# derive the fundamental equation from and equation of state

by babbagee
Tags: derive, equation, fundamental, state
 P: 74 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+$\frac{P}{T}$dv I 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!

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