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A Carnot engine and a Carnot refrigerator operate between

Chapter 18, Problem 96GP

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QUESTION:

Problem 96GP

A Carnot engine and a Carnot refrigerator operate between the same two temperatures. Show that the coefficient of performance, COP, for the refrigerator is related to the efficiency, e,of the engine by the following expression; COP = (1 – e)/e.

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QUESTION:

Problem 96GP

A Carnot engine and a Carnot refrigerator operate between the same two temperatures. Show that the coefficient of performance, COP, for the refrigerator is related to the efficiency, e,of the engine by the following expression; COP = (1 – e)/e.

ANSWER:

Solution 96GP

Step 1 of 2

Efficiency of Carnot engine,

Where,  - Temperature of the cold reservoir

              -  Temperature of the hot reservoir

The coefficient of performance,

 - Heat in the cold reservoir

 - Work done

Where  - Heat in the hot reservoir

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