Answer
$\Delta t=104\ min$
Work Step by Step
$Q_L=mc\Delta T$
Given $m=10\ kg,\ c=4.2\ kJ/kg.°C,\ \Delta T=(28-8)°C$:
$Q_L=4200\ kJ$
$COP_R=\dot{Q}_L/\dot{W}_i$
With $COP_R=1.5,\ \dot{W}_i=0.45\ kW$
$\dot{Q}_L=0.675\ kW$
$Q_L=\Delta t\dot{Q}_L$
Hence $\Delta t=6222s=104\ min$
