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A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by 62°C, the efficiency of the engine is doubled. The temperatures of the source and sink are

1. 99°C, 37°C
2. 80°C, 37°C
3. 95°C, 37°C
4. 90°C, 37°C

Correct answer: 99°C, 37°C

Solution

The efficiency of a Carnot engine is given by η = 1 - (T_sink / T_source). Initially, η = 1/6, which gives T_sink / T_source = 5/6. When T_sink is reduced by 62°C, the efficiency doubles to 2/6 = 1/3, leading to a new equation. Solving these equations gives T_source = 99°C and T_sink = 37°C.

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