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: Quick math question

  1. Sep 19, 2005 #1

    Barley

    User Avatar

    How does the following expand;

    (q + N )*ln(q +N)

    I'm Trying to arrive at sterling approximation for the multiplicity for einstein solid where q>>N. Any tips appreciated.

    Thanks
     
    Barley, Sep 19, 2005
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Sep 19, 2005 #2

    stunner5000pt

    User Avatar

    factor out the bigger of the two

    [tex] q(1 + \frac{N}{q} \ln q(1 + \frac{N}{q}) [/tex]

    i gues you could 'expand it using the log expansion
    [tex] ln (1+x) = x - \frac{1}{2} x^2 + \frac{1}{3} x^3 - ... [/tex]
     
    stunner5000pt, Sep 19, 2005
  4. Sep 20, 2005 #3

    Barley

    User Avatar

    Thanks,

    I'm going to have to see my prof. on this one. I'll let you know how it works out if you'd like.
     
    Barley, Sep 20, 2005
  5. Sep 20, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper
    Insights Author

    I guess N stands for the number of particles (phonons), so it should be the "bigger" one. I also think that Stirling's approximation involves factorials.


    Daniel.
     
    dextercioby, Sep 20, 2005
  6. Sep 20, 2005 #5

    Barley

    User Avatar

    For my next exercise I'm to derive the case where N >> q. In these simple idealized cases of 2 solids interacting. So big q is high temp case- I think.
    I've already used the sterling approximation to get the factorials out of the equation and now I'm just hashing it into best form.

    many thanks.
     
    Barley, Sep 20, 2005
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook