Derive the fundamental equation from and equation of state

  1. 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!
     
    Last edited: Sep 22, 2011
  2. jcsd
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