Difference between einstein and debye theory of specific heat. 2 days ago · Einstein m...
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Difference between einstein and debye theory of specific heat. 2 days ago · Einstein model gives an exponential-like suppression at low T because all oscillators share one energy quantum. The Einstein model predicts an exponential decay of specific heat with decreasing temperature, while the Debye model predicts a T 3 dependence. By fitting experimental data with γT + βT³, one can separate the lattice part from electronic contribution. The Einstein and Debye models were developed to explain that drop using quantum mechanics. Debye Theory of Specific Heat In this model, the vibrational motion of the crystal as a whole was considered to be equivalent to the vibrational motion of system of complete harmonic oscillator which can propagate a range of frequency rather than a single frequency. Estimate the heat capacity of B at 5Kº and that of A at 2Kº. Debye’s theory of heat capacities Debye improved on Einstein’s theory by treating the coupled vibrations of the solid in terms of 3N normal modes of vibration of the whole system, each with its own frequency. The total specific heat of complex crystals is best described by a hybrid model: a Debye term for collective acoustic modes and Einstein terms for localized optical modes. Experiments show this works well at high temperatures but fails badly at low temperatures, where heat capacity drops toward zero. It indicates that all oscillators under high T essentially have the same energy, even though the oscillators follow that Bose-Einstein distribution.
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