A Carnot heat pump is used to heat and maintain a residential building at 75F. An energy

Question:

A Carnot heat pump is used to heat and maintain a residential building at 75°F. An energy analysis of the house reveals that it loses heat at a rate of 2500 Btu/h per °F temperature difference between the indoors and the outdoors. For an outdoor temperature of 35°F, determine
(a) The coefficient of performance and
(b) The required power input to the heat pump.