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Thermal Physics - energy, microstates, and probabilities

  1. Sep 17, 2015 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    The first part I'm not worried about, but the second part is worked out in the "relevant equations" section. Honestly, it looks like more magic than a Harry Potter movie going on there to me. I'm at a loss as to what mathematical method/s are being utilized to get to that answer?
  2. jcsd
  3. Sep 19, 2015 #2


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    I'm not sure that I understand your concern. From the equations, you can prove exactly that:

    [itex]\Omega(E=(r-s) \Delta) = \Omega(E=r \Delta)[\dfrac{r^s}{(N-r)^s}] [\dfrac{ (1-\frac{1}{r}) (1-\frac{2}{r}) ... (1 - \frac{s-1}{r})}{ (1 + \frac{1}{N-r}) (1 + \frac{2}{N-r}) ... (1 + \frac{s}{N-r})}][/itex]

    Then the only issue is proving that if [itex]s \ll r[/itex] and [itex]s \ll (N-r)[/itex], then the last factor is approximately 1.
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