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Thermodynamics without partition function

  1. Feb 23, 2014 #1
    Is there a way to derive entropy or free energy without using partition function?
     
  2. jcsd
  3. Feb 23, 2014 #2

    DrClaude

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    Staff: Mentor

    Yes.

    If you want a more complete answer, you'll have to post a more detailed question.
     
  4. Feb 24, 2014 #3
    Thermodynamics came before statistical mechanics.
     
  5. Feb 24, 2014 #4
    As you all know, N=∑ni, U=∑εi, F=Nμ-kT∑Z and S=(U-F)/T

    Here, I do not want to use partition function Z. How do I write F and S then?
     
    Last edited: Feb 24, 2014
  6. Feb 24, 2014 #5

    DrClaude

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    Staff: Mentor

    The Helmoholtz free energy is defined as
    $$
    F \equiv U - TS
    $$
    Entropy you can get from the heat capacity:
    $$
    C_V \equiv T \left( \frac{\partial S}{\partial T} \right)_V
    $$
     
  7. Feb 24, 2014 #6
    Let me specify the problem. I am using grand canonical ensemble and I am in Fermi-Dirac statistics.

    Considering these, entropy is written as S=k[lnZ+β(E-μN)]. How do I write S, without using Z?
     
    Last edited: Feb 24, 2014
  8. Feb 25, 2014 #7
    Heat capacity is a derived quantity. It is really complicated to extract S from Cv.
     
  9. Feb 25, 2014 #8
    Ok. Then, how do I derive S without using partition function (a statistical mechanics tool)? Btw, by deriving S, I mean I'll calculate the entropy of a system over momentum states, I am not talking about S=klnΩ which apparently does not include partition function.
     
  10. Feb 25, 2014 #9
    Anyway, I found the answer by myself. Thread can be closed.
     
  11. Feb 25, 2014 #10
    It would be nice to share with us the answer you found :smile:
     
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