Dulong and Petit’s rule

The heat capacity, the heat required to raise 1 g-mole drrough one kelvin, can be calculated at temperatures generally above 300 K by two simple empirical rules. The first of these, Dulong and Petit s rule, was discovered in the course of calorimeU ic smdies of the heat capacities of the elements and shows drat the heat capacity has a value,... 

According to Dulong and Petit s rule the specific heat per gramatom amounts to about 6 cal./deg. Since now the specific heat per grammol. is 11.9 cal./deg. for NaCl at o° C, it follows that there must be two particles per molecule of NaCl. The specific heat depends, however, on the temperature, and deviations from this rule, both upwards and downwards, are numerous so that the argument is not so significant. For LiCl, LiH and MgO at o° C one finds 9.7, 7.8 and 8.4 cal./deg., respectively, for the molecular heat nevertheless these are also ionic lattices. 

Formerly these metallic properties were attributed to the presence of free electrons. The classical theory of this electron gas (Lorentz) leads, however, to absurdities for instance, a specific heat of 3/2 R had to be expected for this monatomic gas, contrary to the experience that Dulong and Petit s rule (atomic specific heat 6/2 R) holds for both conductors and non-conductors. The calculated ratio of heat conductivity to electrical conductivity (Wiedemann-Franz constant) also did not agree with observation. 

Another paper of Einstein s showed that quantization of energy also predicted that Dulong and Petit s heat capacity rule would only be valid at high temperatures. Assume that the only allowed energies are E = 0, hv, 2hv,... nhv, where n can be arbitrarily large. The average energy is... 

The rule of Dulong and Petit, dealing with the relation between the heat capacity of an element and its atomic weight, has been mentioned in Chapter 8. It is closely related to Kopp s rule. 

Dulong s rule 613 and Petit s law 200 dumai ine (ketopentamethylene) 3 54 Dutch liquid 355,361,396 dyad 13... 

Although much work has been done on the three reference substances described here, there are still needs for refinement of heat capacity measurements and frequency spectra fit. Most emjdiasis has been placed on obtaining a picture of the vibrations in the ideal crystal lattice. The questions about vibrations in small and defect crystals has at pre nt only been opened. Historically, the universal Dulong Petit-Rule of heat capacity which fits only well at elevated temperatures was replaced between 1900 and 1920 mainly throi h the work of Einstein, Debye. Nemst, and Lindemaim by a theory with one characteristic constant for each substance, the 0-temperature. The Tarasov treatment of the 1950 s shows that in case of strong anisotropy of forces, as in one or two dimensionally strongly bonded crystals, a second constant... 

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