 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/39c/c/solution

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

Using

T \propto p / ρ

together with the supplied density ratio and

p_{2} / p_{1} = [2 γ M_{1}^{2} - (γ - 1)] / (γ + 1)

gives

\frac{T _{2}}{T _{1}} = \frac{[ 2 γ M _{1}^{2} - ( γ - 1 )] [ 2 + ( γ - 1 ) M _{1}^{2} ]}{( γ + 1 ) ^{2} M _{1}^{2}} .

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