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Fundamental equation and state equations of the ideal gas

  1. May 5, 2012 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    Find the fundamental equation of a monoatomic ideal gas in the Helmholtz potential representation, in the enthalpy representation, and in the Gibbs function representation. Assume the fundamental equation [itex]S= \frac{NS_0}{N_0} +NR \ln \left [ \left ( \frac {U}{U_0} \right ) ^{3/2} \left ( \frac{V}{V_0} \right ) \left ( \frac {N}{N_0} \right ) ^{-5/2} \right ][/itex]. In each case find the equations of state by differentiation of the fundamental equation.


    2. Relevant equations
    Helmholtz: F=U-TS. But F(T,V,N)
    PV=NRT.
    [itex]U=\frac{3NRT}{2}[/itex].


    3. The attempt at a solution
    I first deal with Helmholtz.
    If I understand well, I must get F(T,V,N)=U-TS. I already have U in terms of T and N. The last task is therefore to get S in terms of T,V and N which seems easily made by using the given fundamental equation.
    It gives me [itex]F(T,V,N)=\frac {3NRT}{2}-T \{ NK_1 +NR \ln \left [ \left ( \frac{V}{V_0} \right ) \left ( NTK_2 \right ) ^{3/2} \left ( \frac{N}{N_0} \right ) ^{-5/2} \right ] \}[/itex].
    So far I wonder if my approach is a right one. Is it ok so far?
     
  2. jcsd
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