A heat pump operates on a Carnot heat pump cycle with a COP of 8.7. It keeps a space at 24°C by consuming 2.15 kW of power. Determine the temperature of the reservoir from which the heat is absorbed and the heating load provided by the heat pump.

Heat Absorbed = 263 K, Heating Load = 18.7 KW

Explanation:

Since the heat is being absorbed from a reservoir the COP (Coefficient of Performance) is COP is COPhp, max which is given by

COP (hp, max) = Th / (Th - Tl) = (24 + 273) / { (24 + 273) - Tl}

8.7 = 297/297 - Tl

Tl = 263 K

263 K of heat is absorbed from the reservoir.

For Heating Load we may use the equation relating COP, Heating Load and the input Power, which is

COP (hp, max) = Qh/Win, where Qh is the Heating Load and Win is the Input Power

8.7 = Qh/2.15

Qh = 8.7 x 2.15 = 18.7 KW

The heating load provided by the heat pump is 18.7 KW.