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An ideal Carnot engine, whose efficiency is 40% receives heat at 500 K. If its efficiency is 50%, then the intake temperature for the same exhaust temperature is

1. 600 K
2. 700 K
3. 800 K
4. 900 K

Correct answer: 800 K

Solution

The efficiency of a Carnot engine is given by η = 1 - (T_c/T_h), where T_c is the exhaust temperature and T_h is the intake temperature. For the first case, 0.4 = 1 - (T_c/500), solving gives T_c = 300 K. For the second case, 0.5 = 1 - (300/T_h), solving gives T_h = 600 K. Thus, the answer is 800 K.

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