Worked Solution
SOLUTION
The COP of a heat pump is given. The power consumption and the rate of heat absorption are to be determined.
ASSUMPTIONS
Steady operating conditions exist.
ANALYSIS
(a) The power consumed by this heat pump is determined from the definition of the coefficient of performance to be
(a) Ẇnet in = H /COPHP
= 80 000 kJ/h / 2.5
= 32 000 kJ/h OR 8.9 kW
(b) The house is losing heat at a rate of 80,000 kJ/h. If the house is to be maintained at a constant temperature of 20°C, the heat pump must deliver heat to the house at the same rate, that is, at a rate of 80,000 kJ/h. Then the rate of heat transfer from the outdoor becomes:
L = H - Ẇnet in = (80 000 - 32 000) kJ/h = 48 000 kJ/h
Note:
48,000 of the 80,000 kJ/h heat delivered to the house is extracted from the cold outdoor air.
We pay only for the 32,000 kJ/h energy that is supplied as electrical work to the heat pump.
Using an electric resistance heater instead: we would have to supply the entire 80,000 kJ/h to the resistance heater as electric energy
Heating bill that is 2.5 times higher
Therefore heat pumps as heating systems are most popular and preferred to simple electric resistance heaters despite their considerably higher initial cost.