JEE Advanced · 2025 · 18 May 2025 · Paper 2 · Heat & Thermodynamics

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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:

(A)Work extracted from the Carnot engine in one cycle is 60 J.✓ Correct
(B)Temperature of the cold reservoir of the Carnot engine is 600 K.✓ Correct
(C)Temperature of the cold reservoir of the heat pump is 270 K.✓ Correct
(D)Heat supplied to the hot reservoir of the heat pump in one cycle is 540 J.

Answer: (A), (B), (C)

Solution

Carnot engine:

W = η Q_{1} = 0.4 \times 150 = 60 J

η = 1 - \frac{T _{2}}{T _{1}} ⟹ 0.4 = 1 - \frac{T _{2}}{1000} ⟹ T_{2} = 600 K

Heat pump:

COP = \frac{Q _{3}}{W} = 10 ⟹ Q_{3} = 10 \times 60 = 600 J

COP = \frac{T _{3}}{T _{3} - T _{4}} = 10 ⟹ \frac{300}{300 - T _{4}} = 10 ⟹ T_{4} = 270 K

Options (A), (B), (C) are correct. Option (D) states 540 J, but the correct value is 600 J.

JEE Advanced · 2025 · 18 May 2025 · Paper 2 · One or more correct options

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JEE Advanced · 2025 · 18 May 2025 · Paper 2 · Heat & Thermodynamics

Solution

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