A Carnot engine whose source temperature is at 400 K takes 100 kcal of heat at this temperature in each cycle and gives 70 kcal to the sink. Calculate, (i) the temperature of the sink and (ii) the efficiency of the engine.
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Question

A Carnot engine whose source temperature is at 400 K takes 100 kcal of heat at this temperature in each cycle and gives 70 kcal to the sink. Calculate, (i) the temperature of the sink and (ii) the efficiency of the engine.

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G1 Physics · Accepted Answer

Use the first law Q=ΔU+W (W by the gas), ΔU=nCᵥΔT for an ideal gas, and the appropriate process relation. For Carnot devices, let T₁ be the cold-reservoir temperature and T₂ be the hot-reservoir temperature; η=1−T₁/T₂ and COP=T₁/(T₂−T₁). Evaluating the given data/statements gives A: 280 K, 30 %. Therefore the correct answer is A.