A heat pump is receiving absorbing heat from outdoor at 4deg

A heat pump is receiving (absorbing) heat from outdoor at 4degreeC and supplying heat to indoor of a house at 2 4degreeC at a rate of 4.2 kj/s. Determine minimum value of power supplied to the heat pump for this purpose.

Solution

Coefficient of performance= COP_HP,rev = 1/[1-(T_L/T_H)] = 1/[1-((4+273 K)/(24+273 K))] = 14.85

The required power input to this reversible heat pump can be determined from the definition of the

coefficient of performance to be

W= Q_h/COP_HP = 4.2 kJ/s / 14.85 = 0.282828 kW