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## Homework Statement

If the compressability factor is given at a certain temperature as a function of pressure: Z(T) = 1+αP+βP

^{2}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 + an

^{2}/V - abn

^{3}/V = nRT

I'm guessing my next step would be to somehow eliminate V, but not sure how.