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Chapter 21: Q. 31 (page 595)
A heat engine operating between a hot reservoir at and a cold reservoir at is as efficient as a Carnot engine. If this heat engine and the Carnot engine do the same amount of work, what is the ratio
The ratio of heat engine and the carnot engine with same workis.
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A Carnot refrigerator operates between reservoirs at and in a room. The refrigerator is a box. Five of the walls are perfect insulators, but the sixth is a thick piece of stainless steel. What electric power does the refrigerator require to maintain the inside temperature at ?
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?
of water is placed in a refrigerator. The refrigerator's motor must supply an extra localid="1649311273753" of power to chill the water to in . What is the refrigerator's coefficient of performance?
A freezer with a coefficient of performance that of a Carnot refrigerator keeps the inside temperature at in a room. of water at are placed in the freezer. How long does it take for the water to freeze if the freezer’s compressor does work at the rate of while the water is freezing?
shows the thermodynamic cycles of two heat engines. Which heat engine has the larger thermal efficiency? Or
are they the same? Explain.
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