Answer
a) $\dot{m}_r=0.0498\ kg/s$
b) $\dot{Q}_L=5.07\ kW$
c) $COP_R=1.54$
d) $\dot{W}_{i,min}=1.13\ kW$
Work Step by Step
From tables A-11 to A-13:
Inlet ($P_1=1.2\ MPa, T_1=50°C$): $T_{sat}=46.3°C,\ h_1=278.28\ kJ/kg$
Outlet ($P_2=1.2\ MPa, T_2=T_{sat}-5°C$): $h_2=110.19\ kJ/kg$
From tables A-4 to A-6:
Inlet ($x_3=0, T_3=18°C$): $h_3=75.54\ kJ/kg$
Outlet ($x_4=0, T_4=26°C$): $h_4=109.01\ kJ/kg$
For the water $\dot{m}_w=0.25\ kg/s$:
$\dot{Q}_H=\dot{m}_w(h_4-h_3)$
$\dot{Q}_H=8.367\ kW$
For the refrigerant:
$\dot{Q}_H=\dot{m}_r(h_1-h_2)$
$\dot{m}_r=0.0498\ kg/s$
$\dot{Q}_H=\dot{W}_i+\dot{Q}_L$
Given $\dot{W}_i=3.30\ kW$:
$\dot{Q}_L=5.07\ kW$
$COP_R=\dot{Q}_L/\dot{W}_i$
$COP_R=1.54$
$COP_{R,max}=\dfrac{1}{1-\frac{T_L}{T_H}}=\dot{Q}_L/\dot{W}_{i,min}$
Given $T_L=-35°C,\ T_H=T_3=18°C$:
$\dot{W}_{i,min}=1.13\ kW$
