Question 318: Thermodynamics & KTG

Question

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 :

Accepted Answer

From Newton's cooling law $${{dQ} \over {dt}} =  - k(T - {T_s})$$ the statement A is correct.
For B
$$U = \sigma eA{T^4}$$
So, $${{{U_1}} \over {{U_2}}} = {\left( {{{283} \over {293}}} \right)^4} \simeq {1 \over {1.15}}$$
Statement B is correct
For C
$$\eta  = 1 - {{{T_1}} \over {{T_2}}} = 1 - {{100} \over {400}} = {3 \over 4}$$
So, efficiency is 75% C is correct
For D
From Newton's law of cooling $${{dQ} \over {dt}} =  - k(T - {T_s})$$
The statement is wrong.

Answer

A, B, C only

Answer

A, B only

Answer

A, C only

Answer

B, C, D only

Thermodynamics & KTG

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