In extremely cold weather conditions where the inside thermostat is set to 27 C and the outside temperature is -20 C, your 1200 square ft house might lose heat through the walls at a rate of 4270 W. So the amount of energy you lose is 2.58×109 J and this cost for 1 week at 0.1 kw per hour $71.70. My question is this For an air conditioner used as a heat pump, the coefficient of performance can be as high as the inverse of the Carnot efficiency which is run between the temperature inside (27 C) and the temperature outside (-20 C). How much would it cost to heat your house for one week using such a heat pump? (note that a real air conditionier usually has a COP which is half that for a Carnot cycle)