1
$\begingroup$

I'm studying Bose Einstein Condensation.

In the book "Huang K Statistical Mechanics 2 edition", page 288, the author gets the following result for the fugacity ($z$) as a function of temperature and specific volume (lambda is the thermal wavelength and small $v$ the specific volume):

enter image description here enter image description here

I understand how $z$ is equal to 1. I don't understand how can one obtain the last result for the value of $z$ above the critical temperature.

$\endgroup$

1 Answer 1

1
$\begingroup$

I am assuming you don't know how to get from 12.41 to the second equation of 12.52?

If you start from 12.41:

$$ \frac{1}{v} = \frac{1}{\lambda^3}g_{3/2}(z) + \frac{1}{V}\frac{z}{1-z}, $$

and take the infinite volume limit $V\rightarrow \infty$, so that the $1/V$ term above goes to $0$.

Then, you are left with: $$ \frac{1}{v} = \frac{1}{\lambda^3}g_{3/2}(z), \\ g_{3/2}(z) = \frac{\lambda^3}{v}. $$

Then you solve it graphically by plotting each side of the equation and find their intersection (the "root"):

enter image description here

For finite volumes, the error goes as $\mathcal{O}(1/V)$.

$\endgroup$
1
  • 1
    $\begingroup$ Thank you very much, it was "the root of" the source of my confusion. $\endgroup$
    – cmmigl
    Jan 1, 2021 at 19:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.