Each ion of a paramagnetic salt has two low-lying levels separated by an energy…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Lattice dynamics and thermal properties of solids

Thermal Physics, Ch Two-level systems, paramagnets and the Einstein solid

Problem

Each ion of a paramagnetic salt has two low-lying levels separated by an energy equivalent to a temperature of

2.0\,\mathrm{K}

, that is

\varepsilon/k_B = 2.0\,\mathrm{K}

, with the lower level taken as zero energy. The salt is held at

T = 0.50\,\mathrm{K}

by a reservoir. ((a)) Find the contribution of one ion to the heat capacity, as a multiple of

k_B

. ((b)) Diamond is described by the Einstein model with

\theta_E = 1300\,\mathrm{K}

. Find

C_V/3Nk_B

for diamond at

1000\,\mathrm{K}

, counting only the lattice vibrations.

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