A Carnot heat pump is to be used to heat a house and

QUESTION:

A Carnot heat pump is to be used to heat a house and maintain it at \(25^{\circ} \mathrm{C}\) in winter. On a day when the average outdoor temperature remains at about \(2^{\circ} \mathrm{C}\), the house is estimated to lose heat at a rate of \(55,000 \mathrm{~kJ} / \mathrm{h}\). If the heat pump consumes \(4.8 \mathrm{~kW}\) of power while operating, determine (a) how long the heat pump ran on that day; (b) the total heating costs, assuming an average price of \(11 \mathrm{c} / \mathrm{kWh}\) for electricity; and (c) the heating cost for the same day if resistance heat-ing is used instead of a heat pump.

Equation Transcription:

25°C

2°C

4.8 kW

Text Transcription:

25 degree celsius

2 degree celsius

4.8 kW

55,000 kJ/h

11¢/kWh