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Homework Help: Taking the derivative of the van der waals equation

  1. Oct 27, 2011 #1
    1. The problem statement, all variables and given/known data

    I'm trying to find dT/dVm for the van der waals equation. I was looking at http://courses.washington.edu/bhrchem/c456/vdw_jtc.pdf" [Broken] page, but I'm confused about how they reached their result:


    3. The attempt at a solution

    I honestly have no idea what they did. dT/dVm of RT(Vm-b) is obviously -RT/(Vm-b)^2, and dT/dVm of -a/Vm^2 is 2a/Vm^3, and dT/dVm of P is 0, but I have no idea where [R/(Vm-b)](dT/dVm) came from. Am I missing something obvious here? It's been a while since calc.
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 28, 2011 #2


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    The first term is the product of RT and 1/(V_m-b), so you need to use the product rule: (fg)'(x)=f'(x)g(x)+f(x)g'(x).
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