The discussion centers around the molar specific heat of carbon, specifically why its measured value (6.1 J/mol·K) differs significantly from the predicted value based on the Dulong-Petit law (approximately 25 J/mol·K). The conversation explores theoretical, empirical, and temperature-dependent aspects of specific heat in relation to carbon and other materials.
Participants express differing views on the significance of temperature dependence in specific heat and the applicability of the Dulong-Petit law to carbon. There is no consensus on a definitive explanation for the observed values or a universally accepted method for determining molar specific heat capacity.
The discussion highlights limitations in understanding the temperature dependence of specific heat and the assumptions underlying the Dulong-Petit law, particularly in relation to the quantization of vibrational modes in solids.
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 ??