Question

A heat pump is used to meet the heating requirements of a house and
maintain it at 20°C. On a day when the outdoor air temperature drops to
-2°C, the house is estimated to lose heat at a rate of 80,000 kJ/h. If the
heat pump under these conditions has a COP of 2.5, determine (a) the
power consumed by the heat pump and (b) the rate at which heat is
absorbed from th

Answer 1

Answer on Question # 83008, Physics / Electromagnetism

Question 1. A heat pump is used to meet the heating requirements of a house and maintain it at $20{}^{\circ}C$. On a day when the outdoor air temperature drops to $-2{}^{\circ}C$, the house is estimated to lose heat at a rate of $80000\,kJ/h$. If the heat pump under these conditions has a COP of $2.5$, determine

(a) the power consumed by the heat pump and

(b) the rate at which heat is absorbed from th

Proof. $COP=\dfrac{Q_{\rm consumer}}{W}$, where $Q_{\rm consumer}$ is a heat received by the consumer and $W$ is pump work.

$Q_{\rm consumer}=80000\,kJ$ because if we lose $80000\,kJ/h$, then we must replenish $80000\,kJ/h$ to maintain the temperature.

So the power is $P=\Delta W/\Delta t=W=\dfrac{Q_{\rm consumer}}{COP}=32000\,kJ/h=32000000/3600\,J/s\approx 8888.888888889\,W.$

And the rate at which heat is absorbed from the outdoor is $80000\,kJ/h$. $\Box$