Dulong–Petit law

The Dulong–Petit law states that the molar heat capacity of most simple crystalline solids is approximately 3R ≈ 24.9 J/(mol·K), nearly independent of which element it is. Lead, copper, iron, and silver all cluster near this value at room temperature, so that elements with heavy atoms have small specific heats per gram and light-atom elements have large ones, but all have nearly the same heat capacity per atom.

The classical explanation is equipartition: each atom in a solid lattice vibrates in three dimensions, contributing both kinetic and potential energy, for a total of six half-units of (1/2)R each — hence 3R per mole. The law was historically used to estimate atomic weights of newly isolated elements by measuring their specific heats.

Its breakdown at low temperatures — where measured heat capacities fall well below 3R toward zero — was a genuine anomaly for classical physics, resolved only by the quantum theories of Einstein (1907) and Debye (1912), which freeze out vibrational modes as temperature drops.

Announced by Pierre Louis Dulong and Alexis Petit in 1819; its low-temperature failure became one of the motivating puzzles of early quantum theory.