A heat pump supplies 40 kW of heat to maintain the inside of a house at 25C in cold winter months when the ambient temperature is 0C. Power required to operate the heat pump cycle is provided by a heat engine cycle which receives 10 kW of heat from a reservoir at 500C. The heat engine has thermal efficiency of 50%. The heat engine rejects heat to the ambient reservoir at 0C.
(a) Calculate the coefficient of performance of the heat pump.
(b) Determine the net rate of heat transfer (kW) for the ambient reservoir.