One mole of an ideal gas undergoes two different cyclic processes I and II , as shown in the P - V diagrams…

One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the P-V diagrams below. In cycle I, processes a, b, c and d are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes a', b', c' and d' are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle I is WI and that during cycle II is WII. The ratio WIWII is _____.

           

Solution

           

For first case:

WI=Wa+Wb+Wc+Wd

=4P02V0-V0+nRT ln4V02V0+2P0V0-4V0+0

=4P0V0+nR8P0V0nRln2-6P0V0

=8P0V0 ln2-2P0V0

For second case: 

WII=W'a+W'b+W'c+W'd

=nRT ln2V0V0+0+P0V0-2V0+0

=nR4P0V0nRln2-P0V0

=4P0V0 ln2-P0V0

Therefore, required ratio is WIWII=8P0V0ln2-2P0V04P0V0ln2-P0V0=2

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Asked in: JEE Advanced 2023 (Paper 2)

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