Question
(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of $50.0^\circ\textrm{C}$ and a cold reservoir temperature of $-20.0^\circ\textrm{C}$? (b) How much heat transfer occurs into the warm environment if $3.60 \times 10^7 \textrm{ J}$ of work ($10.0\textrm{ kW} \cdot \textrm{h}$) is put into it? (c) If the cost of this work input is $10.0 \textrm{ cents / kW} \cdot \textrm{h}$, 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 $1.055 \times 10^8 \textrm{ J}$.)
1. $4.62$
2. $1.66 \times 10^8 \textrm{ J}$
3. Cost of using the heat pump = $1.00 Cost of burning natural gas =$1.34
Solution Video