The coefficient of performance (COP) for a heat pump used as a heater (of a house, for example) is defined as 0=-QH/W, the ratio of the total heat flow -QH into the hot place (the house) to the work input W. (a) Find an expression for as a function of TL and TH, which are the temperatures of the low-temperature reservoir (the outside air, or the ground, depending on the type of heat pump installation) and the high-temperature reservoir (the inside of your house). Hint: how is related to the Carnot efficiency? (15 pts) (b) Evaluate the COP for TH = 68 F and TL = 10F (winter day air as the low-temperature reservoir). (5 pts) (c) Repeat part (b) for TH = 68 F and TL = 45 F (typical ground temperature below the frost line as the low-temperature reservoir in a "geothermal heat pump"). (5 pts)