Van der Waals derivation

1. Oct 12, 2009

Quelsita

QUESTION:

Van der Waals derived the expression:
(P+(a/v^2))(v-b)=RT
which is a useful approximation of the equation of state of a real gas. Here a and b are gas
dependent constants and v =V/n is the specific volume (Volume V divided by the # of
moles of gas molecules)
Show that at constant volume V and temperature T but decreasing number N=n NA (NA:
Avogadro’s constant) of particles the Van der Waals equation of state approaches the
equation of state of an ideal gas.

I know that I have to rearrange the VdW equation into the P=P(v,T) form and then use a Taylor series.

I have rearranged the eqution:

(P+(a/v2))(v-b)=RT
P=P(v,T)
P(v,T)=a0T - b0ln(v/v0)

thus,

a0T - b0ln(v/v0) + (a/v2))(v-b)= RT

but I'm uncertain what to do next....

Is this even correct thus far?
Any tips on where to go from here?

Thanks!