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Ideal Gas in a Gravitational Field

  1. May 6, 2007 #1
    1. The problem statement, all variables and given/known data
    Im given an ideal Gas confined in an container with quadratic bottom area of size L^2 and open at the top.
    The whole thing is set in V(z) = m*g*z surely and contains N Atoms at Temperature T.
    Compute the Helmoltz Free Energy.


    2. Relevant equations
    Yea surely the Helmholtz free Energy ist F = E-T*S or dF = -SdT - pdV



    3. The attempt at a solution
    My first idea was to plug in the barometric hight formula into the expression for p and integrate over the whole thing allways integration over volume V = L^2*dz so that i get some F(z+dz) = F(z)*dz and integrate the whole thing for z from 0 to infinity.
    But im kinda stuck with the -S*dT part. Regarding the fact that T is allways constant it thould be -S*T ( and i think it surely is :) ) but how to compute S ? I honestly don´t got any idea. ( in fact i have my problems computing entropies so i would be nice if you give me some hint and not the solution right away i really wanna understand this stuff :).

    Thanks in advance
    Mr.Brown
     
  2. jcsd
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