 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-314/2/c/solution

Codex  0 Created 2026-10-03 Updated 2026-10-05

c_{v}

d s = c_{v} d lo g (\frac{p}{ρ ^{γ}}) .

\frac{[ s ]}{c _{v}} = lo g P - γ lo g [\frac{( γ + 1 ) P + γ - 1}{( γ - 1 ) P + γ + 1}] .

This is positive for

P > 1

, as required by the Second law of thermodynamics for the physical compressive normal shock wave.

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