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Chemical potential

  1. Sep 5, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the chemical potential for an ideal gas as a function of temperature and pressure. Use the "Gibbs-Duhen relation".

    2. Relevant equations
    [tex]\mu=\frac{\partial U}{\partial N}[/tex]
    [tex]dU=TdS-pdV+\sum\limits_{i}\mu_{i}dN_{i}[/tex]
    [tex]U=Q+W[/tex]
    Gibbs-Duhen relation: [tex]0=SdT-Vdp+\sum\limits_{i}N_{i}d\mu_{i}[/tex]
    Ideal gas law: [tex]pV=Nk_{b}T[/tex]

    3. The attempt at a solution
    Well first I just tried putting the second equation (above) into the first one, but that just resulted in [itex]\mu[/itex] again, so that was a dead end.
    I also tried plugging in everything I could from the ideal gas equation into the second equation (above) and the Gibbs-Duhen equation, because the problem asks for an ideal gas, hoping something would pop out after that, but I had no luck.

    Thermodynamics has always been my weakest subject in physics.
    I have several problems like this to do, so I'm not actually looking for a solution for this particular problem, I'm looking for general information on how to solve this type of problem that will help me on all of them.
    I have no trouble like this with other areas of physics, but there's something about thermodynamics that my mind just doesn't get.. Maybe I just haven't learned it properly but I don't feel like there's any consistent set of fundamental equations, or underlying theory that I can cling to when I'm lost.
     
  2. jcsd
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