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Multiplicity of a Large einstein solid

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

    Use the equation ln(q+N) to derived an equation similar to the equation, omega(N,q)=e^(N*ln(q/N))*e^(N)=(eq/N)^N only when q >> N, for a multiplicity of an einstein solid in the "low temperature" limit , q<<N

    2. Relevant equations

    ln(q+N)

    ln (omega)=ln((q+N)!/(q!N!))=(q+N)ln(q+N)-q*ln(q)-N*ln(N)
    3. The attempt at a solution

    now that N>>q, I should factor out a N rather than a q.

    ln(q+N)=ln(N*(q/N+1))=ln(N)+ln(q/N+1)
    =ln(N)+q/N, since ln(x+1)=x and 1>>abs(x)

    ln(N)+q/N=ln(N) since q/N approximates to zero since N>>q, right?
     
  2. jcsd
  3. Mar 5, 2009 #2
    Anybody not understand the question ?
     
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