Talk:Dulong–Petit law

dulong and petit's work were not perfect. infact, they had large errors on their specific heat calculations. LARGE errors. that is why dulong and petit died unhappy. and im sure you will too. with love <3 -emi To be fair the Dulong and Petit rule works remarkably well at oridianry temperatures e.g room temperature.. It is consistent with the Equipartiion of Energy Theroem. As early as 1819 Dulong and Petit discovered that the molat specific heat of solids at about 6 cal/mole.deg C. This can now be explaind by recognizing that the atom 0r molecule in a solid has 3 degrees of translational freedom and 3 degress of vibrational freedon ( 2 degees 0f freedom each for the X, Y, and Z axis). The Equipartion of Energy Theorem states that there is an average of 1/2 RT of energy per mole. i.e. 6(1.2) RT for the each mole of solid. The molar specific heat will then be 3R. R ia about 2 calories/mole. deg C. 3*2= 6. i.e., C= 6 cla/mole.deg C. That is remarkable. Let's try for it e.g. for Aluminium M= 27 grams/mole. C = 6/27 =0.22 Cal/gram. deg C. Which is fairly accurate.

"high T"
By itself the phrase "high temperatures" is meaningless. High compared to what? --Starwed 05:27, 25 September 2007 (UTC)

Chemical Law?
This law is to do with the vibrations of the atoms (as oscillators) in crystals and therefore to dub it as a chemical law is misleading. 71.103.51.35 (talk) 06:35, 28 February 2008 (UTC)Ur

Dulong-Petit and heat capacity of water: a contradiction?
The molar mass of water is (2*1.008+15.999)g/mol = 18,015 g/mol. In 1g of water are therefore 2*0.055509 mol H-atoms(!) and 0.055509 mol O-atoms.

The specific heat capacity is therefore -according to Dulong-Petit- max. 2*0.055509g/mol*3R + 0.055509g/mol*3R = 0.499958g/mol * 8.3145 J/molK =4.154 J/gK.

But according to textbooks and physical tables is c = 4,18 to 4,19 J/gK  (that's about 0,7% more)!

(I had posted that question nearly 5 years ago in another wikipedia - discussion of an article.) --Bgm2011 (talk) 11:10, 28 August 2011 (UTC)

Units for M and c
In tables you usually find c given in either kJ per K per kg or J per K per g, J per K per kg is unusual. Also M is usually grams per mole. The units should be changed to avoid errors. Gp4rts (talk) 06:25, 1 September 2012 (UTC)

Elements, not "substances"
The article needs some editing. Reference to the article cited in the External Link shows that Dulong and Petit made reference only to 13 elements, not compounds. Expansion of the Dulong-Petit law to compounds was due to Kopp and Neumann, much later. Also, "specific heat capacity" is redundant. "Specific heat" and "heat capacity" are synonyms. I will carry out the necessary edits.Ajrocke (talk) 13:38, 14 June 2015 (UTC)

Not true - "specific heat" has a complicated etymology (was originally based on water). Heat capacity is most definitely not assumed to be mass-specific; in fact, molar/volume specific, Cv, would be the most rigorously utilized. Wikibearwithme (talk) 07:14, 6 January 2016 (UTC)

derivation of what?
What does the derivation section have to do with the DP "law" ; and what does the statement for Cv, "which is independent of temperature" have to do with physical reality? Wikibearwithme (talk) 07:23, 6 January 2016 (UTC)

Boltzmann's contribution
ReyHahn, you wrote that Boltzmann in 1896 explained the Dulong-Petit law quantitatively. I do not find anything he wrote in 1896 in this regard. What I did find was his article "Analytischer Beweis des zweiten Hauptsatzes..." from 1871, where on the last two pages he explicitly states that if restoring forces are proportional to displacements (i.e., for harmonic oscillators), the specific heat of solids is double the value for gases. There is no additional reference given there, so in today's convention this would mean that this was his idea, and presented there for the first time. However, this was 150 years ago, where the conventions were different, so the idea could have been older (and also by somebody else). Seattle Jörg (talk) 09:56, 23 February 2022 (UTC)
 * the book I cited insists several times that it was Boltzmann idea. Unfortunately, no source is given. I would have to check Boltzmann's papers, do you know where I can find an archive/list of them? --ReyHahn (talk) 14:08, 23 February 2022 (UTC)
 * the second source I have recently found cites 1877 Über die Natur der Gasmoleküle Wie.Ber. but I have not found a preview of the article yet.--ReyHahn (talk) 20:13, 23 February 2022 (UTC)
 * I did not know about this ping function, I hope I use it correctly. Can you read German? I have his complete works (about 200 MB in total, but I could give you also the specific articles you want). Seattle Jörg (talk) 08:40, 24 February 2022 (UTC)
 * Yes, in Über die Natur der Gasmoleküle (which is from 1876, however) he states that, but explicitly (my translation) "... thus, on average the total added energy is double of that which increases the kinetic energy [vis viva] ... this agrees well with the result I had derived earlier that half of the added energy goes into the vis viva, half into the work [meaning potential energy], if the restoring forces are proportional to the displacements". Thus, he himself states that it was earlier than 1876, but gives no explicit reference what he himself sees as the first publication. Seattle Jörg (talk) 08:57, 24 February 2022 (UTC)
 * you are using the ping right. Does he say something about Dulong-Petit explicitly? I cannot read German but thanks for the offer. --ReyHahn (talk) 21:08, 25 February 2022 (UTC)
 * Yes. You can find the work at the link http://www.zobodat.at/pdf/SBAWW_63_2_0712-0732.pdf -- you can copy the text out of the pdf, and DeepL does a quite good job of translating the last paragraph: "the amount of heat applied to internal work is equal to that applied to temperature increase, and since in solids the external work can be neglected, the total amount of heat applied is twice as great as that applied to temperature increase. The real specific heat, which we find experimentally, is therefore twice as great as the true heat capacity; and since the latter is proportional to the atomic weight, so must be the former. In the case of solid bodies which obey Dulong-Petit's or Neumann's law, the forces acting on an atom thus appear to be proportional in the first approximation to its distance from the position of rest. In the case of solid bodies which do not obey Dulong's law, however, this should no longer be the case. Translated with www.DeepL.com/Translator (free version)" Seattle Jörg (talk) 08:45, 7 March 2022 (UTC)