Question 7.50: A house that was heated by electric resistance heaters consu......
A house that was heated by electric resistance heaters consumed 1200 \mathrm{kWh} of electric energy in a winter month. If this house were heated instead by a heat pump that has an average COP of 2.4, determine how much money the home owner would have saved that month. Assume a price of 8.5 \& / \mathrm{kWh} for electricity.
A house is heated by resistance heaters, and the amount of electricity consumed during a winter month is given. The amount of money that would be saved if this house were heated by a heat pump with a known COP is to be determined.
Assumptions The heat pump operates steadily.
Analysis The amount of heat the resistance heaters supply to the house is equal to he amount of electricity they consume. Therefore, to achieve the same heating effect, the house must be supplied with 1200 \mathrm{kWh} of energy. A heat pump that supplied this much heat will consume electrical power in the amount of
\dot{W}_{\text {net,in }}=\frac{\dot{Q}_{H}}{\mathrm{COP}_{\mathrm{HP}}}=\frac{1200 \mathrm{kWh}}{2.4}=500 \mathrm{kWh}
which represent a savings of 1200-500=700 \mathrm{kWh}. Thus the homeowner would have saved
(700 \mathrm{kWh})(0.085 \$ / \mathrm{kWh})=\mathrm{\$ 5 9 . 5 0}