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Determination of the equation of isentropic processes

  1. Dec 8, 2013 #1
    I have been given a fundamental equation of a system as
    [tex]
    u = \frac{s^4}{v^2}
    [/tex]
    After writing down the 3 equations of state, namely:
    [tex]
    T = 4\frac{S^3}{VN}
    [/tex]
    [tex]
    P = \frac{1}{2}\frac{S^4}{V^{3}N}
    [/tex]
    [tex]
    \mu = -\frac{S^4}{VN^{2}}
    [/tex]

    I need to determine the equation of isentropic (dS = 0) processes on the P-V diagram. I understand that the relationship should only contain P, v (plus whatever constants), but I'm not sure what to do now. I was thinking that I should put these values into
    [tex]
    dQ = dU + PdV
    [/tex]
    where I know [itex]dQ = TdS = 0[/itex] by above definition, and assuming mols constant. Which would give me
    [tex]
    dU = -PdV \,\rightarrow\,\frac{1}{2}\frac{S^4}{V^{3}N}
    [/tex]

    but I'm not confident that's right. Looking for some suggestions, thanks.
     
  2. jcsd
  3. Dec 11, 2013 #2
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