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Hello,

I'm studying for my final exam on statistical physics, and I found an exercise of which I think it is really easy but I'm unsure of how to do it! So now I wonder if I actually don't understand what I'm doing at all!

The question is as follows:

Calculate for fermionic particles the contribution to the entropy of a one-particle

state with energy ε when the particles chemical potential is μ , and the temperature

is T.

2. Relevant equations

call exp(β(ε - μ) = a

U = TS - PV + μN (1) (contributions to total)

βPV = log Z (2)

Z = Ʃ_{s}exp(-βE_{s}+ βμN_{s}) (3)

U = ε/(a-1) (4)

N = 1/(a-1) (5)

3. The attempt at a solution

I rewrite (1) to get S = (U + PV - μN)/T

use (2), (4) and (5) to get S = (ε-μ)/(T*(a-1)) + (1/VTβ)*log Z

then rewrite Z as in (3) to ∏_{s}(1/((1-a^1)); <- not sure

so log Z would then be Ʃ_{n}-log(1 - a^1) ?

so then you would have:

contribution to S = (ε-μ)/(T*(a-1)) + (1/VTβ)*log Ʃ_{n}-log(1 - a^1) ?

but now i still have V in the equation! Help! and the sum isn't very pretty as well..

I honestly don't know how to get rid of those, and I hope someone will help me!

Thank you<,

Suske

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# Homework Help: Contribution of one fermion to entropy of one-particle state

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