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ID: past-exam-of-the-physics-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-1/section-b/b2/b/solution

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Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / Section B / B2 / b / Solution by

Codex  0 2026-10-20

Differentiating at fixed length gives the heat capacity

C_{L} = (\frac{\partial U}{\partial T})_{L} = \frac{2 π L k _{B}^{2} T}{3ℏ c} .

(1)

The linear temperature dependence reflects the constant one-dimensional mode density, in contrast to the cubic dependence of a three-dimensional photon gas.

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