1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Thermal Physics - energy, microstates, and probabilities

  1. Sep 17, 2015 #1
    1. The problem statement, all variables and given/known data
    Screen_Shot005.jpg

    2. Relevant equations
    Screen_Shot004.jpg

    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

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Thermal Physics - energy, microstates, and probabilities
  1. Thermal Physics (Replies: 3)

Loading...