A heat engine running backward is called a refrigerator if its purpose is to ext

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 QH, 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 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 7.00, 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=QH/Win.

How much electric power (in kW) does the heat pump use to deliver 16.0 kJ/s of heat energy to the house

An average price for electricity is about 40 MJ per dollar. A furnace or heat pump will run typically 200 hours per month during the winter. What does one month's heating cost in the home with a 16.0 kW electric heater?

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?

Explanation / Answer

a. COP = Th/(Th – Tc) = Qh/W(in) = (Qh)’/P(in) = 16/P(in) = 7

Therefore, P(in) = 16/7 = 2.29 kW

b. 1$/40kWh(16kW)(30)(24) = $288.00

c. 1$/40kWh(2.29kW)(200h) = $11.45

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