Chapter 15, Problem 41PE

(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of $\text{5}0.0°\text{C}$ and a cold reservoir temperature of $–\text{2}0.0°\text{C}$ ? (b) How much heat transfer occurs into the warm environment if $3.60\times {10}^7\text{J}$ of work $(\text{1}0.0\text{kW}\cdot \text{h})$ is put into it? (c) If the cost of this work input is $\text{1}0.0\text{ cent}/\text{kW}\cdot \text{h}$, haw 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 $1.055\times {10}^8\text{J}$ .)