Solution
= Solution
Substitute $v=3b\bar v$, $T=(8a/(27bk))\bar T$, and $p=(a/(27b^2))\bar p$ into the <equation of state>. After cancellation of the material parameters,
$$
\boxed{\bar p=\frac{8\bar T}{3\bar v-1}-\frac3{\bar v^2}.}
$$
This is the <Van der Waals law of corresponding states>: fluids described by this model share the same reduced equation, although real fluids need not obey it exactly.