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Form p = f(V)

  1. May 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Show that the internal energy of a material whose equation of state has the form p = f(V), T is independent of the volume and the pressure. That is

    [tex]\left(\frac{\partial U}{\partial V}\right)_{T} = 0 [/tex]

    [tex]\left(\frac{\partial U}{\partial p}\right)_{T} = 0 [/tex]

    2. Relevant equations
    TdS = dU + pdV


    3. The attempt at a solution
    I know the answer intiutively, i just dont know how one would go about showing it.
    I assume that U = f(p,v) and then take the partial derivatives, but I do not see where T comes into play
     
    Last edited: May 11, 2010
  2. jcsd
  3. May 11, 2010 #2
    Re: Thermodynamics

    Hmmm, Divide through by dv to get T ds/dv= dU/dv + p I am guessing you need to use a maxwell relation to get ds/dv to dp/dT I don't see how you get the partials to equal 0 though.
     
  4. May 11, 2010 #3
    Re: Thermodynamics

    I am trying to use the fundamental relation: Tds = dU + pdV and equate it with the partial expansion of U = U(V,p), however, I keep getting stuck because I do not know how to get the relationship of the change in U with either a change in V or p for a given temperature.
     
  5. May 11, 2010 #4
    Re: Thermodynamics

    not sure this helps but If U=U(V,p) you can use the chain rule to get to dU= (partial U/ partial V) dU + (partial U/partial p) dp
     
  6. May 11, 2010 #5
    Simple Thermodynamics Problem

    Is this a single variable problem?
     
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