A beat pump is a beat engine run in reverse. In winter it pumps heal from the cold air outside into the warmer air inside the building, maintaining the building at a comfortable temperature. In summer it pumps beat from the cooler air inside the building to the warmer air outside, acting as an air conditioner.
(a) If the outside temperature in winter is -5.0°C and the inside temperature is 17.0°C, how many joules of heat will the heat pump deliver to the inside for each joule of electrical energy used to run the unit, assuming an ideal Carnot cycle?
(b) Suppose you have the option of using electrical resistance heating rather than a heal pump. How much electrical energy would you need in order to deliver the same amount of heat to the inside of the house as in part (a)? Consider a Carnot heat pump delivering beat to the inside of a house to maintain it at 68°P. Show that the heat pump delivers less heat for each joule of electrical energy used to operate the unit as the outside temperature decreases. Notice that this behavior is opposite to the dependence of the efficiency of a Carrot heat engine on the difference in the reservoir temperatures. Explain why this is so.