A heat pump is a device that uses a heat engine in reverse to move heat from a cooler to a hotter reservoir. (It's kind of like a refrigerator that cools the outside and dumps the heat inside.) They are often used to heat houses as an alternative to furnaces. Let's analyze the thermodynamics of such a device. a One cycle of a heat pump takes QC of heat from the outside at temperature To, dumps QH of heat to a house at temperature TH, using an amount W' of work from the outside. What is the relationship between QC, QH, and 1W? (Let us choose the signs so that QC is positive when energy is removed from the outsider QH is positive when energy is added to the house, W is positive when electricity is delivered to the heat pump.) a \"that is the entropy decrease of the outside in one cycle? 1What is the entropy increase of the inside in one cycle? I For a maximally efficient heat pump, the total entropy change would be zero. Com- pute the coefcient of performance (25 /W for such a heat pump in terms of TH and To. This describes how much heat can be transferred for a certain amount of work used to drive the heat pump. 0 If the outside is at {l 0C and the inside is at 20 DC, how much more efficient is a perfect heat pump at heating the house than running a space heater (which just converts the work W\" into heat directly)