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Question: Answered & Verified by Expert
An ideal gas expands isothermally from volume V1 to V2 and then it is adiabatically compressed back to its original volume V1. The initial and final pressures of the gas are P1 and P3 respectively and the net work done by the gas is W, then
PhysicsThermodynamicsJEE Main
Options:
  • A P3>P1, W>0
  • B P3<P1, W<0
  • C P3>P1, W<0
  • D P3=P1, W=0
Solution:
2552 Upvotes Verified Answer
The correct answer is: P3>P1, W<0
The two processes are shown in the following P-V diagram:


             


For iothermal process:

         P1V1 = P2V2

i.e.,       P 1 = V 2 V 1 P 2

For adiabatic process:

             P 3 V 1 γ = P 2 V 2 γ

i.e.            P 3 = V 2 V 1 γ P 2

As  γ > 1 , hence P3 > P1

Further, as slope of adiabatic curve is greater than that of isothermal process curve, adiabatic curve will lie above the isothermal curve. That is, area under adiabatic curve > area under isothermal curve

i.e., Negative work > Positive work

i.e., W < 0

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