Talk:Second virial coefficient

Hello! Could someone please explain the meaning of those angle brackets in the expression of B(T)? 178.140.206.61 07:14, 28 April 2011 (CEST)

In statistical mechanics angle brackets are used to indicate an average, either a time average or, as in this case, an ensemble average. -- Carl McBride (talk) 12:17, 28 April 2011 (CEST)

Yeah, I know it. But the thing is that the common expression for second virial coefficient doesn't have an averaging in it. Anyway, it is said in the article that "Notice that the expression within the parenthesis of the integral is the Mayer f-function." However Mayer f-function has no averaging in it. I was asking because recently I was told that something is wrong with the common expression for the second virial coefficient. Indeed I was referred to the article by Hill by I haven't get it yet.

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)