Answer
$\dot{Q}_H=11,560\ kJ/h$
Work Step by Step
For the heat pump:
$COP_{HP}=\dfrac{1}{1-\frac{T_L}{T_H}}$
$T_L=2°C,\ T_H=22°C$
$COP_{HP}=14.75$
$COP_{HP}=\dot{Q}_H/\dot{W}_i$
$\dot{Q}_H=62,000\ kJ/h$
$\dot{W}_i=4203\ kJ/h$: this is half of the output of the engine
For the engine:
$\eta=1-\frac{T_L}{T_H}$
$T_L=293\ K,\ T_H=1073\ K$
$\eta=0.727$
$\eta = \dot{W}_e/\dot{Q}_H$
$\dot{W}_e=8406\ kJ/h$
$\dot{Q}_H=11,560\ kJ/h$
