An electric heat pump used as a heater operates on a Carnot cycle. The low-temperature reservoir consists of a pipe driven \(10 \mathrm{~m}\) into the ground to a region where the temperature is always \(10^{\circ} \mathrm{C}\). The high-temperature reservoir is the interior of a house, kept at \(20^{\circ} \mathrm{C}\).

(a) For every \(1.0 \mathrm{~J}\) of electrical energy used to run the heat pump, what quantity of thermal energy is delivered to the house?

(b) If the low-temperature reservoir were the air outside the house at \(-23^{\circ} \mathrm{C}\) rather than underground, what quantity of thermal energy would \(1.0 \mathrm{~J}\) of electrical energy deliver to the house? Does it seem to be worth the added expense of drilling to tap the underground reservoir?

(c) What is the coefficient of performance of heating of the heat pump in part \(a\) and in part \(b\) ?