Hi, I get two contradicting sections of the book "Concepts in Thermal Physics":(adsbygoogle = window.adsbygoogle || []).push({});

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##?

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# Mean Occupation Number of Non-interacting quantum fluids

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