Question

what is dulong and Petit's law

Answer 1

The law was formulated (1819) on the basis of observations by the French chemist Pierre-Louis Dulong and the French physicist Alexis-Thérèse Petit. If the specific heat of an element is measured, its atomic weight can be calculated using this empirical law; and many atomic weights were originally so derived. Dulong–Petit law. science. Alternative Title: Dulong and Petit's law. Dulong–Petit law, statement that the gram-atomic heat capacity (specific heat times atomic weight) of an element is a constant; that is, it is the same for all solid elements, about six calories per gram atom.

Answer 2

The specific heat of copper is 0.093 cal/gm K (.389 J/gm K) and that of lead is only 0.031 cal/gm K(.13 J/gm K). Why are they so different? The difference is mainly because it is expressed as energy per unit mass; if you express it as energy per mole, they are very similar. It is in fact that similarity of the molar specific heats of metals which is the subject of the Law of Dulong and Petit. The similarity can be accounted for by applying equipartition of energy to the atoms of the solids.
From just the translational degrees of freedom you get 3kT/2 of energy per atom. Energy added to solids takes the form of atomic vibrations and that contributes three additional degrees of freedom and a total energy per atom of 3kT. The specific heat at constant volume should be just the rate of change with temperature (temperature derivative) of that energy.