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Question

An ideal gas expands isothermally from volume V1 to V2 and is then compressed to original volume V1 adiabatically. Initial pressure is P1 and final pressure is P3. The total work done by gas during the whole process is W. Then identify the correct statement.

A
P3>P1, W>0
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B
P3<P1, W<0
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C
P3>P1, W<0
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D
P3=P1, W=0
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Solution

The correct option is C P3>P1, W<0
The two processes are shown in the following PV diagram.


As slope of adiabatic curve is greater than that of isothermal process curve, adiabatic curve will lie above the isothermal curve.
For isothermal process(12), For adiabatic process (23)

From, the shown graph it is clear that pressure P3 is greater than P1.
P3>P1

Area under the curve for adiabatic process (23) is greater than area under curve for isothermal process (12)
(23) gives a ve work done by gas (due to compression) and (12) gives a +ve work done by gas (due to expansion)
Negative Work>Positive Work
Hence net work done by gas during whole process is ve.
W<0

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