3
$\begingroup$

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 $6.1 \frac{\mathrm{J}}{\mathrm{K}\cdot \mathrm{mol}}$:
$\hspace{50px}$.

Question: Why is the molar specific heat capacity of carbon so low?

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ 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. $\endgroup$
    – user137289
    Commented Oct 8, 2017 at 7:46
  • $\begingroup$ Can I get any reference in support of this? $\endgroup$
    – SunLight
    Commented Oct 11, 2017 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/… $\endgroup$
    – user137289
    Commented Oct 11, 2017 at 6:32

2 Answers 2

Reset to default
1
$\begingroup$

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.

Improve this answer
$\endgroup$
1
$\begingroup$

What I think is diamond has C atoms closely packed, inhibiting expected vibration about the mean position for each atom. As quantum mechanical approach requires a minimum non zero amount of energy before a degree of freedom comes into play, we would not have the expected amount of KT. Subsequently, dU would be less than 3RT, and C=dU/dT = less than 3R Let me know what you think

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.