One mole of a monatomic ideal gas initially at a volume of 10 L and temperature 300 K is heated at constant volume to a temperature of 600 K, allowed to expand isothermally to its initial pressure, and finally compressed isobarically (that is, at constant pressure) to its original volume, pressure and temperature. (a) We have to compute the heat input to the system during one cycle; (b) find out the net work done by the gas during one cycle; (c) and find out the efficiency of this cycle.
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Solution: Click For PDF Version We have drawn the cycle on a p-V diagram as shown in the figure. Starting point of the cycle is at A in the diagram. We determine the pressure at A using the ideal gas equation of state.
Therefore,
During the AB
part of the cycle no work is done on the gas, as the gas is heated
at constant volume. The quantity of heat absorbed by the gas,
We next
calculate
As the pressure at C is the same as that at A but the temperature of the gas at C is two times that at A, the volume of the gas at C will be two times of its volume at A. That is
And
As the process BC is isothermal, there is no change in the internal energy of the gas. That is
and from the first law of thermodynamics, we get
The CA part of the cycle takes place isobarically, that is at constant pressure. Therefore, the work done on the gas during this part of the cycle
And the change in internal energy of the gas during CA will be
From the first law of thermodynamics, we have
Therefore, the heat absorbed by the gas during CA will be
As
(a) The total heat absorbed by the gas in one cycle will be
(b) The net work done by the gas on the external system during one cycle will be
(c) Efficiency of the cycle will be
That is 13.4%.
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,
will be equal to the change in the internal energy of the gas. As
the ideal gas is monatomic,
during the isothermal expansion of the gas from B
to A.
is negative, heat is released by the gas into the system during this
part of the cycle.
