Answer
$C_s=\$13.71$
Work Step by Step
For air:
$COP_{HP}=\dfrac{1}{1-\frac{T_L}{T_H}}$
$T_L=0°C,\ T_H=25°C$
$COP=11.92$
$COP_{HP}=\dot{Q}_H/\dot{W}_i,\ \dot{Q}_H=140,000\ kJ/h$
$\dot{W}_i=3.262\ kW$
$C=\dot{W}_i\times p_e\times\Delta t,\quad p_e=\ 0.105\ kWh,\ \Delta t=100h$
$C=\$34.26$
For lake water:
$COP_{HP}=\dfrac{1}{1-\frac{T_L}{T_H}}$
$T_L=10°C,\ T_H=25°C$
$COP=19.87$
$COP_{HP}=\dot{Q}_H/\dot{W}_i,\ \dot{Q}_H=140,000\ kJ/h$
$\dot{W}_i=1.957\ kW$
$C=\dot{W}_i\times p_e\times\Delta t,\quad p_e=\ 0.105\ kWh,\ \Delta t=100h$
$C=\$20.55$
$C_s=C_a-C_l=\$13.71$
