Chapter 6 - The Second Law of Thermodynamics - Problems - Page 325: 6-151

a) $\dot{W}_i=0.830\ kW$ b) $\dot{m}_w=0.651\ kg/s$

$COP_{HP, max}=\dfrac{1}{1-\frac{T_L}{T_H}}$ $T_L=6°C,\ T_H=23°C$ $COP=17.41$ $COP_{HP}=\dot{Q}_H/\dot{W}_i,\ \dot{Q}_H=52,000\ kJ/h=14.4\ kW$ $\dot{W}_i=0.830\ kW$ $\dot{Q}_H=\dot{W}_i+\dot{Q}_L$ $\dot{Q}_L=13.61\ kW$ $\dot{Q}_L=\dot{m}_wc_p\Delta T,\quad c_p=4.18\ kJ/kg.°C,\ \Delta T=5°C$ $\dot{m}_w=0.651\ kg/s$