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Math Help - gas equation differenciate

  1. #1
    Newbie
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    Oct 2007
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    9

    gas equation differenciate

    I have no idea to how I should proceed . Here is the question:

    Dieterici's equation of state for gas is

    P(V-b)e^{\frac{a}{RVT}} = RT

    Where a, b, and R are constants. Regard volume V as a function of temperature T and pressure P and prove that

    \frac{\partial{V}}{\partial{T}} = \frac{(R+\frac{a}{TV})}{(\frac{RT}{V-b} - \frac{a}{V^2})}
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  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
    Posts
    802
    Hi

    V-b=\frac{RT\exp\left(-\frac{a}{RVT}\right)}{P}

    Take the log (it'll be easier to differentiate) : \ln(V-b)=\ln R +\ln T -\frac{a}{RVT} -\ln P +b

    And then differentiate with respect to T. Good luck
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