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An engine has an efficiency of 1/6. When the temperature of sink is reduced by 62°C, its efficiency is doubled. Temperature of the source is

1. 37°C
2. 62°C
3. 99°C
4. 124°C

Correct answer: 99°C

Solution

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

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