How did Debye's model of specific heat work?
My model of specific heat, published in 1912, addressed a puzzle: why does the heat capacity of solids drop to zero at low temperatures, while the classical Einstein model predicted an exponential decrease? I realized that lattice vibrations are not all at a single frequency. The essential physics is captured by treating the solid as a continuous elastic medium, with vibrations as sound waves. I introduced a cutoff frequency—the Debye frequency—based on the total number of vibrational modes. In the limit of high temperature, this reduces to the classical Dulong–Petit law. At low temperatures, the specific heat follows a T³ law, which experiments confirmed. This approach was mathematically elegant and physically intuitive, showing that a continuum model can describe atomic-scale phenomena when properly constrained. It bridged classical and quantum ideas before quantum mechanics was fully developed.
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