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The temperature of source and sink of a heat engine are 127°C and 27°C respectively. An inventor claims its efficiency to be 26%, then:

1. it is impossible
2. it is possible with high probability
3. it is possible with low probability
4. data are insufficient

Correct answer: it is possible with high probability

Solution

The Carnot efficiency is calculated as 1 - (T_sink/T_source), where temperatures are in Kelvin. Converting to Kelvin, T_source = 400 K and T_sink = 300 K. The maximum efficiency is 1 - (300/400) = 0.25 or 25%. Since the claimed efficiency of 26% exceeds this, it is impossible.

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