Problem $4$ Serway & Jewett $21\mathrm{.}34$ Suppose an ideal $($Carnot$)$ heat pump could be constructed for use as an air conditioner. $($a$)$ Obtain an expression for the coefficient of performance $($COP$)$ for such an air conditioner in terms of Th and Tc$.($b$)$ Would such an air conditioner operate on a smaller energy input if the difference in the operating temperatures were greater or smaller? $($c$)$ Compute the COP for such an air conditioner if the indoor temperature is $20\mathrm{.}0$C and the outdoor temperature is $40\mathrm{.}0$C$.$