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Heat Engines

A heat engine...

Question

A heat engine takes in heat at 750 degrees Celsius and expels heat at 250 degrees Celsius. What is this engine's theoretically ideal (Carnot) efficiency?

A

33 percent

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B

67 percent

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C

49 percent

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D

300 percent

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E

23 percent

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Solution

The correct option is E 49 percent
Temperature of source $T_{H} = 750^{o} C = 750 + 273 = 1023$ K
Temperature of sink $T_{L} = 250^{o} C = 250 + 273 = 523$ K

Efficiency of engine $η = 1 - \frac{T_{L}}{T_{H}} = 1 - \frac{523}{1023} = 0.49$
Thus the engine is $49$ % efficient.

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