 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-3/35c/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

For a homogeneous dispersion

E (p) = A ∣ p ∣^{α}

, the kinetic expression for pressure gives

p V = \frac{1}{d} \sum_{r} \overline{n}_{r}, p_{r} \cdot \nabla_{p} E (p_{r}) = \frac{α}{d} \sum_{r} \overline{n}_{r} E_{r} .

Thus $p V = D E$ with $D = α / d$ .

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