An ideal heat pump is used to maintain the inside temperature of a house at Tin = 22◦C when the outside temperature is Tout. Assume that when it is operating, the heat pump does work at a rate of 1500W. Also assume that the house loses heat via conduction through its walls and other surfaces at a rate given by (650 W / C◦) (Tin - Tout).

(a) For what outside temperature would the heat pump have to operate all the time in order to maintain the house at an inside temperature of 22°C?

(b) If the outside temperature is 8°C, what percentage of the time does the heat pump have to operate in order to maintain the house at an inside temperature of 22°C?