Chapter 20, Problem 28P

(II) (a) Given that the coefficient of performance of a refrigerator is defined (Eq. 20–4a) as

$\text{COP}=\frac{Q_{\text{L}}}{W},$

show that for an ideal (Carnot) refrigerator.

${\text{COP}}_{\text{ideal}}=\frac{T_{\text{L}}}{T_{\text{H}}-T_{\text{L}}}.$

(b) Write the COP in terms of the efficiency e of the reversible heat engine obtained by running the refrigerator backward. (c) What is the coefficient of performance for an ideal refrigerator that maintains a freezer compartment at – 18°C when the condenser’s temperature is 24°C?