A heat engine using a diatomic gas follows the cycle shown in FIGURE P. Its temperature at point is .
a. Determine , and for each of the three processes in this cycle. Display your results in a table.
b. What is the thermal efficiency of this heat engine?
c. What is the power output of the engine if it runs at ?
a. Table for the process is ,
b. The heat engine thermal efficiency is .
c. The power output of the engine is .
The area beneath the surface can be used to determine the work in the first procedure.
It is going to be
The pressure was tripled and the volume was quadrupled in this procedure. This translates to a twelve-fold increase in temperature.
As a result, the temperature differential is eleven times greater than before. The change in internal energy can be calculated as follows:
Isochoric cooling is the second procedure, in which the pressure lowers by a third.
As a result, the temperature decreases by the same factor, resulting in an eight-fold change in temperature.
This means that the heat applied to the gas will be more intense.
The change in internal energy will be the same because the work in the isochoric process is zero.
In the third process we go isobarically from a temperature of four times is,
On the other hand, the work done on the other side can be represented by the rectangle under the graph. We can locate it right away.
The change in internal energy is ,
From the table,
The total heat input is .
The work done is .
The efficiency is,
work is done.
Engine performs cycles per minute,.
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?
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