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Van der Waals, temperature decrease

  1. May 4, 2012 #1
    1. The problem statement, all variables and given/known data

    I need to find a p-V region where the temperature is decreasing

    ## (p + \frac{a}{V^2} ) (V-b) = RT ##


    3. The attempt at a solution

    So I thought that a place to start would be

    ## dT = \frac{\partial T}{\partial P} dP + \frac{\partial T}{\partial V} dV < 0 ##

    So ##\frac{\partial T}{\partial P} dP < - \frac{\partial T}{\partial V} dV ##

    Do I now, ## \int \frac{\partial T}{\partial P} dP < - \int \frac{\partial T}{\partial V} dV ##?

    ## \frac{\partial T}{\partial P} = V - b ##

    ##\frac{\partial T}{\partial V} = p + a \log (V) -2 \frac{a b}{V^3} ##

    Is this the way to do it? The integrals are complicated and I can't really do them
     
  2. jcsd
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