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Q. 34

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 596

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Short Answer

A Carnot heat engine with thermal efficiency is run backward as a Carnot refrigerator. What is the refrigerator’s coefficient of performance?

Refrigerator's coefficient of performance will be 2.

See the step by step solution

Step by Step Solution

Step 1 : Given Information

The efficiency of Carnot engine

Step 2 : Explanation

Formula used :

We know that the thermal efficiency of heat engine is the ratio of the work done by the engine to the heat drawn out of the hot reservoir.

Here, is the temperature of the hot reservoir that is source and is the temperature of cold reservoir i.e. sink. The efficiency is given by

Therefore,

Coefficient of performance of refrigerator is defined as the reciprocal of the ideal efficiency of the Carnot engine, where k is the coefficient of performance of a refrigerator.

Substituting the value of in above equation, the coefficient of performance of a refrigerator is calculated as

Step : 3 Calculation

Substituting the value of in the above equation

Conclusion :

Refrigerator coefficient of performance is .

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