We have a system, with fixed energy E, of N >> 1 noninteracting and distinguishable particles whose energies are either "0" or "€". Determine the entropy of the system, the temperature as a function of E, and say for which values of the occupation numbers n0 and n1 we have T < 0.
I have some difficult to solve to answer to the last question on the occupation numbers.
Statistical mechanics problem

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 Joined: Fri Aug 02, 2019 12:04 am
Re: Statistical mechanics problem
n1=E/e;n0=Nn1;W=N!/(n1! n0!);S=S(N,E)=k Ln W; use Stirling approximation to simplify your expression...
1/T=DS/DE=k/e Ln (NeE)/E;
to have T<0, Ne<2E=2 n1 e, so that n1>N/2.
1/T=DS/DE=k/e Ln (NeE)/E;
to have T<0, Ne<2E=2 n1 e, so that n1>N/2.