Dulong–Petit law

The Dulong–Petit law, a thermodynamic rule proposed in 1819 by French physicists Pierre Louis Dulong and Alexis Thérèse Petit, states the classical expression for the molar specific heat capacity of certain chemical elements. Experimentally the two scientists had found that the heat capacity per weight (the mass-specific heat capacity) for a number of elements was close to a constant value, after it had been multiplied by a number representing the presumed relative atomic weight of the element. These atomic weights had shortly before been suggested by Dalton.

In modern terms, Dulong and Petit found that the heat capacity of a mole of many solid elements is about 3R, where R is the modern constant called the universal gas constant. Dulong and Petit were unaware of the relationship with R, since this constant had not yet been defined from the later kinetic theory of gases. The value of 3R is about 25 joules per kelvin, and Dulong and Petit essentially found that this was the heat capacity of certain solid elements, per mole of atoms they contained.

The modern theory of the heat capacity of solids states that it is due to lattice vibrations in the solid, and was first derived in crude form from this assumption by Albert Einstein, in 1907. The Einstein solid model thus gave for the first time a reason why the Dulong–Petit law should be stated in terms of the classical heat capacities for gases.

An equivalent statement of the Dulong–Petit law in modern terms is that, regardless of the nature of the substance, the specific heat capacity c of a solid element (measured in joule per kelvin per kilogram) is equal to 3R/M, where R is the gas constant (measured in joule per kelvin per mole) and M is the molar mass (measured in kilogram per mole). Thus, the heat capacity per mole of many elements is 3R.

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