Question

A heat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. The same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. Heat pumps are widely used for home heating. You can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat Q H , warming the indoors. Perhaps this seems a little silly, but consider the following. Electricity can be directly used to heat a home by passing an electric current through a heating coil. This is a direct, 100 % conversion of work to heat. That is, 16.0 \rm kW of electric power (generated by doing work at the rate 16.0 kJ/s at the power plant) produces heat energy inside the home at a rate of 16.0 kJ/s . Suppose that the neighbor's home has a heat pump with a coefficient of performance of 6.00, a realistic value. NOTE: With a refrigerator, "what you get" is heat removed. But with a heat pump, "what you get" is heat delivered. So the coefficient of performance of a heat pump is K= Q H / W in . An average price for electricity is about 40 MJ per dollar. A furnace or heat pump will run typically 300 hours per month during the winter. (Part A How much electric power (in kW ) does the heat pump use to deliver 16.0 kJ/s of heat energy to the house? /Part B What does one month's heating cost in the home with a 16.0 kW electric heater? & Part C What does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?

Answer 1