Virial coefficients of the van der Waals gas ($B_2=b-a/(k_{B}T),B_j=b^{j-1}(j\ge 3)$)

Expanding $p=n{k}_{B}T/(1-nb)-a{n}^2$ at $nb\ll 1$ gives the second virial coefficient $B_2=b-a/(k_{B}T)$ and the displayed higher density-series coefficients. These are the Van der Waals gas predictions, not exact coefficients for every fluid. The vanishing of $B_2$ at the Boyle temperature removes only the leading density correction.