Answer
$\Delta t=19.2\ min$
Work Step by Step
$Q_H=mc_v\Delta T$
$m=1500\ kg,\ c_v=0.718\ kJ/kg.K,\ \Delta T=(22-7)°C=15°C$
$Q_H=16,155\ kJ$
$COP_{HP}=\dot{Q}_H/\dot{W}_i,\ COP=2.8,\ \dot{W}_i=5\ kW$
$\dot{Q}_H=14\ kW$
$\dot{Q}_H=Q_H/\Delta t$
$\Delta t=1154s=19.2\ min$
