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Question

An ideal gas is expanded isothermally from a volume V1 to volume
V2 and then compressed adiabatically to original volume V1. The initial pressure is P1 and the final pressure iss P3. If the net work done is W, then


A

P3>P1,W>0

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B

P3<P1,W<0

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C

P_3 > P_1, W < 0

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D

P_3 = P_1, W = 0

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Solution

The correct option is C

P_3 > P_1, W < 0


For an isothermal process: PV = constant and for an adiabatic process:
PVγ = constant, where γ is the ratio of the two specific heats (CpCv) of the gas. When a gas is compressed from a volume V to a volume (VΔV), the increase in pressure is
(ΔP)adia=γΔVPV for an adiabatic compression and (ΔP)iso=ΔVPV for isothermal compression.
Hence P3 will be greater than P1, Therefore, the P - V diagrams of isothermal expansion from V2, P2 to V1, P3 are as shown in Fig. 17.19. Let W1 and W2 be the work done in isothermal expansion and adiabatic compression respectively. Therefore, net work done is
W=W1+(W2)=W1W2
Now, the area under the adiabatic curve is more than that under the isothermal curve. Hence W2>W1. Therefore, W<0.


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