Chapter 21, Problem 48EAP

48. 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 ex-

haust warm air into the hot reservoir. Heat pumps are widely used

for home heating. You can think of a heat pump as a refrigera-

tor 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, 15 kW of

electric power (generated by doing work at the rate of 15 kJ/s at

the power plant) produces heat energy inside the home at a rate of

15 kJ/s. Suppose that the neighbor's home has a heat pump with

a coefficient of performance of 5.0, a realistic value. Note that

"what you get" with a heat pump is heat delivered, Q_H, so a heat

pump's coefficient of performance is defined as K = Q_H/ W_in.

a. How much electric power (in kW) does the heat pump use to

deliver 15 kJ/s of heat energy to the house?

b. An average price for electricity is about 40 MJ per dollar. A

furnace or heat pump will run typically 250 hours per month

during the winter. What does one month's heating cost in the

home with a 15 kW electric heater and in the home of the

neighbor who uses a heat pump?