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Homework Help: Internal energy of a hydrostatic system in a reversible adiabatic process

  1. Feb 11, 2010 #1
    1. The problem statement, all variables and given/known data
    A simple hydrostatic system is such that [tex]PV^k[/tex] is constant in a reversible adiabatic process, where k > 0 is a given constant. Show that its internal energy has the form
    [tex]E=\frac{1}{k-1}PV+NF(\frac{PV^k}{N^k}[/tex]
    where f is an arbitrary function. Hint: [tex]PV^k[/tex] must be a function of S (why?) so that [tex](\partial{E}{S})_S = g(S)V^-k[/tex] where g(S) is an arbitrary function.


    2. Relevant equations



    3. The attempt at a solution
    I used dE + dW = dQ = 0. so dW = PdV. Then we want to find [tex]W=\int PdV[/tex] using the limits V1 and V2 and substituting [tex]P=\frac{P_1}{V_1*V}[/tex]. This works ok to get the first term of the energy out, but not the second. we end up with a term that looks like this as the second term [tex]\frac{P_1*V^k_1}{(1-k)*V^(k-1)_2}[/tex] which doesn't look much like [tex]N\frac{PV^k}{N^k}[/tex]
     
  2. jcsd
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