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269.


Problem 10.14 (Zemansky)

Two identical bodies of constant heat capacity are at the same initial temperature . A refrigerator operates between these two bodies until one body is cooled to temperature . If the bodies remain at constant pressure and undergo no change of phase, we have to show that the minimum amount of work needed to do this is


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 We are given that we have two identical bodies each of mass m at temperature . A refrigerator operates between these two bodies until one body is cooled to temperature . Let the amount of work done on the refrigerator in cooling of body 2 from temperature to be W. The quantity of heat extracted out of body 2 will be

And the amount of heat delivered by the refrigerator to the body 1 will be

Temperature of body 1 will have got raised from to such that

From this equation, we find

We next calculate the change in entropy of the body 1 and that of the body 2.

And

The total change of entropy in the process will be

From the entropy principle

Minimum amount of work will be done on the refrigerator in the process for which

That is

or