# 6.21. A refrigerator is the opposite of a heat engine: it uses work supplied from theenvironment to move heat from a cold to a hot reservoir, effectively keepingthe former at a lower temperature. The coefficient of performance measures the efficiency of this process, defined by omaximum value of o that is possible according to the second law.Qcl/W. Find anexpression for the

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This problem is (6.21) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"

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Step 1

Efficiency of refrigerator is measured by coefficient of performance

COP  of a refrigerator is written as:

Where QC = Heat removed from the cold reservoir

W = work required to lift the liquid

Step 2

From the second law of thermodynamic it is not possible to transfer heat from lower temperature to higher temperature.

From the first law of thermodynamic work required  W is given as:

Where Qh is heat transfer to the hot reservoir

Qc is heat transfer from the cold reservoir

Step 3

Carnot engine is the most efficient engine. It is an ideal engine.

From the Carnot cycle it can be written as

Where Th = source temperatu...

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