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Question

Two moles of helium gas undergo a cyclic process as shown in figure. Assuming the gas to be ideal, the net work done by the gas is:
945089_17735a3ae7734f2d86f832402703d297.PNG

A
200Rln2
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B
100Rln2
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C
300Rln2
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D
400Rln2
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Solution

The correct option is D 200Rln2
Work done during process AB(AB) (Isobaric process)
WAB=nR(TBTA)
=100nR
Work done during process BC(BC) (Isothernal process)
WBC=nRTB ln(PnPc)
=nRTB ln(2)

Work done during process CD(CD)
WCD=nR(TCTD)
=100nR

Wnet=WAB+WDC+WCD+WDA

=nR 300 ln(12)+nR 400 ln(2)

=100 nR[3ln(12)+4 ln(2)]

=100 nR[ln(12)3×(2)4]

=100 nR ln(2)

Wnet=200 R ln(2) [n=2]

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