= Critical-isochore compressibility of a van der Waals gas
{title2=$\kappa_T=4b/[3R(T-T_c)]$}
For molar equation $p=RT/(v-b)-a/v^2$, the critical values are $v_c=3b$ and $T_c=8a/(27Rb)$. At $v=v_c$, $(\partial p/\partial v)_T=-R(T-T_c)/(4b^2)$. Thus $\kappa_T=-v_c^{-1}(\partial v/\partial p)_T=4b/[3R(T-T_c)]$ on the stable branch above $T_c$. The mean-field compressibility exponent is one; the continuation below the <critical temperature> is unstable rather than an equilibrium negative compressibility.
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