A Carnot engine works between two heat reservoirs at

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QUESTION:

A Carnot engine works between two heat reservoirs at temperatures and (a) What is its efficiency? (b) If it absorbs 100 J of heat from the hot reservoir during each cycle, how much work does it do each cycle? (c) How much heat does it release during each cycle? (d) What is the COP of this engine when it works as a refrigerator between the same two reservoirs? SSM

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QUESTION:

A Carnot engine works between two heat reservoirs at temperatures and (a) What is its efficiency? (b) If it absorbs 100 J of heat from the hot reservoir during each cycle, how much work does it do each cycle? (c) How much heat does it release during each cycle? (d) What is the COP of this engine when it works as a refrigerator between the same two reservoirs? SSM

ANSWER:

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The efficiency of the Carnot engine is the maximum theoretical efficiency that any heat engine can achieve, and it depends on the temperatures of the hot and cold reservoirs between which the engine operates.

The efficiency of the Carnot engine is given by the ratio of the net work output to the heat input, and it is expressed as

Efficiency = Net work output / Heat input

From the definition of the efficiency of the Carnot engine using

 

The work done per cycle from

 

Apply the conservation of energy to find the heat rejected each cycle from the heat absorbed and the work done each cycle also finds the COP of the engine working as a refrigerator from its definition.

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