A carnot heat pump is to be used to heat a house and maintain it at 25C in the winter. On a day when the average outdoor temp remains at about 2C , the house is estimated to lose heat at a rate 55000 kj/h. If the heat pump consumes 6.6 kW of power while operating , determine (a) how long the heat pump ran that day; (b) the total heating cost ,assuming an average price of 8.5 cents /kWh for eletricity; and (c) the heating cost for the same day if resistance heating is used instead of of a heat pump.