 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/ii/paper-4/34d/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-05

Substitute

v = 3 b \overset{v}{ˉ}

T = (8 a / (27 bk)) \overset{ˉ}{T}

, and

p = (a / (27 b^{2})) \overset{p}{ˉ}

into the equation of state. After cancellation of the material parameters,

\overset{p}{ˉ} = \frac{8 T ˉ}{3 v ˉ - 1} - \frac{3}{v ˉ ^{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.

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