Answer
a) $\dot{W}_i=3.702\ kWh$
b) $T_2=72.0°F$
c) $COP_{max}=11.2$
Work Step by Step
$COP_R=\dot{Q}_L/\dot{W}_i$
$COP_R=1.9,\ \dot{Q}_L=24,000\ Btu/h$
$\dot{W}_i=12,632\ Btu/h=3.702\ kWh$
$\dot{Q}_H=\dot{W}_i+\dot{Q}_L$
$\dot{Q}_H=36,632\ Btu/h$
$\dot{Q}_H=\dot{m}c_p(T_2-T_1)$
$\dot{m}=1.45\ lbm/s,\ c_p=1.0\ Btu/lbm.°F,\ T_1=65°F$
$T_2=72.0°F$
$COP_{max}=\dfrac{1}{1-\frac{T_L}{T_H}}$
$T_L=25°F,\ T_H=0.5(65+72.0)°F=68.51°F$
$COP_{max}=11.2$
