 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2016/s26/2/3/solution

Degenerate electrons conduct heat efficiently, making most of the interior nearly isothermal while an outer nondegenerate insulating envelope sustains a large temperature gradient. Nuclei have much larger masses and much smaller thermal de Broglie wavelengths than electrons, so their quantum degeneracy is weak at these temperatures/densities, although Coulomb coupling and crystallization can matter. Under the stipulated classical ideal-carbon-ion approximation,

U = \frac{3}{2} \frac{M}{12 m _{u}} k_{B} T_{c} = \frac{M k _{B} T _{c}}{8 m _{u}} .

This excludes crystallization, latent heat and low-temperature heat-capacity changes; nondegenerate does not automatically mean weakly interacting.

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