Chapter 1, Problem 1.38P

An internally reversible refrigerator has a modifiedcoefficient of performance accounting for realistic heattransfer processes of
   $CO{P}_m=\frac{q_m}{\stackrel{\dot{}}{W}}=\frac{q_{in}}{q_{out}-q_{in}}=\frac{R_{c,i}}{T_{n,i}-T_{c,i}}$
where $q_{in}$ ¡s the refrigerator cooling rate, $q_{out}$ is the heatrejection rate, and W is the power input. Show that $CO{P}_m$ ,can be expressed in terms of the reservoir temperatures $T_c$ and $T_h$ , the cold and hot thermal resistances $R_{t,c}$ and $R_{t,h}$ , and $q_{in}$ , as
   $CO{P}_m=\frac{T_c-q_{in}{R}_{tot}}{T_h-T_c+q_{in}{R}_{tot}}$
where $R_{tot}=R_{t,c}+R_{t,h}$ . Also, show that the power inputmay be expressed as
   $\stackrel{\dot{}}{W}=q_{in}\frac{T_h-T_c+q_{in}{R}_{tot}}{T_c-q_{in}{R}_{tot}}$