# Isothermal Compression/Expansion

1. Sep 11, 2014

### opprobe

1. The problem statement, all variables and given/known data
Gas obeys Equation of State, PV=RT/(1-bP), where b is a temperature dependent constant.
Isothermal process (T is constant)
V goes from V1 to V2
P goes from P1 to P2

Show that the amount of Work is
W=(P1V1-P2V2)+RTln[(P22V2)/(P12V1)

2. Relevant equations
W=-∫P(V)dV
ΔU=Q+W

3. The attempt at a solution
Solved PV=RT/(1-bP) for P in terms of V
P=(-1$\pm$Sqrt[1-4bRT/V])/(2b)

I don't know how to really integrate that expression. I used Wolfram to eventually get this expression:

∫P(V)dV=-V/(2b)$\pm$RTln(2V(Sqrt[1-4bRT/V]+1)-4bRT)-V*Sqrt[1-4bRT/V]

I'm pretty sure that this isn't the approach to solve this problem. Can someone point me in the right direction?

Thanks in advance!

2. Sep 11, 2014

### Staff: Mentor

Try integrating PdV by parts.

Chet

3. Sep 11, 2014

### opprobe

That did it. Thanks for the help!

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