- #1
Suske
- 7
- 0
Homework Statement
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.
Homework Equations
call exp(β(ε - μ) = a
U = TS - PV + μN (1) (contributions to total)
βPV = log Z (2)
Z = Ʃsexp(-βEs + βμNs) (3)
U = ε/(a-1) (4)
N = 1/(a-1) (5)
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 Ʃn -log(1 - a^1) ?
so then you would have:
contribution to S = (ε-μ)/(T*(a-1)) + (1/VTβ)*log Ʃn -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