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Homework Help: When is Grand Potential minimized?

  1. May 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Is Grand Potential minimized in a process at constant volume, temperature and potential?

    2. Relevant equations

    Ω = A − ΣμN = −PV
    Ω(V,T,μ) = −SdT − PdV − ΣNdμ

    3. The attempt at a solution

    As seen in the cases of U, H, A and G, I guess that when the differentiated variables used to express their infinitesimal changes are kept constant, each potential tends to a minimum.

    Thus, in analogy, I guess that Ω tends to a minimum when temperature, volume and potential are constant. So ΔΩ in an spontaneous process like that is negative.

    However the thermodynamic potential associated to G − ΣμN is constant = 0
    So, I guess that the analogy is wrong?
  2. jcsd
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