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Isothermal Compression/Expansion

  1. Sep 11, 2014 #1
    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[itex]\pm[/itex]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)[itex]\pm[/itex]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. jcsd
  3. Sep 11, 2014 #2
    Try integrating PdV by parts.

    Chet
     
  4. Sep 11, 2014 #3
    That did it. Thanks for the help!
     
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