JEE Advanced 2025 Paper 2 Q08 Physics Thermal Physics Kinetic Theory of Gases Medium

JEE Advanced 2025 Paper 2 · Q08 · Kinetic Theory of Gases

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of $1000$ K is $0.4$. It extracts $150$ J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance $10$. The hot reservoir of the heat pump is at a temperature of $300$ K. Which of the following statements is/are correct:

  1. A. Work extracted from the Carnot engine in one cycle is $60$ J.
  2. B. Temperature of the cold reservoir of the Carnot engine is $600$ K.
  3. C. Temperature of the cold reservoir of the heat pump is $270$ K.
  4. D. Heat supplied to the hot reservoir of the heat pump in one cycle is $540$ J.
JEE Advanced multi-correct — pick every correct option, then check.
Reveal answer + step-by-step solution

Correct answer:A, B, C

Solution

Carnot engine: $W = \eta\,Q_h = 0.4 \times 150 = 60$ J. (A) TRUE. $T_{\text{cold}}/T_{\text{hot}} = 1 - \eta = 0.6 \to T_{\text{cold}} = 600$ K. (B) TRUE. Heat pump (heating COP $= 10 = Q_{\text{hot,pump}}/W_{\text{input}}$): $Q_{\text{hot,pump}} = 10 \times 60 = 600$ J. (D) FALSE (claims $540$ J). $Q_{\text{cold,pump}} = Q_{\text{hot,pump}} - W_{\text{input}} = 600 - 60 = 540$ J. For a Carnot heat pump, $T_{\text{cold,pump}}/T_{\text{hot,pump}} = Q_{\text{cold,pump}}/Q_{\text{hot,pump}} = 540/600 = 0.9 \to T_{\text{cold,pump}} = 270$ K. (C) TRUE. Correct: (A), (B), (C).

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