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.
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.