Chapter 6 - The Second Law of Thermodynamics - Problems - Page 320: 6-109

$COP_R=\dfrac{1}{T_H/T_L-1}$

$\dot{Q}_H=\dot{W}_i+\dot{Q}_L$ $COP_R=\dot{Q}_L/\dot{W}_i$ $COP_R=\dot{Q}_L/(\dot{Q}_H-\dot{Q}_L)$ $COP_R=1/(\dot{Q}_H/\dot{Q}_L-1)$ Since $\left (\frac{Q_H}{Q_L}\right)_{rev}=\frac{T_H}{T_L}$ $COP_R=\dfrac{1}{T_H/T_L-1}$