Question

A heat pump operates between reservoirs at 310 K (inside the house) and 254 K (outside). It is not a reversible heat pump; it only pumps 72% of the maximum possible heat into the house. How much work must be done to

Answer 1

$COP_{heating}=\frac{T_{hot}}{T_{hot}-T_{cool}}=\frac{310}{310-254}=5.53$

Actual COP,

$COP_{heating}|_{a}=5.53\times 0.72=3.98$

$COP_{heating}|_{a}=\frac{\Delta Q_{hot}}{\Delta W}=3.98$

$\Delta W=\frac{5470}{3.98}=1374.37J$