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.

Question

Engineering

Patience Bush

10 November, 18:10

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.

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Aspen · Answer 1

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.