Comparing final volume in isothermal vs adiabatic processes

[arhont]

Homework Statement

Two identical samples of ideal gas are initially at P1 and V1. The first sample undergoes an isothermal transformation to P2, V2 and second sample undergoes an adiabatic transformation to P3, V2. If P3<P2, is V2 higher or lower than V1? Explain

Homework Equations

Ideal Gas Law, Thermo Laws.

The Attempt at a Solution

P1V1 --isotherm-->P2V2
P1V1 --adiabatic-->P3V2
If P2>P3, is V2>V1 or V2<V1?
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For isotherm we have ΔU=Q+W, but since there is ΔT=0, then via 1st law of Thermo - ΔU=0 and Q=-W.
For adiabatic we have constant heat, Q=0, W=PΔV, ΔU=W=PΔV. Yet... it seems useless. My gut tells me V2>V1, though somehow I am having trouble wrapping my mind around it.

 

[haruspex]

There are two very useful equations relating pressure and volume, one for isothermal and one for adiabatic. You've met these, I would think.