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Absolute entropy debye4/14/2024 ![]() The copper shows a departure from the cubic dependence, showing evidence of electron specific heat. ![]() The data below show that the Debye phonon model with its cubic dependence on temperature matches the silicon data to very low temperatures. Note that the vibrational part is only the low temperature limit of the more general Debye specific heat. When these were combined, they produced the expression The final step in explaining the low temperature specific heats of metals was the inclusion of the electron contribution to specific heat. Explaining the drastic departure from the Law of Dulong and Petit was a major contribution of the Einstein and Debye models. The Einstein-Debye phonon model produced agreement with the low-temperature cubic dependence of specific heat upon temperature. It has the correct limiting values at both high and low temperatures. The full expression for the Debye specific heat must be evaluated by numerical procedures. The measurement of the low temperature specific heat variation with temperature has led to tabulation of the Debye temperatures for a number of solid materials. ![]() The dependence upon the cube of the temperature agreed with experimental results for nonmetals, and for metals when the electron specific heat was taken into account. In the treatment of specific heat, we define a Debye temperature byįor low temperatures, Debye's treatment led to a specific heat To impose a finite limit on the number of modes in the solid, Debye used a maximum allowed phonon frequency now called the Debye frequency υ D. The density of states for these modes, which are called " phonons", is of the same form as the photon density of states in a cavity. He pictured the vibrations as standing wave modes in the crystal, similar to the electromagnetic modes in a cavity which successfully explained blackbody radiation. The quantitative fit to experiment was improved by Debye's recognition that there was a maximum number of modes of vibration in a solid. Debye Theory of Specific Heat Debye's Contribution to Specific Heat TheoryĮinstein's oscillator treatment of specific heat gave qualitative agreement with experiment and gave the correct high temperature limit (the Law of Dulong and Petit).
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