JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Heat & Thermodynamics

A Carnot engine takes 5000 kcal of heat from a reservoir at

72 7^{\circ}

C and gives heat to a sink at

12 7^{\circ}

C. The work done by the engine is :

(A) $3 \times 1 0^{6}$ J
(B)Zero
(C) $12.6 \times 1 0^{6}$ J✓ Correct
(D) $8.4 \times 1 0^{6}$ J

Answer: (C)

Solution

Carnot efficiency:

η = 1 - \frac{T _{L}}{T _{H}} = 1 - \frac{400}{1000} = 0.6

. Work done:

W = η Q_{H} = 0.6 \times 5000

kcal

= 3000

kcal

= 3000 \times 4.2 \times 1 0^{3}

= 12.6 \times 1 0^{6}

J. (Note:

T_{H} = 727 + 273 = 1000

T_{L} = 127 + 273 = 400

JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Single correct option

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