Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 4 / 34D / iii / 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,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.