pressure and volume respectively and ' \gamma ' is \mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{v}} then \mathrm{C}_{\mathrm{p}}= ( \mathrm{R}= universal gas constant)
Options:
A) \frac{\gamma \mathrm{R}}{\gamma-1}
B) \gamma \mathrm{R}
C) \frac{1+\gamma}{1-\gamma}
D) \frac{\mathrm{R}}{\gamma-1}
781
Medium
The change in the internal energy of the mass of gas, when the volume changes from ' V ' to ' 2 V ' at constant pressure ' P ' is ( \gamma is the ratio of specific heat of gas at constant pressure to specific heat at constant volume)
Options:
A) \frac{\mathrm{PV}}{\gamma-1}
B) \frac{\mathrm{PV}}{\gamma+1}
C) \frac{\gamma-1}{\mathrm{PV}}
D) \frac{\gamma+1}{\mathrm{PV}}
782
Medium
A pergect gas of volume 5 litre is compressed isothermally to volume of 1 litre. The r.m.s. speed of the molecules will
Options:
A) increase by 10 times
B) decrease by 10 times
C) increase by 5 times
D) remain unchanged
783
Medium
A real gas behaves as an ideal gas at
Options:
A) low pressure and low temperature.
B) low pressure and high temperature.
C) high pressure and low temperature.
D) high pressure and high temperature.
784
Medium
According to the law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is
Options:
A) \frac{9}{2} \mathrm{R}
B) \frac{5}{2} R
C) \frac{3}{2} R
D) \frac{7}{2} R
785
Medium
A carnot engine, whose efficiency is 40 \% takes heat from a source maintained at temperature 600 K . It is desired to have an efficiency 60 \%, then the intake temperature for the same exhaust (sink) temperature should be
Options:
A) 1800 K
B) 1200 K
C) 900 K
D) 600 K
786
Medium
Two rods of same length \& material transfer a given amount of heat in 12 s when they are joined end to end. But when they are joined length wise parallel to each other they will transfer same amount of heat in same condition in time
Options:
A) 24 s
B) 3 s
C) 1.5 s
D) 48 s
787
Medium
An insulated container contains a monoatomic gas of molar mass ' m '. The container is moving with velocity ' V '. If it is stopped suddenly, the change in temperature is ( R= gas constant)
Options:
A) \frac{\mathrm{mV}^2}{5 \mathrm{R}}
B) \frac{\mathrm{mV}^2}{3 \mathrm{R}}
C) \frac{\mathrm{mV}^2}{7 \mathrm{R}}
D) \frac{m V^2}{9 R}
788
Medium
In an isobaric process of an ideal gas, the ratio of work done by the system to the heat supplied \left(\frac{W}{Q}\right) is
Options:
A) \frac{1}{\gamma-1}
B) \gamma
C) \frac{\gamma}{\gamma-1}
D) \frac{\gamma-1}{\gamma}
789
Medium
A sphere is at temperature 600 K . In an external environment of 200 K , its cooling rate is ' R ' When the temperature of the sphere falls to 400 K , then cooling rate ' R ' will become
Options:
A) \frac{3}{16} \mathrm{R}
B) \frac{9}{16} R
C) \frac{16}{9} R
D) \frac{16}{3} R
790
Medium
A gas expands in such a way that its pressure and volume satisfy the condition \mathrm{PV}^2= constant. Then the temperature of the gas
Options:
A) will decrease.
B) will increase.
C) will not change.
D) may increase or decrease depending upon the values of pressure and volume.
791
Medium
The r.m.s. velocity of gas molecules kept at temperature 27^{\circ} \mathrm{C} in a vessel is 61 \mathrm{~m} / \mathrm{s}. Molecular weight of gas is nearly $\left[\mathrm{R}=8.31 \frac{\mathrm{~J}}{\mathrm{~mol} \mathrm{~K}}\right]
Options:
A) 2
B) 4
C) 28
D) 32
792
Medium
A diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as \mathrm{P} \propto \mathrm{T}^{\mathrm{x}} where the value of x is
Options:
A) 3.5
B) 2.5
C) 4.5
D) 3
793
Medium
A monoatomic gas is heated at constant pressure. The percentage of total heat used for doing external work is
Options:
A) 30%
B) 40%
C) 50%
D) 60%
794
Medium
Two rods, one of copper ( Cu) and the other of iron ( Fe ) having initial lengths \mathrm{L}_1 and \mathrm{L}_2 respectively are connected together to form a single rod of length L_1+L_2. The coefficient of linear expansion of Cu and Fe are \alpha_c and \alpha_i respectively. If the length of each rod increases by the same amount when their temperatures are raised by t^{\circ} \mathrm{C}, then ratio of \frac{L_1-L_2}{L_1+L_2} will be
Options:
A) \frac{\alpha_i}{\alpha_c+\alpha_i}
B) \frac{\alpha_c}{\alpha_c+\alpha_i}
C) \frac{\alpha_i-\alpha_c}{\alpha_c+\alpha_i}
D) \frac{\alpha_c-\alpha_i}{\alpha_c+\alpha_i}
795
Medium
The specific heat of argon at constant pressure and constant volume are C_p and C_v respectively. It's density ' \rho ' at N.T.P. will be [\mathrm{P} and T are pressure and temperature respectively at N.T.P.]
Options:
A) \frac{P}{T\left(C_p-C_v\right)}
B) \frac{\mathrm{PT}}{\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}\right)}
C) \frac{T\left(C_p-C_v\right)}{P}
D) \frac{\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}\right)}{\mathrm{PT}}
796
Medium
The r.m.s. velocity of hydrogen at S.T.P. is ' u ' \mathrm{m} / \mathrm{s}. If the gas is heated at constant pressure till its volume becomes three times, then the final temperature of the gas and the r.m.s. speed are respectively
Options:
A) 819 \mathrm{~K},(\sqrt{3}) \mathrm{um} / \mathrm{s}
B) 1092 \mathrm{~K}, 3 \mathrm{um} / \mathrm{s}
C) 819 \mathrm{~K}, \frac{\mathrm{u}}{\sqrt{3}} \mathrm{~m} / \mathrm{s}
D) 1092 \mathrm{~K}, \frac{\mathrm{u}}{3} \mathrm{~m} / \mathrm{s}
797
Medium
There are two samples A and B of a certain gas, which are initially at the same temperature and pressure. Both are compressed from volume v to \frac{\mathrm{v}}{2}. Sample A is compressed isothermally while sample B is compressed adiabatically. The final pressure of A is
Options:
A) twice that of B.
B) equal to that of B.
C) more than that of B.
D) less than that of B .
798
Medium
Two rods, one of aluminium and the other of steel, having initial lengths ' \mathrm{L}_1 ' and ' \mathrm{L}_2 ' are connected together to form a single rod of length \left(L_1+L_2\right). The coefficients of linear expansion of aluminium and steel are ' \alpha_1 ' and ' \alpha_2 ' respectively. If the length of each rod increases by the same amount, when their temperatures are raised by \mathrm{t}^{\mathrm{L}} \mathrm{C}, then the ratio \frac{L_1}{L_1+L_2} will be
Options:
A) \frac{\alpha_2}{\alpha_1}
B) \frac{\alpha_1}{\alpha_2}
C) \frac{\alpha_2}{\alpha_1+\alpha_2}
D) \frac{\alpha_1}{\alpha_1-\alpha_2}
799
Medium
Given that ' x ' joule of heat is incident on a body. Out of that, total heat reflected and transmitted is ' y ' joule. The absorption coefficient of body is
Options:
A) \frac{x}{y}
B) \frac{y}{x}
C) \frac{x-y}{x}
D) \frac{y-x}{x}
800
Medium
A diatomic ideal gas is used in Carnot engine as a working substance. If during the adiabatic expansion part of the cycle, the volume of the gas increases from V to 32 V , the efficiency of the engine is
Options:
A) 0.25
B) 0.50
C) 0.75
D) 0.90
801
Medium
Two spherical black bodies of radii ' R_1 ' and ' \mathrm{R}_2 ' and with surface temperature ' \mathrm{T}_1 ' and ' \mathrm{T}_2 ' respectively radiate the same power. The ratio of ' R_1 ' to ' R_2 ' will be
Options:
A) \left(\frac{T_2}{T_1}\right)^4
B) \left(\frac{T_2}{T_1}\right)^2
C) \left(\frac{T_1}{T_2}\right)^4
D) \left(\frac{T_1}{T_2}\right)^2
802
Medium
Rate of flow of heat through a cylindrical rod is ' \mathrm{H}_1 '. The temperature at the ends of the rod are ' T_1 ' and ' T_2 '. If all the dimensions of the rod become double and the temperature difference remains the same, the rate of flow of heat becomes ' \mathrm{H}_2 '. Then
Options:
A) \mathrm{H}_2=4 \mathrm{H}_1
B) \mathrm{H}_2=2 \mathrm{H}_1
C) \mathrm{H}_2=\frac{\mathrm{H}_1}{2}
D) \mathrm{H}_2=\frac{\mathrm{H}_1}{4}
803
Medium
A fixed mass of gas at constant pressure occupies a volume ' V '. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecules is doubled. The new volume will be
Options:
A) \frac{V}{2}
B) \frac{\mathrm{V}}{\sqrt{2}}
C) 2 \mathrm{~V}
D) 4 V
804
Medium
In an isobaric process
Options:
A) pressure is constant.
B) volume is constant.
C) temperature is constant.
D) internal energy is constant.
805
Medium
The average translational kinetic energy of nitrogen (molar mass 28) molecules at a particular temperature is 0.042 eV . The translational kinetic energy of oxygen molecules (molar mass 32) in eV at double the temperature is
Options:
A) 0.021
B) 0.048
C) 0.056
D) 0.084
806
Medium
The first operation involved in a carnot cycle is
Options:
A) isothermal expansion.
B) adiabatic expansion.
C) isothermal compression.
D) adiabatic compression.
807
Medium
The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at 47^{\circ} \mathrm{C} is (Molecular weight of hydrogen and oxygen molecules are 2 and 32 respectively)
Options:
A) 47^{\circ} \mathrm{C}
B) 132^{\circ} \mathrm{C}
C) 320^{\circ} \mathrm{C}
D) 405^{\circ} \mathrm{C}
808
Medium
A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is (Molecular wt. of \mathrm{O}_2 \& \mathrm{H}_2 is 32 and 2 respectively)
Options:
A) 1: 4
B) 1: 8
C) 16: 1
D) 12: 1
809
Medium
The P-V graph of an ideal gas, cycle is shown. The adiabatic process is described by the region
Options:
A) AB and BC
B) AB and CD
C) AD and BC
D) BC and CD
810
Medium
Railway track is made of steel segments separated by small gaps to allow for linear expansion. The segment of track is 10 m long when laid at temperature 17^{\circ} \mathrm{C}. The maximum temperature that can be reached is 45^{\circ} \mathrm{C}. Increase in length of the segment of railway track is ' x ' \times 10^{-5} \mathrm{~m}. The value of ' x ' is \left(\alpha_{\text {steel }}=\right. \left.1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)
Options:
A) 168
B) 204
C) 336
D) 530
811
Medium
At S.T.P., the mean free path of gas molecule is 1500 d , where ' d ' is diameter of molecule. What will be the mean free path at 373 K at constant volume?
Options:
A) 1500 d
B) \frac{373}{273} \times 1500 \mathrm{~d}
C) \frac{273}{373} \times 1500 \mathrm{~d}
D) \sqrt{\frac{373}{273}} \times 1500 \mathrm{~d}
812
Medium
One mole of an ideal gas at an initial temperature of ' T ' K does ' 6 R ' of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5 / 3, the final temperature of gas will be \left(\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mole}^{-1} \mathrm{~K}^{-1}\right)
Options:
A) (\mathrm{T}+4 \cdot 2) \mathrm{K}
B) (\mathrm{T}-4 \cdot 2) \mathrm{K}
C) \mathrm{(T+4) K}
D) (\mathrm{T}-4) \mathrm{K}
813
Medium
The frequency ' v_{\mathrm{m}} ' corresponding to which the energy emitted by a black body is maximum may vary with the temperature ' T ' of the body as shown by the curves ' A ', ' B ', ' C ' and ' D ' in the figure. Which one of these represents the correct variation?
Options:
A) straight line D
B) curve C
C) straight line B
D) curve A
814
Medium
A metal rod cools at the rate of $4{ }^{\circ} \mathrm{C} / \mathrm{min} whon its temperature is 90^{\circ} \mathrm{C} and the rate of 1{ }^{\circ} \mathrm{C} / \mathrm{m}{\text {in }} when its temperature is 30^{\circ} \mathrm{C}$. The temperature of the surrounding is
Options:
A) 20^{\circ} \mathrm{C}
B) 15{ }^{\circ} \mathrm{C}
C) 10^{\circ} \mathrm{C}
D) 5^{\circ} \mathrm{C}
815
Medium
The molecular mass of a gas having r.m.s. speed four times as that of another gas having molecular mass 32 is
Options:
A) 2
B) 4
C) 16
D) 32
816
Medium
At constant temperature, increasing the pressure of a gas by $5 \%$ its volume will decrease by
Options:
A) 5 \%
B) 5.26 \%
C) 4.20 \%
D) 4.70 \%
817
Medium
The temperature of a gas is measure of
Options:
A) the average kinetic energy of gas molecules.
B) the average potential energy of gas molecules.
C) the average distance between the molecules of a gas
D) the size of the molecules of a gas
818
Medium
An ideal refrigerator has freezer at a temperature of $-13^{\circ} \mathrm{C}$. The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) is
Options:
A) 320^{\circ} \mathrm{C}
B) 39^{\circ} \mathrm{C}
C) 325 \mathrm{~K}
D) 325^{\circ} \mathrm{C}
819
Medium
The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right) changes adiabatically from (\mathrm{P}, \rho) to \left(\mathrm{P}^{\prime}, \rho^{\prime}\right). If \frac{\rho^{\prime}}{\rho}=32 then \frac{\mathrm{P}^{\prime}}{\mathrm{P}}$ should be
Options:
A) \frac{1}{128}
B) 128
C) 32
D) 64
820
Medium
A sphere and a cube, both of copper have equal volumes and are black. They are allowed to cool at same temperature and in same atmosphere. The ratio of their rate of loss of heat will be
Options:
A) 1: 1
B) \left(\frac{\pi}{6}\right)^{\frac{2}{3}}
C) \left(\frac{\pi}{6}\right)^{\frac{1}{3}}
D) \frac{4 \pi}{3}: 1
821
Medium
A body is said to be opaque to the radiation if (a, r and t are coefficient of absorption, reflection and transmission respectively)
Options:
A) \mathrm{t}=0 and \mathrm{a}+\mathrm{r}=1
B) \mathrm{a}=\mathrm{r}=\mathrm{t}
C) t \neq 0
D) \mathrm{a}=0, \mathrm{r}=1, \mathrm{t}=1
822
Medium
In a thermodynamic system, $\Delta U$ represents the increases in its internal energy and dW is the work done by the system then correct statement out of the following is
Options:
A) \Delta \mathrm{U}=\mathrm{dW}$ is an isothermal process
B) \Delta \mathrm{U}=-\mathrm{dW}$ is an adiabatic process
C) \Delta \mathrm{U}=-\mathrm{dW}$ is an isothermal process
D) \Delta \mathrm{U}=\mathrm{dW}$ is an adiabatic process
823
Medium
The temperature of a gas is $-68^{\circ} \mathrm{C}$. To what temperature should it be heated, so that the r.m.s. velocity of the molecules be doubled?
Options:
A) 357^{\circ} \mathrm{C}
B) 457^{\circ} \mathrm{C}
C) 547^{\circ} \mathrm{C}
D) 820^{\circ} \mathrm{C}
824
Medium
A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same temperature of $200^{\circ} \mathrm{C}$. When these are left in a room.
Options:
A) the sphere reaches room temperature fast
B) the cube reaches room temperature fast
C) the circular plate reaches room temperature fast
D) all will reach the room temperature simultaneously
825
Medium
The efficiency of a heat engine is '$\eta' and the coefficient of performance of a refrigerator is '\beta$'. Then
Options:
A) \eta=\frac{1}{\beta}
B) \eta=\frac{1}{\beta+1}
C) \eta \beta=\frac{1}{2}
D) \eta=\frac{1}{\beta-1}
826
Medium
A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is
Options:
A) 1: 4
B) 4: 1
C) 1: 16
D) 16: 1
827
Medium
The internal energy of a monoatomic ideal gas molecule is
Options:
A) partly kinetic and partly potential
B) totally kinetic
C) totally potential
D) Neither kinetic nor potential
828
Medium
A gas at pressure $p_0$ is contained in a vessel. If the masses of all the molecules are halved and their velocities are doubled, then the resulting pressure would be equal to
Options:
A) 4 p_0
B) 2 p_0
C) p_0
D) p_0 / 2
829
Medium
For an adiabatic process, which one of the following is wrong statement?
Options:
A) Equation of state is $p V=$ constant
B) There is exchange of heat with surrounding
C) All the work is utilised to change the internal energy of the system
D) Temperature of the system changes i.e.
$\Delta T \neq 0
830
Medium
Which one of the following is based on convection?
Options:
A) Heating of a copper utensil
B) Heating a room by heater
C) Heating of iron rod
D) Heat transferred from sun to earth
831
Medium
A carnot engine operates with source at $227^{\circ} \mathrm{C} and sink at 27^{\circ} \mathrm{C}. If the source supplies 50 \mathrm{~kJ}$ of heat energy, the work done by the engine is
Options:
A) 2 kJ
B) 5 kJ
C) 10 kJ
D) 20 kJ
832
Medium
Which one of the following represents correctly the variation of volume (V) of an ideal gas with temperature $(\mathrm{T})$ under constant pressure conditions?
Options:
A) P
B) Q
C) R
D) S
833
Medium
\mathrm{dQ} is the heat energy supplied to an ideal gas under isochoric conditions. If \mathrm{dU} and \mathrm{dW}$ denote the change in internal energy and the work done respectively then
Options:
A) \mathrm{dQ}=\mathrm{dW}
B) \mathrm{dQ}>\mathrm{dU}
C) \mathrm{dQ}<\mathrm{dU}
D) \mathrm{dQ}=\mathrm{dU}
834
Medium
A black body at temperature $127^{\circ} \mathrm{C} radiates heat at the rate of 5 \mathrm{~cal} / \mathrm{cm}^2 \mathrm{~s}. At a temperature 927^{\circ} \mathrm{C}, its rate of emission in units of \mathrm{cal} / \mathrm{cm}^2 \mathrm{~s}$ will be
Options:
A) 405
B) 35
C) 45
D) 350
835
Medium
A Carnot engine has the same efficiency between (i) $100 \mathrm{~K} and 600 \mathrm{~K} and (ii) \mathrm{T} \mathrm{K} and 960 \mathrm{~K}. The temperature \mathrm{T}$ in kelvin of the sink is
Options:
A) 120
B) 160
C) 240
D) 320
836
Medium
For an ideal gas the density of the gas is $\rho_0 when temperature and pressure of the gas are T_0 and P_0 respectively. When the temperature of the gas is 2 \mathrm{~T}_0, its pressure will be 3 \mathrm{P}_0$. The new density will be
Options:
A) \frac{3}{2} \rho_0
B) \frac{4}{3} \rho_0
C) \frac{3}{4} \rho_0
D) \frac{2}{3} \rho_0
837
Medium
The temperature gradient in a rod of length $75 \mathrm{~cm} is 40^{\circ} \mathrm{C} / \mathrm{m}. If the temperature of cooler end of the rod is 10^{\circ} \mathrm{C}$, then the temperature of hotter end is
Options:
A) 50^{\circ} \mathrm{C}
B) 40^{\circ} \mathrm{C}
C) 35^{\circ} \mathrm{C}
D) 25^{\circ} \mathrm{C}
838
Medium
A black body radiates maximum energy at wavelength '$\lambda' and its emissive power is 'E'. Now due to a change in temperature of that body, it radiates maximum energy at wavelength \frac{\lambda}{3}$. At that temperature emissive power is
Options:
A) 16: 1
B) 256: 1
C) 81: 1
D) 128: 1
839
Medium
For polyatomic gases, the ratio of molar specific heat at constant pressure to constant volume is ( $\mathrm{f}=$ degrees of freedom)
Options:
A) \frac{2+\mathrm{f}}{3+\mathrm{f}}
B) \frac{3+\mathrm{f}}{2+\mathrm{f}}
C) \frac{3+\mathrm{f}}{4+\mathrm{f}}
D) \frac{4+\mathrm{f}}{3+\mathrm{f}}
840
Medium
Select the WRONG statement from the following. For an isothermal process
Options:
A) Energy exchanged is used to do work
B) Perfect thermal equilibrium with environment
C) Equation of state PV is not constant.
D) No change internal energy.
841
Medium
Compare the rate of loss of heat from a metal sphere at $627^{\circ} \mathrm{C} with the rate of loss of heat from the same sphere at 327^{\circ} \mathrm{C}, if the temperature of the surrounding is 27^{\circ} \mathrm{C}$. (nearly)
Options:
A) 6.2
B) 5.3
C) 4.8
D) 7.4
842
Medium
The volume of a metal block increases by $0.225 \% when its temperature is increased by 30^{\circ} \mathrm{C}$. Hence coefficient of linear expansion of the material of metal block is
Options:
A) 7.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.
B) 6.75 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.
C) 2.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.
D) 1.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.
843
Medium
A monoatomic ideal gas initially at temperature '$\mathrm{T}_1' is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly the gas is allowed to expand to adiabatically to a temperature '\mathrm{T}_2'. If '\mathrm{L}_1' and '\mathrm{L}_2' are the lengths of the gas columns before and after expansion respectively, then \frac{\mathrm{T}_2}{\mathrm{~T}_1}$ is
Options:
A) \frac{\mathrm{L}_1}{\mathrm{~L}_2}
B) \frac{\mathrm{L}_2}{\mathrm{~L}_1}
C) \left(\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right)^{2 / 3}
D) \left(\frac{\mathrm{L}_2}{\mathrm{~L}_1}\right)^{2 / 3}
844
Medium
Let $\gamma_1 be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and \gamma_2 be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio \frac{\gamma_2}{\gamma_1}$ is
Options:
A) \frac{37}{21}
B) \frac{27}{35}
C) \frac{21}{25}
D) \frac{35}{27}
845
Medium
The molar specific heat of an ideal gas at constant pressure and constant volume is $\mathrm{C}_{\mathrm{p}} and \mathrm{C}_{\mathrm{v}} respectively. If \mathrm{R} is universal gas constant and \gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}} then \mathrm{C}_{\mathrm{v}}=
Options:
A) \frac{1-\gamma}{1+\gamma}
B) \frac{1+\gamma}{1-\gamma}
C) \frac{\gamma-1}{\mathrm{R}}
D) \frac{\mathrm{R}}{\gamma-1}
846
Medium
A composite slab consists of two materials having coefficient of thermal conductivity $\mathrm{K} and 2 \mathrm{~K}, thickness \mathrm{x} and 4 \mathrm{x} respectively. The temperature of the two outer surfaces of a composite slab are \mathrm{T}_2 and \mathrm{T}_1\left(\mathrm{~T}_2 > \mathrm{T}_1\right). The rate of heat transfer through the slab in a steady state is \left[\frac{\mathrm{A}\left(\mathrm{T}_2-\mathrm{T}_1\right) \mathrm{K}}{\mathrm{x}}\right] \cdot \mathrm{f} where '\mathrm{f}$' is equal to
Options:
A) 1
B) \frac{2}{3}
C) \frac{1}{2}
D) \frac{1}{3}
847
Medium
A black sphere has radius '$R' whose rate of radiation is 'E' at temperature 'T'. If radius is made R / 3 and temperature '3 T$', the rate of radiation will be
Options:
A) E
B) 3E
C) 6E
D) 9E
848
Medium
A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma=1.5$, then the increase in its temperature is
Options:
A) 273 K
B) 373 K
C) 473 K
D) 573 K
849
Medium
About black body radiation, which of the following is the wrong statement?
Options:
A) For all wavelengths, intensity is same.
B) For shorter wavelengths, intensity is more.
C) For longer wavelengths, intensity is less.
D) All wavelengths are emitted by a black body.
850
Medium
For a gas, $\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}=0 \cdot 4, where \mathrm{R} is universal gas constant and \mathrm{C}_{\mathrm{v}}$ is molar specific heat at constant volume. The gas is made up of molecules which are
Options:
A) rigid diatomic
B) monoatomic
C) non-rigid diatomic
D) polyatomic
851
Medium
Two bodies $\mathrm{A} and \mathrm{B} at temperatures '\mathrm{T}_1' \mathrm{K} and '\mathrm{T}_2' \mathrm{K} respectively have the same dimensions. Their emissivities are in the ratio 1: 3. If they radiate the same amount of heat per unit area per unit time, then the ratio of their temperatures \left(\mathrm{T}_1: \mathrm{T}_2\right)$ is
Options:
A) 1: 3
B) 3^{1 / 4}: 1
C) 9^{1 / 4}: 1
D) 81: 1
852
Medium
If temperature of gas molecules is raised from $127^{\circ} \mathrm{C} to 527^{\circ} \mathrm{C}$, the ratio of r.m.s. speed of the molecules is respectively
Options:
A) 1: 2
B) 2: 1
C) 1: \sqrt{2}
D) 2: \sqrt{2}
853
Medium
According to Boyle's law, the product PV remains constant. The unit of $\mathrm{PV}$ is same as that of
Options:
A) energy
B) force
C) impulse
D) momentum
854
Medium
The difference in length between two rods $\mathrm{A} and \mathrm{B} is 60 \mathrm{~cm} at all temperatures. If \alpha_{\mathrm{A}}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C} and \beta_{\mathrm{B}}=27 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, the lengths of the two rods are
Options:
A) l_{\mathrm{A}}=200 \mathrm{~cm}, l_{\mathrm{B}}=140 \mathrm{~cm}
B) l_{\mathrm{A}}=180 \mathrm{~cm}, l_{\mathrm{B}}=120 \mathrm{~cm}
C) l_{\mathrm{A}}=160 \mathrm{~cm}, l_{\mathrm{B}}=100 \mathrm{~cm}
D) l_{\mathrm{A}}=120 \mathrm{~cm}, l_{\mathrm{B}}=60 \mathrm{~cm}
855
Medium
An ideal gas expands adiabatically. $(\gamma=1 \cdot 5)$ To reduce the r.m.s. velocity of the molecules 3 times, the gas has to be expanded
Options:
A) 81 times
B) 27 times
C) 9 times
D) 3 times
856
Medium
Two spherical black bodies of radii '$r_1' and 'r_2' at temperature '\mathrm{T}_1' and '\mathrm{T}_2' respectively radiate power in the ratio 1: 2 Then r_1: r_2$ is
Options:
A) \frac{1}{2}\left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)^4
B) \frac{1}{\sqrt{2}}\left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)^2
C) 2\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^4
D) 2\left(\frac{T_1}{T_2}\right)^2
857
Medium
The rate of flow of heat through a metal rod with temperature difference $40^{\circ} \mathrm{C} is 1600 \mathrm{~cal} / \mathrm{s}. The thermal resistance of metal rod in { }^{\circ} \mathrm{C} \mathrm{s} / \mathrm{cal}$ is
Options:
A) 0.025
B) 0.25
C) 2.5
D) 40
858
Medium
If the temperature of a hot body is increased by $50 \%$, then the increase in the quantity of emitted heat radiation will be approximately
Options:
A) 125 \%
B) 200 \%
C) 300 \%
D) 400 \%
859
Medium
A monoatomic gas at pressure '$\mathrm{P}', having volume '\mathrm{V}' expands isothermally to a volume '2 \mathrm{~V}' and then adiabatically to a volume '16 \mathrm{~V}'. The final pressure of the gas is (Take \gamma=5 / 3$ )
Options:
A) \mathrm{P} / 64
B) \mathrm{P} / 32
C) 16 \mathrm{P}
D) 32 \mathrm{P}
860
Medium
A diatomic gas $\left(\gamma=\frac{7}{5}\right) is compressed adiabatically to volume \frac{V_i}{32} where V_i is its initial volume. The initial temperature of the gas is T_i in Kelvin and the final temperature is 'x T_i'. The value of 'x$' is
Options:
A) 5
B) 4
C) 3
D) 2
861
Medium
If a gas is compressed isothermally then the r.m.s. velocity of the molecules
Options:
A) decreases.
B) increases.
C) remains the same.
D) first decreases and then increases.
862
Medium
A black body radiates maximum energy at wavelength '$\lambda' and its emissive power is 'E' Now due to change in temperature of that body, it radiates maximum energy at wavelength \frac{2 \lambda}{3}$. At that temperature emissive power is
Options:
A) \frac{81}{16}
B) \frac{27}{32}
C) \frac{18}{10}
D) \frac{9}{4}
863
Medium
Which of the following graphs between pressure (P) and volume (V) correctly shows isochoric changes?
Options:
A) D
B) B
C) C
D) A
864
Medium
A metal rod $2 \mathrm{~m} long increases in length by 1.6 \mathrm{~mm}, when heated from 0^{\circ} \mathrm{C} to 60^{\circ} \mathrm{C}$. The coefficient of linear expansion of metal rod is
Options:
A) 1.33 \times 10^{-5} /{ }^{\circ} \mathrm{C}
B) 1.66 \times 10^{-5} /{ }^{\circ} \mathrm{C}
C) 1.33 \times 10^{-3} /{ }^{\circ} \mathrm{C}
D) 1.66 \times 10^{-3} /{ }^{\circ} \mathrm{C}
865
Medium
We have a jar filled with gas characterized by parameters $\mathrm{P}, \mathrm{V}, \mathrm{T} and another jar B filled with gas having parameters 2 \mathrm{P}, \frac{\mathrm{V}}{4}, 2 \mathrm{~T}$, where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is
Options:
A) 1: 1
B) 1: 2
C) 2: 1
D) 4: 1
866
Medium
An insulated container contains a monoatomic gas of molar mass '$\mathrm{m}'. The container is moving with velocity '\mathrm{V}$'. If it is stopped suddenly, the change in temperature of a gas is [R is gas constant]
Options:
A) \frac{\mathrm{MV}^2}{\mathrm{R}}
B) \frac{M V^2}{2 R}
C) \frac{\mathrm{MV}^2}{3 \mathrm{R}}
D) \frac{3 \mathrm{MV}^2}{2 \mathrm{R}}
867
Medium
In a vessel, the ideal gas is at a pressure $\mathrm{P}$. If the mass of all the molecules is halved and their speed is doubled, then resultant pressure of the gas will be
Options:
A) 4 \mathrm{P}
B) 2 \mathrm{P}
C) \mathrm{P}
D) \frac{\mathrm{P}}{2}
868
Medium
The average force applied on the walls of a closed container depends on $T^x where T is the temperature of an ideal gas. The value of 'x$' is
Options:
A) 4
B) 3
C) 2
D) 1
869
Medium
A black body radiates maximum energy at wavelength '$\lambda' and its emissive power is \mathrm{E}. Now due to change in temperature of that body, it radiates maximum energy at wavelength \frac{2 \lambda}{3}$. At that temperature emissive power is
Options:
A) \frac{51 \mathrm{E}}{8}
B) \frac{81 \mathrm{E}}{16}
C) \frac{61 E}{27}
D) \frac{71 \mathrm{E}}{19}
870
Medium
A Carnot engine with efficiency $50 \% takes heat from a source at 600 \mathrm{~K}. To increase the efficiency to 70 \%$, keeping the temperature of the sink same, the new temperature of the source will be
Options:
A) 360 \mathrm{~K}
B) 1000 \mathrm{~K}
C) 900 \mathrm{~K}
D) 300 \mathrm{~K}
871
Medium
A piece of metal at $850 \mathrm{~K} is dropped in to 1 \mathrm{~kg} water at 300 \mathrm{~K}. If the equilibrium temperature of water is 350 \mathrm{~K} then the heat capacity of the metal, expressed in \mathrm{JK}^{-1} is (1 \mathrm{~cal}=4.2 \mathrm{~J})
Options:
A) 420
B) 240
C) 100
D) No Solution
872
Medium
Heat energy is incident on the surface at the rate of X J/min . If '$a' and 'r' represent coefficient of absorption and reflection respectively then the heat energy transmitted by the surface in 't$' minutes is
Options:
A) (a+r) x t
B) \frac{(\mathrm{a}+\mathrm{r})}{\mathrm{xt}}
C) -(a+r) x t
D) \frac{\mathrm{xt}}{(\mathrm{a}+\mathrm{r})}
873
Medium
A sample of gas at temperature $T is adiabatically expanded to double its volume. The work done by the gas in the process is \left(\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\gamma=\frac{3}{2}\right) \quad(\mathrm{R}= gas constant )
Options:
A) \operatorname{TR}(\sqrt{2}-2)
B) \frac{\mathrm{T}}{\mathrm{R}}(\sqrt{2}-2)
C) \frac{\mathrm{R}}{\mathrm{T}}(2-\sqrt{2})
D) \mathrm{RT}(2-\sqrt{2})
874
Medium
An ideal gas in a container of volume 500 c.c. is at a pressure of $2 \times 10^{+5} \mathrm{~N} / \mathrm{m}^2. The average kinetic energy of each molecule is 6 \times 10^{-21} \mathrm{~J}$. The number of gas molecules in the container is
Options:
A) 5 \times 10^{25}
B) 5 \times 10^{23}
C) 25 \times 10^{23}
D) 2.5 \times 10^{22}
875
Medium
A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If $\gamma=1.5$, then the final pressure is
Options:
A) 4 times
B) 1.5 times
C) 8 times
D) \frac{1}{4}$ times
876
Medium
A gas is compressed at a constant pressure of $50 \mathrm{~N} / \mathrm{m}^2 from a volume of 10 \mathrm{~m}^3 to a volume of 4 \mathrm{~m}^3. Energy of 100 \mathrm{~J}$ is then added to the gas by heating. Its internal energy is
Options:
A) increased by $400 \mathrm{~J}
B) increased by $200 \mathrm{~J}
C) increased by $100 \mathrm{~J}
D) decreased by $200 \mathrm{~J}
877
Medium
The pressure exerted by an ideal gas at a particular temperature is directly proportional to
Options:
A) the mean speed of the gas molecules.
B) mean of the square of the speed of the gas molecules.
C) the square of the mean speed of the gas molecules.
D) the root mean square speed of the gas molecules.
878
Medium
The side of a copper cube is $1 \mathrm{~m} at 0^{\circ} \mathrm{C}. What will be the change in its volume, when it is heated to 100^{\circ} \mathrm{C} ? \left[\alpha_{\text {copper }}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right]
Options:
A) 45 \times 10^{-4} \mathrm{~m}^3
B) 54 \times 10^{-4} \mathrm{~m}^3
C) 34 \times 10^{-4} \mathrm{~m}^3
D) 64 \times 10^{-4} \mathrm{~m}^3
879
Medium
The temperature of an ideal gas is increased from $27^{\circ} \mathrm{C} to 927^{\circ} \mathrm{C}$. The r.m.s. speed of its molecules becomes
Options:
A) twice
B) four times.
C) half.
D) one-fourth.
880
Medium
A jar '$\mathrm{P}' is filled with gas having pressure, volume and temperature \mathrm{P}, \mathrm{V}, \mathrm{T} respectively. Another gas jar Q filled with a gas having pressure 2 \mathrm{P}, volume \frac{\mathrm{V}}{4} and temperature 2 \mathrm{~T}. The ratio of the number of molecules in jar \mathrm{P} to those in jar Q$ is
Options:
A) 1: 1
B) 1: 2
C) 2: 1
D) 4: 1
881
Medium
For a gas having '$\mathrm{X}' degrees of freedom, '\gamma' is (\gamma= ratio of specific heats =\mathrm{C_P / C_V}$)
Options:
A) \frac{1+X}{2}
B) 1+\frac{X}{2}
C) 1+\frac{2}{x}
D) 1+\frac{1}{x}
882
Medium
Two uniform brass rods $A and B of length 'l' and '2 l' and their radii '2 r' and 'r' respectively are heated to same temperature. The ratio of the increase in the volume of \operatorname{rod} \mathrm{A} to that of \operatorname{rod} \mathrm{B}$ is
Options:
A) 1: 1
B) 1: 2
C) 2: 1
D) 1: 4
883
Medium
A gas at N.T.P. is suddenly compressed to $\left(\frac{1}{4}\right)^{\text {th }} of its original volume. The final pressure in (Given \gamma= ratio of sp. heats =\frac{3}{2} ) atmosphere is ( \mathrm{P}=$ original pressure)
Options:
A) 4 \mathrm{P}
B) \frac{3}{2} \mathrm{P}
C) 8 \mathrm{P}
D) \frac{1}{4} \mathrm{P}
884
Medium
In a thermodynamic process, there is no exchange of heat between the system and surroundings. Then the thermodynamic process is
Options:
A) isothermal
B) isobaric
C) isochoric
D) adiabatic
885
Medium
According to kinetic theory of gases, which one of the following statements is wrong?
Options:
A) All the molecules of a gas are identical.
B) Collisions between the molecules of a gas and that of the molecules with the walls of the container are perfectly elastic.
C) The molecules do not exert appreciable force on one another except during collision.
D) The pressure exerted by a gas is due to the collision between the molecules of the gas.
886
Medium
Three discs $\mathrm{x}, \mathrm{y} and \mathrm{z} having radii 2 \mathrm{~m}, 3 \mathrm{~m} and 6 \mathrm{~m} respectively are coated on outer surfaces. The wavelength corresponding to maximum intensity are 300 \mathrm{~nm}, 400 \mathrm{~nm} and 500 \mathrm{~nm} respectively. If \mathrm{P}_{\mathrm{x}}, \mathrm{P}_{\mathrm{y}} and \mathrm{P}_{\mathrm{z}}$ are power radiated by them respectively then
Options:
A) \mathrm{P}_{\mathrm{X}}$ is maximum
B) \mathrm{P}_{\mathrm{Z}}$ is maximum
C) \mathrm{P}_{\mathrm{y}}$ is maximum
D) \mathrm{P_x=P_y=P_z}
887
Medium
When the rms velocity of a gas is denoted by '$v', which one of the following relations is true? (\mathrm{T}=$ Absolute temperature of the gas.)
Options:
A) \frac{\mathrm{v}^2}{\mathrm{~T}}=$ constant
B) \mathrm{v}^2 \mathrm{T}=$ constant
C) \mathrm{vT}^2=$ constant
D) \frac{\mathrm{v}}{\mathrm{T}^2}=$ constant
888
Medium
A monoatomic gas $\left(\gamma=\frac{5}{3}\right) initially at 27^{\circ} \mathrm{C} having volume '\mathrm{V}' is suddenly compressed to one-eighth of its original volume \left(\frac{\mathrm{V}}{8}\right)$. After the compression its temperature becomes
Options:
A) 580 K
B) 1200 K
C) 1160 K
D) 927 K
889
Medium
Two monatomic ideal gases A and B of molecular masses '$m_1' and 'm_2$' respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas A to that in gas B is given by
Options:
A) \sqrt{\frac{\mathrm{m}_2}{\mathrm{~m}_1}}
B) \frac{\mathrm{m}_1}{\mathrm{~m}_2}
C) \sqrt{\frac{\mathrm{m}_1}{\mathrm{~m}_2}}
D) \frac{\mathrm{m}_2}{\mathrm{~m}_1}
890
Medium
The thermodynamic process in which no work is done on or by the gas is
Options:
A) isochoric process
B) adiabatic process
C) isothermal process
D) isobaric process
891
Medium
Heat given to a body, which raises its temperature by 1ºC is known as
Options:
A) specific heat
B) thermal capacity
C) water equivalent
D) temperature gradient
892
Medium
Which one of the following is NOT a correct expression for an ideal gas? [$\mathrm{C_p}= Molar specific heat of a gas at constant pressure, \mathrm{C_v}= Molar specific heat of a gas at constant volume, \mathrm{Y}= Ratio of two specific heats of a gas, \mathrm{R}=$ Universal gas constant]
Options:
A) C_v=C_p+R
B) R=C_v(\gamma-1)
C) \frac{C_v}{\mathrm{C}_{\mathrm{p}}}=\frac{1}{\gamma}
D) R=\frac{C_{\mathrm{p}}(\gamma-1)}{\gamma}
893
Medium
The molecular masses of helium and oxygen are 4 and 32 respectively. The ratio of r.m.s. speed of helium at 327$^\circ to r.m.s. speed of oxygen at 27^\circ$ will be
Options:
A) 1 : 6
B) 8 : 1
C) 1 : 8
D) 4 : 1
894
Medium
Which one of the following p-V diagram is correct for an isochoric process:
Options:
A) IV
B) II
C) III
D) I
895
Medium
Assume that for solar radiation, surface temperature of the sun is $6000 \mathrm{~K}. If Wien's constant 'b' is 2.897 \times 10^{-3} \mathrm{~mK}$, the value of maximum wavelength will be
Options:
A) 4828$\mathop A\limits^o
B) 3648$\mathop A\limits^o
C) 6400$\mathop A\limits^o
D) 5890$\mathop A\limits^o
896
Medium
A metal sphere cools at the rate of $1.5^{\circ} \mathrm{C} / \mathrm{min} when its temperature is 80^{\circ} \mathrm{C}. At what rate will it cool when its temperature falls to 50^{\circ} \mathrm{C}. [Temperature of surrounding is 30^{\circ} \mathrm{C}$]
Options:
A) 0.9^{\circ} \mathrm{C} / \mathrm{min}
B) 0.6^{\circ} \mathrm{C} / \mathrm{min}
C) 1.5^{\circ} \mathrm{C} / \mathrm{min}
D) 1.2^{\circ} \mathrm{C} / \mathrm{min}
897
Medium
A monoatomic gas is suddenly compressed to $(1 / 8)^{\text {th }} of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is (\gamma=5 / 3)
Options:
A) 32
B) 8
C) \frac{40}{3}
D) \frac{24}{5}
898
Medium
A monoatomic ideal gas initially at temperature $\mathrm{T}_1 is enclosed in a cylinder fitted with 8 frictionless piston. The gas is allowed to expand adiabatically to a temperature \mathrm{T}_2 by releasing the piston suddenly. \mathrm{L}_1 and \mathrm{L}_2 are the lengths of the gas columns before and after the expansion respectively. Then \frac{\mathrm{T}_2}{\mathrm{~T}_1}$ is
Options:
A) \left(\frac{\mathrm{L}_2}{\mathrm{~L}_1}\right)^{2 / 3}
B) \left(\frac{L_1}{L_2}\right)^{2 / 3}
C) \left(\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right)^{1 / 2}
D) \left(\frac{\mathrm{L}_2}{\mathrm{~L}_1}\right)^{1 / 2}
899
Medium
For a monoatomic gas, the work done at constant pressure is '$\mathrm{W}' The heat supplied at constant volume for the same rise in temperature of the gas is [\gamma=\frac{C_p}{C_v}=\frac{5}{2}$ for monoatomic gas]
Options:
A) 2 \mathrm{~W}
B) \mathrm{W}
C) \frac{W}{2}
D) \frac{3 W}{2}
900
Medium
An ideal gas with pressure $\mathrm{P}, volume \mathrm{V} and temperature \mathrm{T} is expanded isothermally to a volume 2 \mathrm{~V} and a final pressure \mathrm{P}_{\mathrm{i}}. The same gas is expanded adiabatically to a volume 2 \mathrm{~V}, the final pressure is \mathrm{P}_{\mathrm{a}}. In terms of the ratio of the two specific heats for the gas '\gamma', the ratio \frac{P_i}{P_a}$ is
Options:
A) 2^{\gamma+1}
B) 2^{\gamma-1}
C) 2^{1-\gamma}
D) 2^\gamma
901
Medium
At what temperature does the average translational kinetic energy of a molecule in a gas becomes equal to kinetic energy of an electron accelerated from rest through potential difference of 'V' volt? ($\mathrm{N}= number of molecules, \mathrm{R}= gas constant, \mathrm{c}=$ electronic charge)
Options:
A) \frac{2 \mathrm{eVN}}{3 \mathrm{R}}
B) \mathrm{\frac{e V N}{R}}
C) \mathrm{\frac{e V N}{4 R}}
D) \mathrm{\frac{3 e V N}{2 R}}
902
Medium
The temperature difference between two sides of an iron plate, $1.8 \mathrm{~cm} thick is 9^{\circ} \mathrm{C}. Heat is transmitted through the plate 10 \mathrm{k} \mathrm{cal} / \mathrm{sm}^2$ at steady state. The thermal conductivity of iron is
Options:
A) 0.02 \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}
B) 0.04 \frac{\mathrm{kcal}}{\mathrm{ms}{ }^{\circ} \mathrm{C}}
C) 0.05 \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}
D) 0.004 \frac{\mathrm{kcal}}{\mathrm{ms}{ }^{\circ}}
903
Medium
Internal energy of $n_1 moles of hydrogen at temperature 'T' is equal to internal energy of 'n_2' moles of helium at temperature 2 T, then the ratio \mathrm{n}_1: \mathrm{n}_2 is [Degree of freedom of \mathrm{He}=3, Degree of freedom of \mathrm{H}_2=5$]
Options:
A) 5: 3
B) 6: 5
C) 2: 3
D) 3: 5
904
Medium
For an ideal gas, $R=\frac{2}{3} C_v. This suggests that the gas consists of molecules, which are [\mathrm{R}=$ universal gas constant]
Options:
A) polyatomic
B) diatomic
C) monoatomic
D) a mixture of diatomic and polyatomic molecules
905
Medium
The rms speed of a gas molecule is '$\mathrm{V}' at pressure '\mathrm{P}$'. If the pressure is increased by two times, then the rms speed of the gas molecule at the same temperature will be
Options:
A) \mathrm{V}
B) \sqrt{2} \mathrm{~V}
C) \frac{V}{3}
D) \frac{V}{2}
906
Medium
Equal volumes of two gases, having their densíties in the ratio of $1: 16 exert equal pressures on the walls of two containers. The ratio of their rms speads (\mathrm{C}_1: \mathrm{C}_2)$ is
Options:
A) 1: 4
B) 4: 1
C) 8: 1
D) 1: 8
907
Medium
A cylindrical rod has temperatures '$T_1' and 'T_2' at its ends. The rate of flow of heat is 'Q_1' cal \mathrm{s}^{-1}. If length and radius of the rod are doubled keeping temperature constant, then the rate of flow of heat '\mathrm{Q}_2$' will be
Options:
A) \mathrm{Q}_2=\frac{\mathrm{Q}_1}{2}
B) \mathrm{Q}_2=\frac{\mathrm{Q}_1}{4}
C) \mathrm{Q_2=4 Q_1}
D) \mathrm{Q}_2=2 \mathrm{Q}_1
908
Medium
The initial pressure and volume of a gas is '$\mathrm{P}' and '\mathrm{V}' respectively. First by isothermal process gas is expanded to volume '9 \mathrm{~V}' and then by adiabatic process its volume is compressed to '\mathrm{V}' then its final pressure is (Ratio of specific heat at constant pressure to constant volume =\frac{3}{2}$)
Options:
A) 6 P
B) 27 P
C) 3 P
D) 9 P
909
Medium
If $\mathrm{m}' represents the mass of each molecules of a gas and \mathrm{T}$' its absolute temperature then the root mean square speed of the gas molecule is proportional to
Options:
A) \mathrm{m^{-\frac{1}{2}}T^{\frac{1}{2}}}
B) mT
C) \mathrm{m^{\frac{1}{2}}T^{-\frac{1}{2}}}
D) \mathrm{m^{\frac{1}{2}}T^{\frac{1}{2}}}
910
Medium
An ideal gas at pressure '$p' is adiabatically compressed so that its density becomes twice that of the initial. If \gamma=\frac{c_p}{c_v}=\frac{7}{5}$, then final pressure of the gas is
Options:
A) p
B) 2p
C) \frac{7}{5}$p
D) 2.63p
911
Medium
Which one of the following statements is wrong for an isobaric process?
Options:
A) The pressure of the system remains constant
B) There is change in volume, when work is done
C) Temperature of the system remains constant
D) Energy exchanged is used to do work to change internal energy
912
Medium
For a perfectly black body, coefficient of emission is
Options:
A) zero
B) infinity
C) unity
D) less than one (non-zero)
913
Medium
Two rods of different metals have coefficients of linear expansion '$\alpha_1' and '\alpha_2' respectvely. Their respective lengths are '\mathrm{L}_1' and '\mathrm{L}_2'. At all temperatures (\mathrm{L}_2-\mathrm{L}_1$) is same. The correct relation is
Options:
A) \mathrm{L}_1 \alpha_1^2=\mathrm{L}_2 \alpha_2^2
B) \mathrm{L}_1^2 \alpha_1^2=\mathrm{L}_2^2 \alpha_2^2
C) \mathrm{L}_1 \alpha_2=\mathrm{L}_2 \alpha_1
D) \mathrm{L}_1 \alpha_1=\mathrm{L}_2 \alpha_2
914
Medium
The temperature of a black body is increased by $50 \%$, then the percentage increase in the rate of radiation by the body is approximated
Options:
A) 50%
B) 100%
C) 400%
D) 150%
915
Medium
The emissive power of sphere of area $0.04 \mathrm{~m}^2 is 0.7 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~m}^{-2}$. The amount of heat radiated in 20 second is
Options:
A) 2.8 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~m}^{-2}
B) 0.28 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~m}^{-2}
C) 5.6 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~m}^{-2}
D) 0.56 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~m}^{-2}
916
Medium
The rate of flow of heat through a copper rod with temperature difference $28^{\circ} \mathrm{C} is 1400 \mathrm{~cal} \mathrm{~s}^{-1}$. The thermal resistance of copper rod will be
Options:
A) 0.05 \frac{{ }^{\circ} \mathrm{C} \mathrm{s}}{\mathrm{cal}}
B) 0.02 \frac{{ }^{\circ} \mathrm{C} \mathrm{s}}{\mathrm{cal}}
C) 5 \frac{{ }^{\circ} \mathrm{C} \mathrm{s}}{\mathrm{cal}}
D) 2 \frac{{ }^{\circ} \mathrm{Cs}}{\text { cal }}
917
Medium
The change in internal energy of the mass of a gas, when the volume changes from '$\mathrm{V}' to '2 \mathrm{~V}' at constant pressure 'P' is (\gamma=$ Ratio of Cp to Cv)
Options:
A) \frac{\mathrm{PV}}{(\gamma-1)}
B) \frac{\mathrm{P}}{(\gamma-1)}
C) PV
D) \frac{\gamma \mathrm{PV}}{(\gamma-1)}
918
Medium
If the pressure of an ideal gas is decreased by $10 \%$ isothermally, then its volume will
Options:
A) decrease by $8 \%
B) decrease by $9 \%
C) increase by $8 \%
D) increase by $11.1 \%
919
Medium
An ideal gas having molar mass '$\mathrm{M}_0$', has r.m.s. velocity 'V' at temperature 'T'. Then
Options:
A) \mathrm{VT}^2=$ constant
B) \frac{\mathrm{v}^2}{\mathrm{~T}}=$ constant
C) \mathrm{V}^2 \mathrm{T}=$ constant
D) \mathrm{V} is independent of \mathrm{T}
920
Medium
An ideal gas at $27^{\circ} \mathrm{C} is compressed adiabatically to (8 / 27) of its original volume. If ratio of specific heats, \gamma=5 / 3$ then the rise in temperature of the gas is
Options:
A) 500 K
B) 125 K
C) 250 K
D) 375 K
921
Medium
The translational kinetic energy of the molecules of a gas at absolute temperature (T) can be doubled
Options:
A) by increasing $\mathrm{T} to 4 \mathrm{~T}
B) by increasing $\mathrm{T} to 2 \mathrm{~T}
C) by decreasing $\mathrm{T} to \mathrm{T} / 2
D) by increasing $\mathrm{T} to \sqrt{2} \mathrm{~T}
922
Medium
A polyatomic gas $(\gamma=4 / 3) is compressed to \left(\frac{1}{8}\right)^{\text {th }} of its volume adiabatically. If its initial pressure is \mathrm{P}_0$, its new pressure will be
Options:
A) 2 \mathrm{P}_0
B) 8 \mathrm{P}_0
C) 6 \mathrm{P}_0
D) 16 \mathrm{P}_0
923
Medium
If the temperature of the sun is doubled, the rate of energy received by the earth will be increased by a factor
Options:
A) 8
B) 2
C) 4
D) 16
924
Medium
Which of the following statements is true? ($\Delta \mathrm{U}= increase in internal energy, \mathrm{dW}=$ work done by the system)
Options:
A) In an adiabatic process $\Delta \mathrm{U}=\mathrm{dW}
B) In an adiabatic process $\Delta \mathrm{U}=-\mathrm{dW}
C) In an isothermal process $\Delta \mathrm{U}=-\mathrm{dW}$.
D) In an isothermal process $\Delta \mathrm{U}=\mathrm{dW}
925
Medium
Let '$\mathrm{W}_1' be the work done in blowing a soap bubble of radius 'r' from soap solution at room temperature. The soap solution is now heated and second soap bubble of radius '2 r' is blown from the heated soap solution. If 'W_2$' is the work done in forming this bubble then
Options:
A) \mathrm{W}_2=2 \mathrm{~W}_1
B) \mathrm{W}_2=4 \mathrm{~W}_1
C) \mathrm{W}_2>4 \mathrm{~W}_1
D) \mathrm{W}_2<4 \mathrm{~W}_1
926
Medium
A cylindrical rod is having temperatures $\theta_1 and \theta_2 at its ends. The rate of heat flow is 'Q' \mathrm{J}{\mathrm{s}}^{-1}$. All the linear dimensions of the rod are doubled by keeping the temperatures constant. What is the new rate of flow of heat?
Options:
A) \frac{Q}{2}
B) \frac{Q}{4}
C) 2 \mathrm{Q}
D) \frac{3 Q}{2}
927
Medium
For a gas molecule with 6 degrees of freedom, which one of the following relation between gas constant '$\mathrm{R}' and molar specific heat '\mathrm{C}_{\mathrm{v}}$' is correct?
Options:
A) R=\frac{C_v}{3}
B) \mathrm{R}=\frac{5 \mathrm{C}_{\mathrm{v}}}{4}
C) \mathrm{R}=\frac{\mathrm{C}_{\mathrm{v}}}{2}
D) \mathrm{R}=\frac{3 \mathrm{C}_{\mathrm{v}}}{4}
928
Medium
What is the ratio of the velocity of sound in hydrogen $\left(\gamma=\frac{7}{5}\right) to that in helium \left(\gamma=\frac{5}{3}\right)$ at the same temperature? (Molecular weight of hydrogen and helium is 2 and 4 respectively.)
Options:
A) \frac{\sqrt{42}}{5}
B) \frac{5}{\sqrt{42}}
C) \frac{\sqrt{21}}{5}
D) \frac{5}{\sqrt{21}}
929
Medium
Equal volumes of two gases are kept in different containers having densities in the ratio 1 : 16. They exert equal pressures on the wall of their respective containers. Then the ratio of their r.m.s. velocities is
Options:
A) 16 : 1
B) 1 : 8
C) 4 : 1
D) 1 : 12
930
Medium
In thermodynamics, for an isochoric process, which one of the following statement is INCORRECT?
Options:
A) Energy exchanged is used to do work and also to change internal energy.
B) No work is done in the process.
C) It is a constant volume process.
D) Temperature of the system changes during the process.
931
Medium
If '$\mathrm{E}' is the kinetic energy per mole of an ideal gas and '\mathrm{T}$' is the absolute temperature, then the universal gas constant is given as
Options:
A) \frac{2 \mathrm{~T}}{3 \mathrm{E}}
B) \frac{2 \mathrm{E}}{3 \mathrm{~T}}
C) \frac{3 \mathrm{~T}}{2 \mathrm{E}}
D) \frac{3 \mathrm{E}}{2 \mathrm{~T}}
932
Medium
Two rods of same length and material are joined end to end. They transfer heat in 8 second. When they are joined in parallel they transfer same amount of heat in same conditions in time
Options:
A) 3 s
B) 2 s
C) 1 s
D) 4 s
933
Medium
The molar specific heats of an ideal gas at constant pressure and volume are denoted by '$\mathrm{C}_{\mathrm{p}}' and 'C_v' respectively. If \gamma=\frac{C_p}{C_v} and 'R' is universal gas constant, then C_v$ is equal to
Options:
A) \frac{\mathrm{R}}{\gamma-1}
B) \gamma \mathrm{R}
C) \frac{1+\gamma}{1-\gamma}
D) \frac{\gamma-1}{\mathrm{R}}
934
Medium
The temperature difference bewtween two sides of metal plate, $3 \mathrm{~cm} thick is 15^{\circ} \mathrm{C}. Heat is transmitted through plate at the rate of 900 \mathrm{~kcal} per minute per \mathrm{m}^2$ at steady state. The thermal conductivity of metal is
Options:
A) 1.8 \times 10^{-2} \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}
B) 4.5 \times 10^{-2} \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}
C) 3 \times 10^{-2} \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}
D) 6 \times 10^{-2} \frac{\mathrm{kcal}}{\mathrm{ms}^{\circ} \mathrm{C}}
935
Medium
A black body has maximum wavelength '$\lambda_{\mathrm{m}}' at temperature 2000 \mathrm{~K}. Its corresponding wavelength at temperature 3000 \mathrm{~K}$ will be
Options:
A) \frac{4 \lambda_m}{9}
B) \frac{2 \lambda_m}{3}
C) \frac{3 \lambda_{\mathrm{m}}}{2}
D) \frac{9}{4} \lambda_{\mathrm{m}}
936
Medium
A monoatomic gas at pressure '$\mathrm{P}' having volume '\mathrm{V}' expands isothermally to a volume 2 \mathrm{~V} and then adiabatically to a volume 16 \mathrm{~V}. The final pressure of the gas is \left(\gamma=\frac{5}{3}\right)
Options:
A) \frac{P}{64}
B) \frac{\mathrm{P}}{128}
C) \frac{P}{8}
D) \frac{\mathrm{P}}{32}
937
Medium
A black reactangular surface of area '$a' emits energy '\mathrm{E}' per second at 27^{\circ} \mathrm{C}. If length and breadth is reduced to \left(\frac{1}{3}\right)^{\text {rd }} of initial value and temperature is raised to 327^{\circ} \mathrm{C}$ then energy emitted per second becomes
Options:
A) \frac{16 \mathrm{E}}{9}
B) \frac{8 \mathrm{E}}{9}
C) \frac{4 \mathrm{E}}{9}
D) \frac{12 \mathrm{E}}{9}
938
Medium
Find the value of $-197^\circ$C temperature in Kelvin.
Options:
A) 47 K
B) 76 K
C) 470 K
D) 760 K
939
Medium
Which one of the following equations specifies an isobaric process? $[Q= heat supplied \Delta P, \Delta V and \Delta T$ are change in pressure, volume and temperature respectively]
Options:
A) Q=0
B) \Delta \mathrm{T}=0
C) \Delta \mathrm{V}=0
D) \Delta \mathrm{P}=0
940
Medium
A perfect gas of volume 10 litre n compressed isothermally to a volume of 1 litre. The rms speed of the molecules will
Options:
A) decrease 5 times
B) remain unchanged
C) increase 5 times
D) increase 10 times
941
Medium
The relation obeyed by a perfect gas during an adiabatic process is $\mathrm{PV}^{3 / 2}. The initial temperature of the gas is '\mathrm{T}$'. When the gas is compressed to half of its Initial volume, the final temperature of the gas is
Options:
A) 2 \sqrt{2} \mathrm{~T}
B) 4 \mathrm{~T}
C) \sqrt{2} \mathrm{~T}
D) 2 \mathrm{~T}
942
Medium
A black rectangular surface of area '$\mathrm{A}' emits energy '\mathrm{E}' per second at 27^{\circ} \mathrm{C}. If length and breadth is reduced to (1 / 3)^{\text {rd }} of its initial value and temperature is raised to 327^{\circ} \mathrm{C}$ then energy emitted per second becomes
Options:
A) \frac{20 \mathrm{E}}{9}
B) \frac{8 \mathrm{E}}{9}
C) \frac{16 \mathrm{E}}{9}
D) \frac{4 \mathrm{E}}{9}
943
Medium
A monoatomic gas is suddenly compressed to (1/8)th of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is ($\gamma=5/3$)
Options:
A) 32
B) 8
C) \frac{40}{3}
D) \frac{24}{5}
944
Medium
A conducting rod of length $1 \mathrm{~m} has area of cross-section 10^{-3} \mathrm{~m}^2. One end is immersed in baiting water \left(100^{\circ} \mathrm{C}\right) and the other end in Ice \left(0^{\circ} \mathrm{C}\right). If coefficient of thermal conductivity of \mathrm{rod} is 96 \mathrm{~cal} / \mathrm{sm}^{\circ} \mathrm{C} and latent heat for ice is 8 \times 10^{-4} \mathrm{cal} / \mathrm{kg}$ then the amount of ice which will melt in one minute is
Options:
A) 5.4 \times 10^{-3} \mathrm{~kg}
B) 7.2 \times 10^{-3} \mathrm{~kg}
C) 1.8 \times 10^{-3} \mathrm{~kg}
D) 3.6 \times 0^{-3} \mathrm{~kg}
945
Medium
Two stars 'P' and 'Q' emit yellow and blue light respectively. The relation between their temperatures $\left(\mathrm{T}_{\mathrm{P}}\right. and \left.\mathrm{T}_{\mathrm{Q}}\right)$ is
Options:
A) \mathrm{T_P=T_Q}
B) \mathrm{T}_{\mathrm{P}}=\frac{\mathrm{T}_{\mathrm{Q}}}{2}
C) \mathrm{T}_{\mathrm{P}}>\mathrm{T}_{\mathrm{Q}}
D) \mathrm{T}_{\mathrm{P}}<\mathrm{T}_{\mathrm{Q}}
946
Medium
A perfectly black body emits a radiation at temperature 'T$_1' K. If it is to radiate at 16 times this power, its temperature 'T_2$' K should be
Options:
A) 8T$_1
B) 4T$_1
C) 2T$_1
D) 16T$_1
947
Medium
One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $T \propto {1 \over {\sqrt V }}. The value of \gamma for the gas is (\gamma = {{{C_p}} \over {{C_v}}},V = $ Volume of the gas)
Options:
A) 1.8
B) 1.5
C) 1.3
D) 1.4
948
Medium
On an imaginary linear scale of temperature (called 'W' scale) the freezing and boiling points of water are 39$^\circ W and 239^\circ W respectively. The temperature on the new scale corresponding to 39^\circ$C temperature on Celsius scale will be
Options:
A) 139$^\circ$ W
B) 78$^\circ$ W
C) 117$^\circ$ W
D) 200$^\circ$ W
949
Medium
Specific heats of an ideal gas at constant pressure and volume are denoted by $\mathrm{C}_{\mathrm{p}} and \mathrm{C}_{\mathrm{v}} respectively. If \gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}} and \mathrm{R} it's the universal gas constant then \mathrm{C}_{\mathrm{v}}$ is equal to
Options:
A) \frac{(\gamma-1)}{(\gamma+1)}
B) \frac{(\gamma-1)}{\mathrm{R}}
C) \mathrm{R} \gamma
D) \frac{R}{(\gamma-1)}
950
Medium
For a monoatomic gas, work done at constant pressure is W. The heat supplied at constant volume for the same rise in temperature of the gas is
Options:
A) W
B) \mathrm{\frac{5W}{2}}
C) \mathrm{\frac{W}{2}}
D) \mathrm{\frac{3W}{2}}
951
Medium
The root mean square velocity of molecules of a gas is 200 \mathrm{~m} / \mathrm{s}. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?
Options:
A) 50 \mathrm{~m} / \mathrm{s}
B) 200 \mathrm{~m} / \mathrm{s}
C) 100 \mathrm{~m} / \mathrm{s}
D) \frac{100}{\sqrt{2}} \mathrm{~m} / \mathrm{s}
952
Medium
Two spherical black bodies of radius $r_1 and r_2 with surface temperature T_1 and T_2 respectively, radiate same power, then r_1: r_2$ is
Options:
A) \left(\frac{T_2}{T_1}\right)^4
B) \left(\frac{T_2}{T_1}\right)^2
C) \left(\frac{T_1}{T_2}\right)^2
D) \left(\frac{T_1}{T_2}\right)^4
953
Medium
A diatomic gas undergoes adiabatic change. Its pressure $p and temperature T are related as p \propto T^x, where x$ is
Options:
A) 3.0
B) 1.5
C) 2.5
D) 3.5
954
Medium
For a gas, $\frac{R}{C_V}=0.4, where R is universal gas constant and C_V$ is the molar specific heat at constant volume. The gas is made up of molecules, which are
Options:
A) polyatomic
B) rigid diatomic
C) monoatomic
D) non-rigid diatomic
955
Medium
A monoatomic gas of pressure $p having volume V expands isothermally to a volume 2V and then adiabatically to a volume 16 \mathrm{~V}. The final pressure of the gas is (ratio of specific heats =\frac{5}{3}
Options:
A) \frac{p}{8}
B) \frac{p}{16}
C) \frac{p}{64}
D) \frac{p}{32}
956
Medium
The SI unit and dimensions of Stefan's constant \sigma in case of Stefan's law of radiation is
Options:
A) \frac{\mathrm{J}}{\mathrm{m}^3 \mathrm{~s}^4},
\left[M^1 L^0 T^{-3} K^{-4}\right]
B) \frac{\mathrm{J}}{\mathrm{m}^2 \mathrm{~s}^4 \mathrm{~K}}, \left[M^1 L^0 T^{-3} K^3\right]
C) \frac{\mathrm{J}}{\mathrm{m}^3 \mathrm{~s} \mathrm{~K}^4},\left[\mathrm{M}^{1} \mathrm{L}^0 \mathrm{~T}^{-3} \mathrm{~K}^4\right]
D) \frac{\mathrm{J}}{\mathrm{m}^2 \mathrm{~s} \mathrm{~K}^4},\left[\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^{-3} \mathrm{~K}^{-4}\right]
957
Medium
The rms speed of oxygen molecule in a gas is u, If the temperature is doubled and the molecules dissociates into two atoms, the rms speed will be
Options:
A) 4u
B) u
C) 2u
D) u\sqrt2
958
Medium
The equation of state for 2 g of oxygen at a pressure ' P ' and temperature ' T, when occupying a volume ' V ' will be
Options:
A) p V=16 R T
B) p V=R T
C) p V=\frac{1}{16} R T
D) p V=2 R T
959
Medium
The maximum wavelength of radiation emitted by a star is 289.8 nm . Then intensity of radiation for the star is (Given : Stefan's constant =5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}, Wien's constant, b=2898 \mu \mathrm{mK} )
Options:
A) 5.67 \times 10^{-12} \mathrm{Wm}^{-2}
B) 10.67 \times 10^{14} \mathrm{Wm}^{-2}
C) 5.67 \times 10^8 \mathrm{Wm}^{-2}
D) 10.67 \times 10^7 \mathrm{Wm}^{-2}
960
Medium
If ' C_P ' and ' C_V ' are molar specific heats of an ideal gas at constant pressure and volume respectively. If ' \lambda ' is the ratio of two specific heats and ' R ' is universal gas constant then ' C_p ' is equal to
Options:
A) \frac{R \gamma}{\gamma-1}
B) \gamma R
C) \frac{1+\gamma}{1-\gamma}
D) \frac{R}{\gamma-1}
961
Medium
A clock pendulum having coefficient of linear expansion. \alpha=9 \times 10^{-7} /{ }^{\circ} \mathrm{C}^{-1} has a period of 0.5 s at 20^{\circ} \mathrm{C}. If the clock is used in a climate, where the temperature is 30^{\circ} \mathrm{C}, how much time does the clock lose in each oscillation? ( g= constant)
Options:
A) 25 \times 10^{-7} \mathrm{~s}
B) 5 \times 10^{-7} \mathrm{~s}
C) 1.125 \times 10^{-6} \mathrm{~s}
D) 2.25 \times 10^{-6} \mathrm{~s}
962
Medium
If \alpha is the coefficient of performance of a refrigerator and ' Q ' is heat released to the hot reservoir, then the heat extracted from the cold reservoir ' Q_2 ' is
Options:
A) \frac{\alpha Q_1}{\alpha-1}
B) \frac{\alpha-1}{\alpha} Q_1
C) \frac{\alpha Q_1}{1+\alpha}
D) \frac{1+\alpha}{\alpha} Q_1
963
Medium
Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2 K while that in the middle has thermal conductivity K. The left end of the combination is maintained at temperature 3 T and the right end at T. The rods are thermally insulated from outside. In steady state, temperature at the left junction is T_1 and that at the right junction is T_2. The ratio T_1 / T_2 is
Options:
A) \frac{5}{3}
B) \frac{5}{4}
C) \frac{3}{2}
D) \frac{4}{3}
964
Medium
A container has two chambers of volumes V_1=2 litres and V_2=3 litres separated by a partition made of a thermal insulator. The chambers contain n_1=5 and n_2=4 moles of ideal gas at pressures p_1=1 \mathrm{~atm} and p_2=2 \mathrm{~atm}, respectively. When the partition is removed, the mixture attains an equilibrium pressure of
Options:
A) 1.4 atm
B) 1.8 atm
C) 1.3 atm
D) 1.6 atm
965
Medium
An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressures at temperature 27^{\circ} \mathrm{C}. The mass of the oxygen withdrawn from the cylinder is nearly equal to: [Given, R=\frac{100}{12} \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, and molecular mass of \mathrm{O}_2=32,1 atm pressure =1.01 \times 10^5 \mathrm{~N} / \mathrm{m}]
Options:
A) 0.116 kg
B) 0.156 kg
C) 0.125 kg
D) 0.144 kg
966
Hard
Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius r_A and r_B, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas A and B are displaced by 16 cm and 9 cm , respectively. If the change in their internal energy is the same, then the ratio \frac{r_A}{r_B} is equal to
Options:
A) \frac{2}{\sqrt{3}}
B) \frac{\sqrt{3}}{2}
C) \frac{4}{3}
D) \frac{3}{4}
967
Medium
Given below are two statements: One is labelled as Assertion $\mathbf{A} and the other is labelled as Reason \mathbf{R}$. Assertion A: Houses made of concrete roofs overlaid with foam keep the room hotter during summer. Reason R: The layer of foam insulation prohibits heat transfer, as it contains air pockets. In the light of the above statements, choose the correct answer from the options given below.
Options:
A) A is true but R is false.
B) A is false but R is true.
C) Both A and R are true and R is the correct explanation of A.
D) Both A and R true but R is NOT the correct explanation of A.
968
Medium
The equilibrium state of a thermodynamic system is described by A. Pressure B. Total heat C. Temperature D. Volume E. Work done Choose the most appropriate answer from the options given below.
Options:
A) A, B and E only
B) B, C and D only
C) A, B and C only
D) A, C and D only
969
Medium
According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant $\gamma=\frac{C_p}{C_v} is (C_P where C_V$ are the specific heat capacities of the gas at constant pressure and constant volume, respectively):
Options:
A) \frac{4+3 \gamma}{\gamma-1}
B) \frac{3+4 \gamma}{\gamma-1}
C) \frac{4-3 \gamma}{\gamma-1}
D) \frac{3-4 \gamma}{\gamma-1}
970
Medium
A thermodynamic system is taken through the cycle $abcda. The work done by the gas along the path b c$ is:
Options:
A) Zero
B) 30 J
C) -$90 J
D) -$60 J
971
Medium
The following graph represents the $T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures P_1, P_2 and P_3$ compared with those of Charles's law represented as dotted lines. Then the correct relation is :
Options:
A) P_3>P_2>P_1
B) P_1>P_3>P_2
C) P_2>P_1>P_3
D) P_1>P_2>P_3
972
Medium
For the given cycle, the work done during isobaric process is:
Options:
A) 200 J
B) Zero
C) 400 J
D) 600 J
973
Medium
A container of volume $200 \mathrm{~cm}^3 contains 0.2 mole of hydrogen gas and 0.3 mole of argon gas. The pressure of the system at temperature 200 \mathrm{~K} (\mathrm{R}=8.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$) will be :-
Options:
A) 6.15 \times 10^5 \mathrm{~Pa}
B) 6.15 \times 10^4 \mathrm{~Pa}
C) 4.15 \times 10^5 \mathrm{~Pa}
D) 4.15 \times 10^6 \mathrm{~Pa}
974
Medium
The temperature of a gas is $-50^{\circ} \mathrm{C}. To what temperature the gas should be heated so that the rms speed is increased by 3$ times?
Options:
A) 3295^{\circ} \mathrm{C}
B) 3097 \mathrm{~K}
C) 223 \mathrm{~K}
D) 669^{\circ} \mathrm{C}
975
Medium
A Carnot engine has an efficiency of $50 \% when its source is at a temperature 327^{\circ} \mathrm{C}$. The temperature of the sink is :-
Options:
A) 15^{\circ} \mathrm{C}
B) 100^{\circ} \mathrm{C}
C) 200^{\circ} \mathrm{C}
D) 27^{\circ} \mathrm{C}
976
Medium
An ideal gas follows a process described by the equation $P{V^2} = C from the initial ({P_1},\,{V_1},\,{T_1}) to final ({P_2},\,{V_2},\,{T_2})$ thermodynamic states, where C is a constant. Then
Options:
A) If ${P_1} > {P_2} then {V_1} > {V_2}
B) If ${P_1} > {P_2} then {T_1} < {T_2}
C) If ${V_2} > {V_1} then {T_2} > {T_1}
D) If ${V_2} > {V_1} then {T_2} < {T_1}
977
Medium
Two rods one made of copper and other made of steel of same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are 385 J s$-1 K-1 m-1 and 50 J s-1 K-1 m-1 respectively. The free ends of copper and steel are held at 100^\circC and 0^\circ$C respectively. The temperature at the junction is, nearly :
Options:
A) 88.5^\circ C
B) 12^\circ C
C) 50^\circ C
D) 73^\circ C
978
Medium
Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following is :
Options:
A) The root mean square speed of sulfur hexafluoride is the largest
B) All vessels contain unequal number of respective molecules
C) The root mean square speed of molecules is same in all three cases
D) The root mean square speed of helium is the largest
979
Medium
An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is
Options:
A) 1
B) 2
C) 3
D) 4
980
Medium
The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is
Options:
A) 5.6 $\times$ 106 m3
B) 5.6 $\times$ 103 m3
C) 5.6 $\times 10-$3 m3
D) 5.6 m3
981
Medium
A cup of coffee cools from 90$^\circC to 80^\circC in t minutes, when the room temperature is 20^\circC. The time taken by a similar cup of coffee to cool from 80^\circC to 60^\circC at a room temperature same at 20^\circ$C is :
Options:
A) {5 \over {13}}$t
B) {13 \over {10}}$t
C) {13 \over {5}}$t
D) {10 \over {13}}$t
982
Medium
Match Column - I and Column - II and choose the correct match from the given choices. Column - I Column - II (A) Root mean square speed of gas molecules (P) ${1 \over 3}nm{\overline v ^2} (B) Pressure exerted by ideal gas (Q) \sqrt {{{3RT} \over M}} (C) Average kinetic energy of a molecule (R) {5 \over 2}RT (D) Total internal energy of 1 mole of a diatomic gas (S) {3 \over 2}{k_B}T
Options:
A) (A) - (R), (B) - (Q), (C) - (P), (D) - (S)
B) (A) - (R), (B) - (P), (C) - (S), (D) - (Q)
C) (A) - (Q), (B) - (R), (C) - (S), (D) - (P)
D) (A) - (Q), (B) - (P), (C) - (S), (D) - (R)
983
Medium
The average thermal energy for a mono-atomic gas is : (kB is Boltzmann constant and T absolute temperature)
Options:
A) {3 \over 2}{k_B}T
B) {5 \over 2}{k_B}T
C) {7 \over 2}{k_B}T
D) {1 \over 2}{k_B}T
984
Medium
The mean free path for a gas, with molecular diameter d and number density n can be expressed as :
Options:
A) {1 \over {\sqrt 2 n\pi {d^2}}}
B) {1 \over {\sqrt 2 {n^2}\pi {d^2}}}
C) {1 \over {\sqrt 2 {n^2}{\pi ^2}{d^2}}}
D) {1 \over {\sqrt 2 n\pi d}}
985
Medium
A cylinder contains hydrogen gas at pressure 249 kPa and temperature 27$^\circ $CIts density is : (R = 8.3 J mol-1 K-1)
Options:
A) 0.2 kg/m3
B) 0.1 kg/m3
C) 0.02 kg/m3
D) 0.5 kg/m3
986
Medium
The quantities of heat required to raise the temperature of two solid copper spheres of radii r1 and r2 (r1 = 1.5r2) through 1 K are in the ratio :
Options:
A) {9 \over 4}
B) {3 \over 2}
C) {5 \over 3}
D) {27 \over 8}
987
Medium
Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire systems is thermally insulated. The stop cock is suddenly opened. The Process is :
Options:
A) adiabatic
B) isochoric
C) isobaric
D) isothermal
988
Medium
In which of the following processes, heat is neither absorbed nor released by a system?
Options:
A) adiabatic
B) isobaric
C) isochoric
D) isothermal
989
Medium
Increase in tempertaure of a gas filled in a container would lead to :
Options:
A) increase in its kinetic energy
B) decrease in intermolecular distance
C) decrease in its pressure
D) increase in its mass
990
Medium
The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is
Options:
A) {2 \over 5}
B) {2 \over 3}
C) {1 \over 3}
D) {2 \over 7}
991
Medium
A sample of 0.1 g of water at 100°C and normal pressure (1.013 × 105 N m–2) requires 54 cal of heat energy to convert to steam at 100°C. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample, is
Options:
A) 104.3 J
B) 208.7 J
C) 42.2 J
D) 84.5 J
992
Medium
At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? (Given : Mass of oxygen molecule (m) = 2.76 × 10–26 kg, Boltzmann’s constant kB = 1.38 × 10–23 J K–1)
Options:
A) 2.508 × 104 K
B) 8.360 × 104 K
C) 5.016 × 104 K
D) 1.254 × 104 K
993
Medium
The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is
Options:
A) 26.8%
B) 20%
C) 6.25%
D) 12.5%
994
Medium
Thermodynamic processes are indicated in the following diagram. Match the following Column-1 Column-2 P. Process I A. Adiabatic Q. Process II B. Isobaric R. Process III C. Isochoric S. Process IV D. Isothermal
Options:
A) P $ \to C, Q \to A, R \to D, S \to $ B
B) P $ \to C, Q \to D, R \to B, S \to $ A
C) P $ \to D, Q \to B, R \to A, S \to $ C
D) P $ \to A, Q \to C, R \to D, S \to $ B
995
Medium
A carnot engine having an efficiency of ${1 \over {10}}$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is
Options:
A) 90 J
B) 99 J
C) 100 J
D) 1 J
996
Medium
A gas mixture consists of 2 moles of O2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
Options:
A) 15 RT
B) 9 RT
C) 11 RT
D) 4 RT
997
Medium
A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas ?
Options:
A) P/(kT)
B) Pm/(kT)
C) P/(KTV)
D) mkT
998
Medium
One mole of an ideal monatomic gas undergoes a process described by the equation PV3 = constant. The heat capacity of the gas during this process is
Options:
A) {3 \over 2}$ R
B) {5 \over 2}$ R
C) 2R
D) R
999
Medium
The temperature inside a refrigerator is t2 oC. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be
Options:
A) {{{t_1}} \over {{t_1} - {t_2}}}
B) {{{t_1} + 273} \over {{t_1} - {t_2}}}
C) {{{t_2} + 273} \over {{t_1} - {t_2}}}
D) {{{t_1} + {t_2}} \over {{t_1} + 273}}
1000
Medium
A refrigerator works between 4oC and 30oC. It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant. The power required is (Take 1 cal = 4.2 Joules)
Options:
A) 236.5 W
B) 2365 W
C) 2.365 W
D) 23.65 W
1000
Total Questions
164
Easy
816
Medium
20
Hard
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