A
gasoline internal combustion engine can be approximated by the cycle
shown in the figure. We will assume that an ideal diatomic gas is
used in the cycle and a compression ratio of
4:1 (
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Solution: Click For PDF Version (a)It is given that the gasoline internal combustion engine can be approximated by an ideal diatomic gas. Therefore, the ratio of specific heats for this gas will be
Let the
volume, pressure, and temperature of the gas at the point a
in the pV diagram be
It is given
that at the point b
in the cycle,
From the
ideal gas equation we note that temperature at b
will be
Part bc of the cycle is an adiabatic process. In an adiabatic process
Therefore, we have
Or
as
Temperature at c will be
Also, the part dc of the cycle is an adiabatic process. Therefore,
And temperature at d will be
(b)
Process ab
(spark) takes place at constant volume, therefore no work is done on
the gas and the heat absorbed
We have assumed that the amount of gas undergoing the cyclic process is n moles and that it is an ideal diatomic gas. Process bc is adiabatic. Therefore, there is no exchange of heat with the external system. In an adiabatic process the work done is given by
Therefore,
And the work done on the gas during the adiabatic process da will be
For the sake
of completeness, we calculate
The total amount of work done on the gas during one cycle will be
As this work is negative, we can say that the work done is done by the engine during one cycle on the external system. Therefore, the efficiency of the engine is
That is the efficiency of the engine is 42%.
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).
We will further assume that
.
(a) We have to
determine the pressure and temperature of each of the vertex points
of the pV diagram in terms of
and
.
(b) We have to calculate the efficiency of the
cycle.
(diatomic
ideal gas)
,
.
.
will be equal to the increase in the internal energy. That is
the amount of heat released by the gas to the external system during
the process cd
(intake). We have
