(adsbygoogle = window.adsbygoogle || []).push({}); 1. ProblemFrom Fitzpatrick we need to derive[itex]ln(Z)=αN-\sum ln(1-e^{-\alpha-\betaε_{r}})[/itex] (Equation 8.45)

2. Relevant equations

This is claimed to be derived from Equations 8.20, 8.30, and 8.43

Eq 8.20

[itex]\overline{n}_{s}=-\frac{1}{\beta}\frac{\partial ln(Z)}{\partial\epsilon_{s}}[/itex]

Eq 8.30

[itex]\alpha\cong\frac{\partial ln(Z)}{\partial N}[/itex]

Eq 8.43

[itex]\overline{n}_{s}=\frac{1}{e^{\alpha+\betaε_{r}}-1}[/itex]

3. The attempt at a solution

My initial attempt involved setting the RHS of 8.20 to the RHS of 8.43 and then integrating to solve for ln(Z)

but this ultimately gave me

[itex]ln(Z)=-\alpha-ln(1-e^{-\alpha-\betaε_{r}})[/itex]

I'm not so concerned with the lack of N and the missing summation since that should come when I apply it to more particles, but as hard as I try everything I do ends up with that -[itex]\alpha[/itex]

Nevermind, solved it. Needed to consider the contribution from all the different portions of the partial and make sure it met all requirements. Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Derivation of ln Z for Bose-Einstein case

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**