15.5 Exercise 10

(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of $\text{50} . 0 º \text{C}$ and a cold reservoir temperature of $- \text{20} .\text{0}º\text{C}$? (b) How much heat transfer occurs into the warm environment if $3 .\text{60} \times \text{10}^{7} \text{ J}$ of work ($\text{10} . 0 \text{ kW} \cdot \text{h}$) is put into it? (c) If the cost of this work input is $\text{10}.\text{0 cents}/\text{kW} \cdot \text{h}$, how does its cost compare with the direct heat transfer achieved by burning natural gas at a cost of 85.0 cents per therm. (A therm is a common unit of energy for natural gas and equals $1 . \text{055} \times \text{10}^{8} \text{ J}$.)