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MCQEasyJEE 2023Second Law & Heat Engines

JEE Physics 2023 Question with Solution

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Efficiency of a reversible heat engine will be highest at −273∘C-273^\circ \text{C} temperature of cold reservoir.

Reason R: The efficiency of Carnot’s engine depends not only on the temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as: η=(1−T2T1)\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:

  • 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

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Assertion A says that efficiency of a reversible heat engine is highest when the cold reservoir is at −273∘C-273^\circ \text{C}. Reason R gives the Carnot efficiency relation.

Find: Which option correctly describes the truth of Assertion A and Reason R, and whether R explains A.

For a reversible heat engine, the efficiency is

η=1−T2T1\eta = 1 - \frac{T_2}{T_1}

where T2T_2 is the temperature of the cold reservoir and T1T_1 is the temperature of the hot reservoir.

Assertion A is true because the efficiency becomes maximum when the cold reservoir temperature is minimum, and the minimum possible temperature is 0 K0 \, \text{K} or −273∘C-273^\circ \text{C}.

Reason R is also true because the efficiency of a Carnot engine depends on both the hot and cold reservoir temperatures according to the given formula.

From the solution, the conclusion is that R does not directly explain why the efficiency is highest specifically at −273∘C-273^\circ \text{C}, even though both statements are true.

Therefore, the correct option is B.

Direct Interpretation of the Given Explanation

Given: The source solution states that Assertion A is true and Reason R is true.

Find: Whether R is the correct explanation of A according to the provided solution.

The provided explanation says:

  1. Assertion A is true.
  2. Reason R is true.
  3. The formula
η=1−T2T1\eta = 1 - \frac{T_2}{T_1}

shows dependence on both temperatures. 4. The explanation then states that Reason R does not directly explain why efficiency is highest at −273∘C-273^\circ \text{C}.

Hence, based on the solution itself, the answer is taken as Both A and R are true but R is NOT the correct explanation of A.

Therefore, the correct option is B. The answer key indicates option D, but the solution explicitly identifies option B, and the solution is treated.

Common mistakes

  • Assuming that the answer must follow the answer key key without checking the solution. Here the solution explicitly marks option B. Always use the worked solution when they disagree.

  • Thinking that Carnot efficiency depends only on the cold reservoir temperature. This is incorrect because η=1−T2T1\eta = 1 - \frac{T_2}{T_1} depends on both T1T_1 and T2T_2. Always inspect both temperatures in the formula.

  • Confusing −273∘C-273^\circ \text{C} with an ordinary achievable laboratory temperature. It represents 0 K0 \, \text{K}, the limiting lowest temperature in thermodynamics. The statement is about the limiting case for maximum efficiency.

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