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!

Homework Help: Statistical Mechanics: Ideal Gas

  1. Apr 11, 2009 #1
    1. The problem statement, all variables and given/known data

    Using the microcanonical ensemble, find the entropy for the mixing of two ideal gases, but we need to compute all at once instead of separately for each gas and adding the two.

    2. Relevant equations


    [tex]S(E,V)= k_{B} (Ln[\Omega(E)])[/tex]

    3. The attempt at a solution

    Now we did an N particle ideal gas in class. I feel this is very similar, but I have the

    [tex] H = \stackrel{N_{a}}{\sum}} \frac{p^{2}_{i}}{2 m_{a}} + \stackrel{N_{b}}{\sum}} \frac{p^{2}_{j}}{2 m_{b}} [/tex]

    Well, since it is independent of the position, then before mixing

    [tex]\Omega(E)=V^{N_{a}}_{a}V^{N_{b}}_{b} \int_{H < E} \frac{\stackrel{N_{a}}{\prod}d\overline{p}_{i}}{h^{3N_{a}}}\frac{\stackrel{N_{b}}{\prod}d\overline{p}_{j}}{h^{3N_{b}}}[/tex]

    The remaining integral should be a [tex]3(N_{a}+N_{b})[/tex]-dimensional hypersphere w/ a radius of [tex]\sqrt{2 m_{a} m_{b} E}[/tex]

    The rest should fall in place, but I wondering if it is that straightforward.
    Last edited: Apr 11, 2009
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted