# Mean Occupation Number of Non-interacting quantum fluids

1. Mar 7, 2014

### unscientific

Hi, I get two contradicting sections of the book "Concepts in Thermal Physics":

Earlier in the section they used the grand partition function to derive the mean occupation number $<n_i> = -\frac{1}{\beta}\frac{\partial ln Z}{\partial E_i}$

Later in the section, they said $<n_k> = \frac{1}{\beta}\frac{\partial Z_k}{\partial \mu}$

Why does the first expression take the differential of $ln Z$ and the second expression simply takes the differential of $Z$?

2. Mar 8, 2014

### unscientific

If it helps, it was earlier defined that $Z = \Pi_i\left( 1 \pm e^{\beta(\mu - E_i)}\right)^{\pm 1}$

3. Mar 11, 2014

### unscientific

bumpp

4. Mar 11, 2014

### Hypersphere

It should be ln Z, it's just an error in the book. And the author is aware of it already, see this errata.

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