Virial equation of state - Taylor expansion I don't get how Taylor expansion over $ \frac{1}{\overline{V}} $ of Virial equation of state is caried out: $Z = \frac{P\overline{V}}{RT} $ which yields
$$ Z = 1 + \frac{B_{2V}(T)}{\overline{V}} + \frac{B_{3V}(T)}{\overline{V^2}} + ...
$$ I thought I understood calc2 Taylor expansion of form $$f(x) = \sum\limits_{k=0}^\infty \frac{f^{(k)}(0)}{k!} x^k $$ so maybe I was in illusion. What's is $Z$ function of? At what expansion point do we expa
Here, Z is explicitly a function of temperature.


  At what expansion point do we expand?


Can you clarify what you mean? I can state that it's common to truncate this particular expansion at the second term, so we'd have:

$$\ce Z = 1 + {B_{2V}(T)\over \overline{V}}$$

The virial coefficient in this case accounts for deviation from the ideal case by accounting for attractive and repulsive forces between the particles in the system.