For the Carnot cycle, we have to show that the work done by the gas during process bc has the same absolute value as the work done on the gas during process da.
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Solution: Click For PDF Version
Let the ratio
of the specific heats of the ideal gas undergoing the Carnot cycle
be
Therefore,
and
Processes bc and da are adiabatic. In an adiabatic process the work done on the gas is given be
Equation of state of an ideal gas is
Therefore, the work done on the gas during the process bc will be
And, the work done on the gas during the process da will be
We note that
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and its amount be n
moles. The process ab
is an isothermal expansion at temperature
and
the process cd is an
isothermal compression at temperature
.
.