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Chapter 21: Q. 2 (page 593)
Rank in order, from largest to smallest, the amount of work done by the gas in each of the cycles shown in FIGURE Q21.2. Explain.
Rank in order is
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A heat engine with of a monatomic ideal gas initially fills acylinder at . The gas goes through the following closed cycle:
Isothermal expansion to .
Isochoric cooling to .
Isothermal compression to .
Isochoric heating to .
How much work does this engine do per cycle and what is its thermal efficiency?
FIGURE CPshows two insulated compartments separated by a thin wall. The left side contains of helium at an initial temperature of and the right side contains of helium at an initial temperature of . The compartment on the right is attached to a vertical cylinder, above which the air pressure is . A -diameter, piston can slide without friction up and down the cylinder. Neither the cylinder diameter nor the volumes of the compartments are known.
a. What is the final temperature?
b. How much heat is transferred from the left side to the right side?
c. How high is the piston lifted due to this heat transfer?
d. What fraction of the heat is converted into work?
A heat engine using a diatomic ideal gas goes through the following closed cycle:
Isochoric cooling until the pressure is restored to its initial value. What are the thermal efficiencies of () this heat engine and
() a Carnot engine operating between the highest and lowest temperatures reached by this engine?
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?
In Problems through you are given the equation(s) used to solve a problem. For each of these, you are to
a. Write a realistic problem for which this is the correct equation(s).
b. Finish the solution of the problem.
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