JEE Advanced 2021 Paper 1 · Physics · Work, Energy and Power · hard

Two identical copper blocks, each of mass 2.0 kg and specific heat 400 J kg^-1K^-1 (independent of temperature), are initially at 300 K and 500 K and…

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Two identical copper blocks, each of mass

2.0\ \mathrm{kg}

and specific heat

400\ \mathrm{J\,kg^{-1}K^{-1}}

(independent of temperature), are initially at

300\ \mathrm{K}

and

500\ \mathrm{K}

and are isolated from the surroundings. Choose the correct statement(s).

A. If they are placed in direct thermal contact, the common final temperature is $400\ \mathrm{K}$ .
B. In this irreversible process the total entropy of the blocks increases by about $51.6\ \mathrm{J\,K^{-1}}$ .
C. If a reversible engine is run between the two blocks until they reach a common temperature, the maximum work obtained is about $20.3\ \mathrm{kJ}$ .
D. In the reversible-engine case the common final temperature is also $400\ \mathrm{K}$ .

Show answer and solution

Answer: A, B, C

(A) Energy conservation for equal heat capacities gives

T_f=(300+500)/2=400

K: correct. (B) For direct contact,

\Delta S=mc\ln\frac{T_f}{300}+mc\ln\frac{T_f}{500}=800\ln\frac{400^2}{300\times500}=800\times0.06454=51.6\ \mathrm{J\,K^{-1}}

, which is positive as the process is irreversible: correct. (C) For a reversible engine, total entropy is constant:

\ln\frac{T_f}{300}+\ln\frac{T_f}{500}=0

, so

T_f=\sqrt{300\times500}=387.3

K. Work equals heat drawn from the hot block minus heat dumped into the cold block:

W=800[(500-387.3)-(387.3-300)]=800\times25.4=20.3

kJ: correct. (D) The reversible final temperature is

387.3

K, lower than

400

K because work is extracted, so (D) is incorrect.

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