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Q. 47

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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 and an ordinary refrigerator with coefficient of performance operate between reservoirs at and . The work done by the Carnot heat engine drives the refrigerator. If the heat engine extracts of energy from the hot reservoir, how much energy does the refrigerator exhaust to the hot reservoir?

The refrigerator rejects thermal energy to the hot reservoir.

See the step by step solution

Step by Step Solution

Step : 1 Given Information

Temperatures of the hot and cold reservoirs between which Carnot heat engine operates are: and respectively. The amount of heat extracted from the hot reservoir (source) is . Let the amount of heat rejected to the cold reservoir (sink) is and the amount of work done by the Carnot heat engine is . This heat engine drives a refrigerator whose coefficient of performance is . Let the amount of heat extracted from the cold reservoir (source) is , and the amount of heat rejected to the hot reservoir (sink) is .

Step : 2 Calculation

Formula used:

Efficiency of a Carnot heat engine, ;Coefficient of performance of Carnot refrigerator,

Calculation:

Efficiency of the Carnot heat engine :

or,

Step : 3 Calculation of 

Thus, While amount of work input to the refrigerator Using this relation between and in coefficient of performance,

or,

Therefore,

Conclusion: The refrigerator rejects 8.57J thermal energy to the hot reservoir.

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