Starting from the Einstein heat capacity C_V = 3R ( _E T )^2 e^ _E/T (e^ _E/T -1 )^2

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

Condensed Matter Physics, Ch Einstein, Debye and the heat capacity of solids

Problem

Starting from the Einstein heat capacity CV=3R(ΘET)2eΘE/T(eΘE/T−1)2,C_V = 3R\left(\frac{\Theta_E}{T}\right)^2\frac{e^{\Theta_E/T}}{\left(e^{\Theta_E/T}-1\right)^2}, show that as T→0T\to0 (equivalently ΘE/T→∞\Theta_E/T\to\infty), CVC_V falls as CV→3R(ΘET)2e−ΘE/T,C_V \to 3R\left(\frac{\Theta_E}{T}\right)^2 e^{-\Theta_E/T}, the exponential collapse quoted in Section 6.4.

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