derive the fundamental equation from and equation of state

babbagee

Hello,

I just need help deriving the fundamental equation from Equation of state for wan der waals fluids.

P=[itex]\frac{RT}{v-b}[/itex]-[itex]\frac{a}{v^2}[/itex]

and

u=cRT-[itex]\frac{a}{v}[/itex]

where a,b, and c are constants.

I know the fundamental equation is

dS=[itex]\frac{1}{T}[/itex]dU+[itex]\frac{P}{T}[/itex]dv


I solved the u equation so it's in terms of u and v and just plugged in the P equation to [itex]\frac{P}{T}[/itex] but then I get an equation of two variables which I am not sure how to integrate. So I get an equation in the form of

dS=f(u,v)dU + f(u,v)dv

Can someone help me with the integration please.

Thanks in advance!