Answer:
a) [tex]\dot W = 1.062\,kW[/tex]
Explanation:
a) Let consider that heat pump is reversible, so that the Coefficient of Performance is:
[tex]COP_{HP} = \frac{T_{H}}{T_{H}-T_{L}}[/tex]
[tex]COP_{HP} = \frac{298.15\,K}{298.15\,K-279.15\,K}[/tex]
[tex]COP_{HP} = 15.692[/tex]
The minimum heat received by the house must be equal to the heat lost to keep the average temperature constant. Hence:
[tex]\dot Q_{H} = 60000\,\frac{kJ}{h}[/tex]
The minimum power supplied to the heat pump is:
[tex]\dot W = \frac{\dot Q_{H}}{COP}[/tex]
[tex]\dot W = \frac{\left(60000\,\frac{kJ}{h} \right)\cdot \left(\frac{1\,h}{3600\,s} \right)}{15.692}[/tex]
[tex]\dot W = 1.062\,kW[/tex]
