2/26/2024 0 Comments Absolute entropy table![]() The Debye theory predicts that, at temperatures near absolute zero, the heat capacity varies as the cube of temperature: \(C_P=AT^3\), where \(A\) is a constant. Debye extended the Einstein model and developed a theory that gives generally excellent quantitative predictions. Einstein’s theory explains all of the qualitative features that are observed when we measure heat capacities at low temperatures, but its predictions are not quantitatively exact. In Section 22.6, we consider a theory of low-temperature heat capacity developed by Einstein. ![]() Why should all solid substances exhibit essentially the same heat capacity (zero) at one temperature (absolute zero)?Īs it turns out, this result has a straightforward molecular interpretation in the theory of statistical thermodynamics. That this is true for all substances seems like an odd sort of coincidence. Heat capacity of mercury versus temperatureĪnother general feature of these curves is that the heat capacity of the solid substance decreases to zero as the absolute temperature decreases to zero the curve meets the abscissa at the zero of temperature and does so asymptotically. The details of the curve are pressure dependent for example, at a low pressure, we might observe sublimation of the material from a solid phase directly into its gas phase. These can be changes from one solid phase to another, melting to convert a solid phase to the liquid, or vaporization to convert the liquid to the gas. ![]() These occur at temperatures where the substance undergoes phase changes. The heat capacity is a smooth, continuous function of temperature except for a small number of discontinuities. If we measure the constant-pressure heat capacity of a pure substance over a wide temperature range, we typically observe a curve like that in Figure 1. It is relatively easy to measure heat capacities as a function of temperature. ![]()
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