Dulong and Petits Law

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

To determine the amount of heat absorbed by the glass of the calorimeter beaker, mark the level of the water in the beaker when running the experiment. Use the data obtained to approximately determine the mass of the glass heated by the water. Consider that the mass of the thermometer glass immersed in the liquid is about 2 g. Use the found specific heat capacity to calculate the atomic mass of lead by the Dulong and Petit law. 

This is not the place for consideration of these methods, so that we shall content ourselves with enumerating the most important this enumeration may show us the diversity both of the measurements, which allow the behaviour of a solid towards the Dulong and Petit law to be foreseen, and of the types of phenomenon which may be brought by its means into one common field of view. 

Dulong and Petite law For a solid element the product of the relative atomic mass and the specific heat capacity is a constant equal to about 25 J mol K . Formulated in these terms in 1819 by the French scientists Pierre Dulong (1785-1838) and Alexis Petit (1791-1820), the law in modern terms states the molar heat capacity of a solid element is approximately equd to 31i where R is the gas constant. The law is only approximate but applies with fair accuracy at normal temperatures to elements with a simple crystal structure. gj fElUlillJlIIIIH. ... 

Dulong and Petit, law of n. The specific heats of the several elements are inversely proportional to their atomic weights. The atomic heats of solid elements are constant and approximately equal to 6.3. Certain elements of low atomic weight and high... 

This is the Dulong and Petit law, which we can deduce from the kinetic theory of gases, noting that 3N vibrational degrees of freedom correspond to 6Nquadratic terms. 

Specific heat behavior in crystalline solids can be characterized by the following three laws law of Dulong and Petit, law of Debye, and Einsteins law. 

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. 

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. 

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. 

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

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. 

You know that technetium has an atomic mass of 100., and substituting this into the law of Dulong and Petit gives you... 

B) The Law of Dulong and Petit states that molar mass x specific heat = 25 J/mole °C... 

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