Dulong

Dulong and Pedt s law The product of the atomic weight and the specific heat of a metal is constant of value approximately 6-2. Although not true for all metals at ordinary temperatures, these metals and several non-metals approximate to the law at high temperatures. 

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,... 

The law of Dulong atid Petit was extended to molecular substances by Neumann and Kopp, who suggested drat die heat capacity of a compound containing n atoms per molecule would be given by... 

Ultimate analysis-an analysis to determine the amounts of basic feed constituents. These constituents are moisture, oxygen, carbon, hydro- gen, sulfur, nitrogen, and ash. In addition, it is typical to determine chloride and other elements that may contribute to air emissions or ash- disposal problems. Once the ultimate analysis has been completed, Dulong s formula can be used to estimate the heating value of the sludge, Dulong s formula is ... 

I8II NCIj prepared by P. L. Dulong who lost an eye and three fingers studying its properties. 

P. L. Dulong Hrst clearly demonsiraled the esistence of two oxides of P. 

The variation of specific heat with temperature was discovered by Dulong and Petit in 1819. It explains why so many different heat units exist (cf. 5), and requires the definition of specific heat to be so framed as to allow for this variation. For this purpose we replace the finite changes by infinitesimal ones. If SQ units of heat are absorbed when unit mass of a substance is raised in temperature from 6— SO) to 0- - SO) underspecified conditions, the true specific heat at the temperature 0 is ... 

The variation of specific heat of a solid with temperature was, as has already been stated, discovered by Dulong and Petit as early as 1819, but it is only quite recently that the remarkable relations exhibited at very low temperatures have come to light (cf. Chap. XVIII.). 

Corollary 3.—All gases, if equal volumes of them are taken under the same conditions of temperature and pressure, evolve or absorb equal quantities of heat if compressed or expanded by equal fractions of their volumes (Dulong s rule). 

Boltzmann (S) extended the theory to solids, and was led to a result which to a certain extent is in harmony with the law of Dulong and Petit. 

Melting-Point and Atomic Volume Law of Dulong and Petit. 

Grimont PAD, F Grimond, HLC Dulong de Rosnay, PHA Sneath (1977) Taxonomy of the genus Serratia. J Gen Microbiol 98 39-66. 

The law of Dulong and Petit states that the molar heat capacity of crystalline elements is approximately 25 J/mol deg. With this law, we can calculate approximate atomic weights from heat capacity data. 

The specific heat of a certain element is 0.119J/g deg. Using the law of Dulong and Petit, calculate its approximate atomic weight. 

Calculate the approximate atomic weight of lead using its specific heat, 0.12 J/g deg, and the law of Dulong and Petit. 

The atomic weight in part (a) is close to that determined from the law of Dulong and Petit, so that the assumption that the atoms react in a 1 1 ratio is correct. 

Dulong and Petit, law of the molar heat capacities of crystalline elements are approximately 25 J/mol deg. 

At high temperatures (T>100K) cv is due to the phonon contribution cph which approaches the classical Dulong and Petit value of 3 nR = 24.94n [J/mol K], where n is the number of atoms in the molecule. 

This rule was stated in 1819 by Dulong and Petit, and it indicates that the specific heat of a metal multiplied by the atomic weight is a constant. This relationship provides a way to estimate the atomic weight of a metal if its specific heat is known. How well the rule holds is indicated by the specific heats of metals shown in Table 7.9. 

The data shown in the table indicate that the law of Dulong and Petit holds surprisingly well for metals. For 1 mole of NaCl, there are 2 moles of particles, so the heat capacity is approximately 12 cal/mol deg or 50 J/mol K. However, the heat capacity of a solid is not a constant, but rather it decreases rapidly at lower temperatures as shown in Figure 7.19 for copper. A more complete explanation of the heat capacity of a solid as outlined next was developed by Einstein. 

Using the Law of Dulong and Petit, find out the atomic weight of the metal and then identify it. 

Since co2 =K/m, the mean potential and kinetic energy terms are equal and the total energy of the linear oscillator is twice its mean kinetic energy. Since there are three oscillators per atom, for a monoatomic crystal U m =3RT and Cy m =3R = 2494 J K-1 mol-1. This first useful model for the heat capacity of crystals (solids), proposed by Dulong and Petit in 1819, states that the molar heat capacity has a universal value for all chemical elements independent of the atomic mass and crystal structure and furthermore independent of temperature. Dulong-Petit s law works well at high temperatures, but fails at lower temperatures where the heat capacity decreases and approaches zero at 0 K. More thorough models are thus needed for the lattice heat capacity of crystals. 

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