The molar specific heat of carbon is measured at 6.1 J/mol·K, significantly differing from the predicted value of 3R (approximately 25 J/mol·K). This discrepancy arises because the specific heat of carbon is temperature-dependent, particularly at low temperatures where vibrational modes are not fully populated. The Dulong-Petit law, which predicts specific heat based on equipartition theory, fails for carbon and beryllium at room temperature due to their high energy vibrational modes requiring much higher temperatures to be excited. Empirical methods or computational approaches are necessary to determine the molar specific heat capacity of carbon accurately.
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strictly speaking it does depend on temperature, but is often ignored due to the insignificance of the deviation.DrClaude said:Is the specific heat independent of temperature?
The deviation is far from insignificant, as at low temperature the heat capacity has to go to zero. And what can be called "low" temperature is very relative. At room temperature, carbon (be it diamond or graphite) is far from the asymptotic limit given by the Dulong-Petit law.Suraj M said:strictly speaking it does depend on temperature, but is often ignored due to the insignificance of the deviation.
The Dulong-Petit law works if you can apply the equipartition theorem, that is if all quadratic degrees of freedom have an average energy ##\langle E \rangle = k_B T / 2##. Since vibration is quantized, this can only be the case for the vibrational modes if there is enough energy to significantly populate excited states. Some solids have such a high threshold that you need to go very high temperatures before you have sufficient excitation and can neglect the discrete (quantized) aspect of vibrational energy.Suraj M said:Yes but why?? carbon and even Beryllium don't go by the Dulong Petit law for specific heat(molar) to be 3R. at room temp.
Everywhere they say, 'due to their high energy vibrational modes not being populated at room temperature' ?
Not that I know. You can do it empirically, by finding a function that fits the observed heat capacity, or computationally.Suraj M said:Oh okay, now i get it. So then, is there any way to find the molar specific heat capacity of carbon, theoretically ??