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A Carnot engine whose efficiency is 50% has an exhaust temperature of 500 K. If the efficiency is to be 60% with the same intake temperature, the exhaust temperature must be (in K)

1. 800
2. 200
3. 400
4. 600

Correct answer: 400

Solution

The efficiency of a Carnot engine is given by η = 1 - (T_c/T_h). For 50% efficiency, T_c = 500 K, so T_h = 1000 K. For 60% efficiency, η = 0.6 = 1 - (T_c/1000), solving gives T_c = 400 K.

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