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Find an Expression for the Helmholtz free energy

  1. Aug 11, 2013 #1
    1. The problem statement, all variables and given/known data
    I am attempting the problem below, I might have the correct answer but would appreciate if someone could confirm this (or tell me where I'm going wrong).
    Consider a statement having 2 states, one at energy 0 and one at energy ε. Find an expression for the Helmholtz free energy as a function of the temperature, T.


    2. Relevant equations
    F = -kBT log Z

    Z = Ʃ e-βEr


    3. The attempt at a solution

    Z = e-β.0 + e-β.ε
    Z = 1 + e-β.ε

    F = -kBT ln(1 + e-β.ε)
     
  2. jcsd
  3. Aug 11, 2013 #2
    Isn't β =1/(kBT)? Shouldn't you substitute that into your equation?
     
  4. Aug 12, 2013 #3
    I'm not sure - is that necessary? Or is it OK to just use β?
     
  5. Aug 12, 2013 #4
    Well you want to at least be consistent. In your final equation, you use both beta and kT.
     
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