Virial coefficient
= Virial coefficient
A <virial coefficient> quantifies an interaction correction to the dilute-gas equation of state. In the number-density convention, $p/(nk_BT)=1+B_2(T)n+B_3(T)n^2+\cdots$, where $n=N/V$. Thus $B_2$ has units of volume; a molar-density expansion uses differently scaled coefficients.
For classical particles with a pair potential $u(r)$, $B_2=-\tfrac12\int[e^{-u(r)/(k_BT)}-1]\,d^3r$. Hard spheres of diameter $d$ exclude separations below $d$, giving $B_2=2\pi d^3/3>0$. Attractive interactions can instead contribute negatively. The expansion is a low-density organization of correlations, not a guarantee of convergence near a <phase transition>.