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!