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14 September, 10:05

A heat engine exhausts 8400 j of heat while performing 3600 j of useful work. what is the efficiency of this engine?

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  1. 14 September, 13:30
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    The maximum possible efficiency, i. e the efficiency of a Carnot engine, is give by the ratio of the absolute temperatures of hot and cold reservoir.

    η_max = 1 - (T_c/T_h)

    For this engine:

    η_max = 1 - [ (20 + 273) K / (600 + 273) K ] = 0.66 = 66%

    The actual efficiency of the engine is 30%, i. e.

    η = 0.3 ∙ 0.664 = 0.20 = 20 %

    On the other hand thermal efficiency is defined as the ratio of work done to the amount of heat absorbed from hot reservoir:

    η = W/Q_h

    So the heat required from hot reservoir is:

    Q_h = W/η = 1000J / 0.20 = 5000J
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