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JEE Main 2023 (30 Jan, Shift 2) · Heat Engines, Refrigerators & Second Law

Heat Engines, Refrigerators & Second Law question from JEE Main 2023 (30 Jan, Shift 2)

Q27JEE Main 2023 · 30 JAN · SHIFT 2Medium

Heat Engines, Refrigerators & Second Law

Given below are two statements: one is labelled as Assertion A\mathbf{A} and the other is labelled as Reason R\mathbf{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 the cold reservoir but it depends on the temperature of the 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

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Answer: (a)

  1. R: η=1−T2T1\eta = 1 - \frac{T_2}{T_1} depends on both T1T_1 and T2T_2, so R is true.
  2. A: at T2=−273∘C=0 KT_2 = -273^\circ\text{C} = 0\text{ K}, η=1−0=1\eta = 1 - 0 = 1, the highest possible value, so A is true (as an idealised limit).
  3. R's formula directly gives A.
  4. So the answer is (a) Both A and R are true and R is the correct explanation of A.
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