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Chapter 21: Q. 2 (page 594)
A heat engine with a thermal efficiency of does of work per cycle. How much heat is (a) extracted from the hot reservoir and (b) exhausted to the cold reservoir per cycle?
(a) The heat extracted from the hot reservoir is .
(b) The heat exhausted to the cold reservoir is .
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A gas following the trajectory of FIGURE does of work per cycle. What is ?
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 , 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, conversion of work to heat. That is, of electric power (generated by doing work at the rate of at the power plant) produces heat energy inside the home at a rate of . Suppose that the neighbor’s home has a heat pump with a coefficient of performance of , a realistic value. Note that “what you get” with a heat pump is heat delivered, , so a heat pump’s coefficient of performance is defined as.
a. How much electric power does the heat pump use to deliver of heat energy to the house?
b. An average price for electricity is about per dollar. A furnace or heat pump will run typically hours per month during the winter. What does one month’s heating cost in the home with a electric heater and in the home of the neighbor who uses a heat pump?
A -efficient electric power plant produces of electric power and discharges waste heat into ocean water. Suppose the waste heat could be used to heat homes during the winter instead of being discharged into the ocean. A typical American house requires an average of for heating. How many homes could be heated with the waste heat of this one power plant?
The electric output of a power plant is . Cooling water flows through the power plant at the rate . The cooling water enters the plant at and exits at. What is the power plant’s thermal efficiency?
A heat engine satisfies Why is there no term in this relationship?
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