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Virial Expansion of Van Der Waals Equation

  1. Sep 7, 2014 #1
    1. The problem statement, all variables and given/known data

    If the compressability factor is given at a certain temperature as a function of pressure: Z(T) = 1+αP+βP2 find α and β in the form α(a, b, T) and β(a, b, T) where a and b are the van der waals coefficients.

    2. Relevant equations

    nRT=(P+a(n/V)2))(V-nb)
    Z=PV/nRT

    3. The attempt at a solution
    I'm pretty sure this is asking for a virial expansion of the VDW equation of state, but I am unsure on how to begin. All I've done so far is expand the VDW equation to obtain:

    PV - Pnb + an2/V - abn3/V = nRT

    I'm guessing my next step would be to somehow eliminate V, but not sure how.
     
  2. jcsd
  3. Sep 12, 2014 #2
    The equation you wrote, Z(T) = 1+αP+βP2 is not the virial equation. Did you really want to have Z expressed as a function of P. It would be the virial equation if the P's were replaced by the molar density n/V.

    Chet
     
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