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Calculating average every from partition function

  1. Jun 14, 2010 #1
    1. I can't seem to get the same answer my textbook does, basically I need to calculate E (average energy) from the Partition function (Z) which is defined as:

    E=(-1/Z)*(dZ/dBeta)

    Where Z=(1/1-exp(-Beta*h*f))
    (where h and f are constants and beta=1/kT for simplicity)


    So for my differentiation I get:
    dZ/dBeta= -h*f*exp(-Beta*h*f)) / (1-2exp(-Beta*h*f))+exp(-2*Beta*h*f))

    Which when multiplied by 1/Z gives:
    -h*f + h*f*exp(-Beta*h*f) / (1-exp(-Beta*h*f) + exp(-2*Beta*h*f)

    When the answer is apparently:

    (h*f) /(exp(Beta*h*f) -1 )


    Any help greatly appreciated!
     
  2. jcsd
  3. Jun 14, 2010 #2

    kuruman

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    Note that

    [tex]\frac{dZ}{d \beta}=-hfe^{-\beta h f}Z^2[/tex]

    Does this help?
     
    Last edited: Jun 14, 2010
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