Physics GRE - #26

An engine absorbs heat at a temperature of 727 degrees Celsius and exhausts heat at a temperature of 527 degrees Celcius. If the engine operates at maximum possible efficiency, for 2000 J of heat the amount of work the engine performs is most nearly:

1. 400 J
2. 1450 J
3. 1600 J
4. 2000 J
5. 2760 J

Solution :

Choice 1 is the answer.

Recall that the Carnot Efficiency of a heat engine is: \[\eta=1-\frac{T_C}{T_H}\] where $T_C$ and $T_H$ are in Kelvins. For this problem, the efficiency is: \[\eta\approx1-\frac{527+273}{727+273}=1-\frac{800}{1000}=0.2.\] Thus the maximum amount of work we can get is \[W=\eta\cdot2000\,J=400\,J.\]