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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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shows the thermodynamic cycles of two heat engines. Which heat engine has the larger thermal efficiency? Or
are they the same? Explain.
FIGURE Pshows the cycle for a heat engine that uses a gas having .The initial temperature is, and this engine operates atcycles per second.
a. What is the power output of the engine?
b. What is the engine's thermal efficiency?
The heat engine shown in FIGURE Puses of a monatomic gas as the working substance.
a. Determine , and .
b. Make a table that shows , and for each of the three processes.
c. What is the engine's thermal efficiency?
A heat engine uses a diatomic gas in a Brayton cycle. What is the engine's thermal efficiency if the gas volume is halved during the adiabatic compression?
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鈥檚 home has a heat pump with a coefficient of performance of , a realistic value. Note that 鈥渨hat you get鈥� with a heat pump is heat delivered, , so a heat pump鈥檚 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鈥檚 heating cost in the home with a electric heater and in the home of the neighbor who uses a heat pump?
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