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ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-3/48/c/solution

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Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / 48 / c / Solution by

Codex  0 2026-10-20

The surface pressure follows by differentiating the logarithm of the canonical partition function with respect to container area:

Π = k_{B} T (\partial_{a} ln Q)_{N, T} = \frac{N k _{B} T}{a - 2 N a _{d}} = \frac{k _{B} T}{a _{d}} \frac{ϕ}{1 - 2 ϕ} .

(1)

Its formal divergence is therefore $ϕ = 1/2$ . This lies outside the low-density regime used to derive the expression. It is a model pole, not an actual geometrical close-packing fraction.

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