A Carnot heat pump is to be used to heat a house and maintain it at 20°C in winter. On a day when the average outdoor temperature remains at about 2°C, the house is estimated to lose heat at a rate of 82,000 kJ/h. If the heat pump consumes 8 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 8.5¢/kWh for electricity; and
(c) The heating cost for the same day if resistance heating is used instead of a heat pump.

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82,000 kJ/h 20°C HP 8 kW 2°C