A heat engine may certainly be run backwards. It is called a fridge if its purpose is to extract heat from an already cold reservoir, such as your food. It is called a heat pump, however, it its primary purpose is to exhaust warm air (QH) into an already warm resevoir, and they are widely used for heating residences. Imagine that your neighbor uses electricity to warm their home. They pass a current through a heating coil and convert 100% of the electrical energy they are billed for into heat. Imagine they do this at the rate of 15kW. Now imagine you decide to install a heat pump, and instead use electricity to power a heat pump with a realistic coefficient of performance of 5.0
(a) If you also want 15kW of heat in your home, how much power does the heat pump require to make this happen? (The answer is less than 15)
(b) If Public Service charges one dollar for 40MJ of energy, what is the monthly bill for both you and your neighbor? Assume that you both run your 'heaters' for 200 hours each month.