# Talk:Second virial coefficient

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And by the way, if this angle brackets mean the average, hence the second virial coefficient should depend on density, i.e $B_2(\rho, T)$.
I highly recommend reading § 12-2 and § 12-3 of "Statistical Mechanics" by Donald A. McQuarrie. The situation is that the integral is often very hard to integrate analytically for anything other than, say, the hard sphere model. (See also the page on cluster integrals). The problem mentioned by Hill arises "...from the treatment of an imperfect gas as a perfect gas mixture of physical clusters". In this case, for $B_2$, the "ensemble" is a collection of pairs of molecules, at various distances and, for non-spherical molecules, orientations. For an example of such a calculation see section 2 of Carlos Menduiña, Carl McBride and Carlos Vega "The second virial coefficient of quadrupolar two center Lennard-Jones models", Physical Chemistry Chemical Physics 3 1289 - 1296 (2001) (a pdf is freely available here) -- Carl McBride (talk) 17:16, 3 May 2011 (CEST)