Answer to Question #5945 in Molecular Physics | Thermodynamics for Taylor
Question #5945
In each cycle of a Carnot engine, 242 J of heat is absorbed from the high-temperature reservoir and 121 J is exhausted to the low-temperature reservoir. What is the efficiency of the engine?
Expert's answer
The efficiency of engine is defined as ratio of the useful work done to the heat provided. We should use the following formula:
<img style="width: 223px; height: 43px;" src="data:image/png;base64,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" alt="">
Thus for our task we have
Efficiency = Wexh/Winp = 121/242 = 0.5.
Often efficiency is written in percentages: in our case we have 50%
<img style="width: 223px; height: 43px;" src="data:image/png;base64,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" alt="">
Thus for our task we have
Efficiency = Wexh/Winp = 121/242 = 0.5.
Often efficiency is written in percentages: in our case we have 50%
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