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## Saturday, 27 August 2011

### 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 $W=\eta\cdot2000\,J=400\,J.$

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