Question 1: Thermodynamics & KTG

Question

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, T
A
and V
A
are constants.
The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.
![](https://imagex.cdn.examgoal.net/1kt3lws36/fc9cfa6e-dcef-4a10-b3e2-0fc14983556f/238e5120-0c4c-11ec-9b18-3116e26e14ca/file-1kt3lws37.jpeg)

Accepted Answer

(I) ${W_{1 	o 2 	o 3}} = {W_{1 	o 2}} + {W_{2 	o 3}} = {P_0}[2{V_0} - {V_0}] + 0 = {P_0}{V_0}$
${W_{1 	o 2 	o 3}} = {P_0}{V_0} = {{R{T_0}} \over 3}$ (I$ 	o $Q)
${U_{1 	o 2 	o 3}} = {3 \over 2}\left[ {{{3{P_0}} \over 2} 	imes 2{V_0} - {P_0}{V_0}} ight] = {3 \over 2} 	imes 2{P_0}{V_0} = 3{P_0}{V_0} = R{T_0}$(II$ 	o $R)
(III) ${Q_{1 	o 2 	o 3}} = {U_{1 	o 2 	o 3}} + {W_{1 	o 2 	o 3}} = R{T_0} + {{R{T_0}} \over 3} = {{4R{T_0}} \over 3}$(III$ 	o $S)
(IV) ${Q_{1 	o 2}} = n{C_p}\Delta T = n{5 \over 2}R({T_2} - {T_1}) = {5 \over 2}[{P_0}2{V_0} - {P_0}{V_0}] = {5 \over 2}{P_0}{V_0} = {5 \over 2}{{R{T_0}} \over 3} = {5 \over 6}{R_0}{T_0}$ (IV$ 	o $U)

Answer

I$ 	o $S, II $ 	o $ R, III $ 	o $ Q, IV $ 	o $ T

Answer

I $ 	o $ Q, II $ 	o $ R, III $ 	o $ P, IV $ 	o $ U

Answer

I $ 	o $ Q, II $ 	o $ S, III $ 	o $ R, IV $ 	o $ U

Answer

I $ 	o $ Q, II $ 	o $ R, III $ 	o $ S, IV $ 	o $ U

Thermodynamics & KTG

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