Statistical mechanics problem

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Joined: Thu Jul 25, 2019 4:36 pm

Statistical mechanics problem

Postby Antmele » Thu Jul 25, 2019 4:45 pm

We have a system, with fixed energy E, of N >> 1 non-interacting 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.

Posts: 1
Joined: Fri Aug 02, 2019 12:04 am

Re: Statistical mechanics problem

Postby guoxinmike » Fri Aug 02, 2019 12:28 am

n1=E/e;n0=N-n1;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 (Ne-E)/E;

to have T<0, Ne<2E=2 n1 e, so that n1>N/2.

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