According to Lennard-Jones, the physical behavior of most real gases can be well understood if the intermolecular potential is assumed to be of the form

\[u(r)=\frac{A}{r^{m}}-\frac{B}{r^{n}}\]

where \(n\) is very nearly equal to 6 while \(m\) ranges between 11 and 13 . Determine the second virial coefficient of a Lennard-Jones gas and compare your result with that for a van der Waals gas; see equation (10.3.8).