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=$\frac{RT}{v-b}$-$\frac{a}{v^2}$

and

u=cRT-$\frac{a}{v}$

where a,b, and c are constants.

I know the fundamental equation is

dS=$\frac{1}{T}$dU+$\frac{P}{T}$dvI solved the u equation so it's in terms of u and v and just plugged in the P equation to $\frac{P}{T}$ 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!

 

[Chestermiller]

The fundamental equation is independent of the equation of state, and follows from the more general 2nd law of thermodynamics. So it is not clear what is being asked here.