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Thermodynamics Finding a fundamental equation.

  1. Feb 11, 2008 #1
    Thermodynamics!! Finding a fundamental equation.

    This is the question:
    "While he Gibbs free energy G is the fundamental function of the atral variables (T,p,N), (T=temperature, p=pressure, N=number of molecules), growing biological cells often regulte not the numbers of molecules N, but the chemical potentials μ. That is, they control concentrations. What is the fundamental function Z of natural variables (T,p,μ)?

    I know a few equations that deal with Gibbs free energy:
    G=H-TS
    G=[tex]\sum[/tex]μN

    Basically, I have no idea where to start with this problem. If anyone can give me a push in the right direction that would be much appreciated!!
     
  2. jcsd
  3. Feb 12, 2008 #2

    Mapes

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    You need to apply a Legendre transform (so check out what this is). An example of of Legendre transform: we use G instead of H because we wish to use T as a natural variable instead of S. Now you've learned that you'd also like to use μ instead of N. This should be enough to get you started.
     
  4. Feb 12, 2008 #3
    Thanks so much, I looked up how to use Legendre transforms for this type of problem and eventually figured it out (not to mention learned something!). Thanks for your help!
     
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