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Most of the solids approximately obey Dulong - Petit law, which says that the molar specific heat of a solid is $3R \approx 24.94 \frac{\mathrm{J}}{\mathrm{K}\cdot \mathrm{mol}}$, where $R$ is the gas constant, near room temperature and atmospheric pressure.

While this appears to hold for most of the solids, I noticed that carbon has an anomalous value of $6.1 \frac{\mathrm{J}}{\mathrm{K}\cdot \mathrm{mol}}$:
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Question: Why is the molar specific heat capacity of carbon so low?

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    $\begingroup$ The low specific heat of diamond was explained by Einstein as a quantum phenomenon. Low mass together with strong bonds gives high vibrational frequencies with quanta larger than $k_BT$ at room temperature. $\endgroup$ – Pieter Oct 8 '17 at 7:46
  • $\begingroup$ Can I get any reference in support of this? $\endgroup$ – SunLight Oct 11 '17 at 4:08
  • $\begingroup$ It is in any textbook of solid state physics. This is a chapter from Tipler's Modern Physics: bcs.whfreeman.com/webpub/Ektron/Tipler%20Modern%20Physics%206e/… $\endgroup$ – Pieter Oct 11 '17 at 6:32
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The value is for diamond. Carbon atoms in Diamond has tightly bond to each other witch result in a hight Einstein frequency. So that the Dulong Petit law only is vailid for higher temperatur than room temperature.

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