A low-temperature calorimetry plot of against for a sample of zinc is fitted by the…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Lattice dynamics and thermal properties of solids · Free electrons, energy bands and electronic structure

Condensed Matter Physics, Ch The free-electron gas: what Drude gets right and what only Fermi fixes

Problem

A low-temperature calorimetry plot of C/TC/T against T2T^2 for a sample of zinc is fitted by the straight line CT=9.7×10−4+6.53×10−5 T2(J mol−1K−2, T in K),\frac{C}{T}=9.7\times10^{-4}+6.53\times10^{-5}\,T^2\qquad(\mathrm{J\,mol^{-1}K^{-2}},\ T\ \text{in}\ \mathrm{K}), where the first term is the intercept and the second is the slope multiplying T2T^2. ((a)) Read off zinc's electronic heat capacity coefficient γ\gamma, in mJ mol−1K−2\mathrm{mJ\,mol^{-1}K^{-2}}. ((b)) Using A=1944/ΘD3 J mol−1K−4A=1944/\Theta_D^3\,\mathrm{J\,mol^{-1}K^{-4}} (Chapter 6), find zinc's Debye temperature ΘD\Theta_D.

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