Electron Contribution to Specific Heat

电子对比热的贡献

One of the great mysteries in physics in the early part of the 20th century was why electrons didn't appear to contribute to specific heat. How could they contribute to electrical conduction and heat conduction and not to specific heat?

20世纪初物理学中的一个重大谜题是为什么电子似乎不贡献于特定热容。它们如何能贡献于电导和热导，却不对特定热容有所贡献？

The electrons in the metal which contribute to conduction are very close to the Fermi level, "ripples on the Fermi sea". But to contribute to bulk specific heat, all the valence electrons would have to receive energy from the nominal thermal energy kT. But The Fermi energy is much greater than kT and the ovewhelming majority of the electrons cannnot receive such energy since there are no available energy levels within kT of their energy.

The small fraction of electrons which are within kT of the Fermi level does contribute a small specific heat, and this electron specific heat becomes significant at very low temperatures.

处于费米能级附近的小部分电子会对特定热容有所贡献，而在极低温度下，这种电子热容变得显著。

金属中参与导电的电子非常接近费米能级，"费米海上的涟漪"。但要对体积比热容做出贡献，所有价电子都必须从名义热能kT获得能量。然而费米能远大于kT，由于没有处于其能量附近kT范围内的可用能级，绝大多数电子无法获得如此能量。

Index

Reference
Rohlf
Ch 14.

索引参考Rohlf第14章。

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Electron Specific Heat

电子比热

Using Fermi-Dirac statistics (as opposed to Einstein-Bose for phonons), a small fraction of the electrons are available to participate in specific heat. This fraction contributes a specific heat:

使用费米-狄拉克统计（与声子的爱因斯坦-玻色统计相对比），仅有少量电子可以参与特定热容的贡献。这一分数贡献了热容：

It is important only for low temperatures in metals where it becomes larger than the T-cubed dependent phonon contribution. At those low temperatures is becomes part of the Einstein-Debye specific heat expression.

在金属中只有低温情况下，它才变得比声子贡献大，而声子贡献与温度的三次方有关。在那些低温下，它成为爱因斯坦-德拜比热表达式的一部分。

Discussion of electron role in specific heat

电子在特定热容中的作用讨论

Index

Reference
Rohlf
Ch 14.

索引参考Rohlf第14章。

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