Silver has a Debye temperature

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

Thermal Physics, Ch Photons and phonons: blackbody radiation and the heat capacity of solids

Problem

Silver has a Debye temperature θD=225 K\theta_D = 225\,\mathrm{K}. A sample is cooled to T=12 KT = 12\,\mathrm{K}, which is well below θD\theta_D, so the low-temperature limit of the Debye model applies. The contribution of the conduction electrons is ignored throughout. ((a)) Find the heat capacity at constant volume of one mole of silver at 12 K12\,\mathrm{K}. ((b)) Express your answer as a fraction of the classical (Dulong-Petit) value 3R3R per mole. Take R=8.314 J K−1 mol−1R = 8.314\,\mathrm{J\,K^{-1}\,mol^{-1}}.

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