## Hy

Also we have EE = IE

giving 0h = [ Wnet +( °L)]. Solving for (—Waet ) and substituting into the effi-

ciency equation, the result becomes jj =

0l 0

. Using the equi-

H y valence equation, the efficiency of a Carnot engine reduces to jj =

Hy v

For a refrigerator, the net effect is the cooling that we get, (QL), from a cold reservoir at (7L). The work required to pump this energy is (Wnet), and the energy given off to the environment at a temperature (TH) is (-QH). Therefore, the performance parameter, coefficient of performance for a refrigerator becomes f m \

V net

v h 1l y for a Carnot refrigerator.

For a heat pump, the net effect is the heating that we get, (-Qh) into a reservoir at a temperature of (TH). The work required to pump this energy is (Wnet), and the energy that is taken out of the environment at a temperature (TL) is (QL). Therefore, the coefficient of performance for a heat pump becomes f m \

Qh which reduces to y=

Carnot heat pump. It is also easy to prove that [y = (1 + ^)}using the results obtained above.

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