Virial Expansion of Van Der Waals Equation

[izchief360]

Homework Statement

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.

Homework Equations

nRT=(P+a(n/V)²))(V-nb)
Z=PV/nRT

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.

 

[Chestermiller]

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