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| Dulong–Petit law | |
|---|---|
| Name | Dulong–Petit law |
| Discovered | 1819 |
| Discoverers | Pierre Louis Dulong; Alexis Thérèse Petit |
| Field | Thermodynamics; Physical chemistry; Solid-state physics |
Dulong–Petit law The Dulong–Petit law is an empirical rule concerning molar specific heats of solid elements, historically significant in chemistry and physics. First reported by Pierre Louis Dulong and Alexis Thérèse Petit in 1819, it influenced work by John Dalton, Amedeo Avogadro, Dmitri Mendeleev, and Jöns Jakob Berzelius on atomic weights and periodic classifications. The law played a role in experimental programs at institutions such as the École Polytechnique, the Collège de France, and laboratories associated with Georg Ohm, André-Marie Ampère, and later researchers like Max Planck and Albert Einstein who developed quantum corrections.
Dulong and Petit published measurements linking atomic masses used by John Dalton, Jöns Jakob Berzelius, and Amedeo Avogadro to thermal properties studied by James Prescott Joule and Joseph Black. Their 1819 communication to the Académie des Sciences was contemporaneous with work at the Royal Society and the Société Philomathique de Paris, and it influenced efforts by William Hyde Wollaston, Friedrich Wöhler, Justus von Liebig, and Hermann von Helmholtz to determine atomic weights and specific heats. The rule was used by Dmitri Mendeleev during formulation of the Periodic table and debated by J. J. Thomson and Ernest Rutherford in the context of atomic structure. Discrepancies noticed by James Dewar, Lord Kelvin, and later by Max Planck pointed toward limitations that quantum theory would later address, with contributions from Albert Einstein, Peter Debye, and Niels Bohr.
The law states that the molar heat capacity at constant volume for many solid elements is approximately constant and close to 3R, where R is the ideal gas constant used in the work of Lavoisier, Claude Louis Berthollet, and Rudolf Clausius. In modern notation the empirical form is C_v ≈ 3R per mole of atoms, a relation utilized by Svante Arrhenius, Walther Nernst, and Hendrik Lorentz in thermal calculations. More explicitly, for a crystalline solid containing N_A atoms per mole, the law connects classical equipartition of energy developed by James Clerk Maxwell, Ludwig Boltzmann, and Josiah Willard Gibbs to measured specific heats employed by Henri Becquerel and Marie Curie in calorimetric studies.
Early confirmations came from calorimetry practiced by Pierre-Simon Laplace, Jean Baptiste Biot, and Joseph Louis Gay-Lussac, and from atomic weight tables compiled by Berzelius and Mendeleev. Deviations were reported for light elements like carbon (in the form of graphite), boron, and beryllium, and for transition metals and elements with complex crystal structures examined by William Ramsay, Arnold Sommerfeld, and Walther Nernst. Low-temperature experiments by Heike Kamerlingh Onnes, Pieter Zeeman, and later by Felix Bloch and Clifford Shull demonstrated marked departures as temperatures approached cryogenic regimes investigated with techniques refined by Ernest Rutherford and Edward Teller-era laboratories. Anomalies were also noted in studies of isotopically substituted materials by Francis Aston and in pressure-dependent work by Gustav Kirchhoff.
Classical explanation invoked the equipartition theorem associated with Ludwig Boltzmann and James Clerk Maxwell, predicting 3 degrees of freedom per atom in a solid and hence 3R molar heat capacity, a viewpoint echoed by Josiah Willard Gibbs and Hermann von Helmholtz. Quantum corrections arose from the work of Max Planck on black-body radiation and the quantum hypothesis, further developed by Albert Einstein who proposed the Einstein solid model, and by Peter Debye who introduced the Debye model using phonons and concepts from Felix Bloch and Walter Heitler. These quantum theories incorporate quantization of vibrational modes and predict low-temperature heat capacity behavior consistent with experiments of Heike Kamerlingh Onnes and later neutron-scattering studies by Clifford Shull and Bertram Brockhouse.
Historically, the law aided atomic weight determinations used by John Dalton, Jöns Jakob Berzelius, and Dmitri Mendeleev in formulating chemical systems at institutions like University of Paris and University of Cambridge. It remains a rule of thumb for simple metals and many crystalline solids at high temperatures near the Debye temperature described by Peter Debye. Limitations arise for light elements, covalent solids (exemplified by carbon in diamond and graphite), low-dimensional systems studied by Paul Dirac-inspired models, and materials with electronic contributions such as copper, gold, and aluminum where conduction electrons treated by Arnold Sommerfeld and Lev Landau affect heat capacity. Modern materials science involving graphene, boron nitride, and complex oxides studied at facilities like CERN and Oak Ridge National Laboratory uses quantum models beyond the classical Dulong–Petit estimate.
Related empirical and theoretical results include the equipartition theorem of Ludwig Boltzmann and James Clerk Maxwell, the Einstein and Debye models developed by Albert Einstein and Peter Debye, and extensions addressing electronic and magnetic contributions explored by Arnold Sommerfeld and Lev Landau. Connections exist with laws and principles named after Nernst (the Nernst heat theorem), Planck (Planck's law), and thermodynamic formalisms by Rudolf Clausius and Josiah Willard Gibbs. Subsequent work by Max Born, John Bardeen, Walter Brattain, and William Shockley incorporated lattice dynamics into semiconductor theory, while scattering techniques advanced by Clifford Shull and Bertram Brockhouse refined understanding of phonons and specific heat in complex materials.