Dulong–Petit law

E287400

The Dulong–Petit law is an early empirical rule in thermodynamics stating that many solid elements have approximately the same molar heat capacity at high temperatures.

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Dulong–Petit law canonical 1

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Predicate Object
instanceOf empirical law
law of thermodynamics
appliesTo crystalline solids
metals
monatomic crystalline solids
solid elements
approximateFor heavy metallic elements
approximateNumericalValue 24.9 J mol−1 K−1
assumes each atom in a solid contributes 3k_B to heat capacity
basedOn classical equipartition theorem
contrastedWith Debye model
surface form: Debye model of specific heat

Debye model
surface form: Einstein model of specific heat
describes molar heat capacity of many solid elements
explainedBy quantum theory of specific heat
field physical chemistry
solid-state physics
thermodynamics
givesApproximateValue 3R
about 25 joules per mole kelvin
historicalContext 19th-century thermodynamics
holdsBestFor simple crystalline metals at room temperature
implies molar heat capacity is independent of atomic mass
involvesConstant gas constant R
lessAccurateAt low temperatures
lessAccurateFor elements with low Debye temperature
light elements
mathematicalForm C_V ≈ 3R for many solid elements
namedAfter Alexis Thérèse Petit
Pierre Louis Dulong
proposedBy Alexis Thérèse Petit
Pierre Louis Dulong
quantityDescribed molar heat capacity at constant pressure (approximately)
molar heat capacity at constant volume
relatedConcept Debye temperature
Einstein solid
equipartition of energy
heat capacity
specific heat capacity
scope classical high-temperature limit of lattice heat capacity
states many solid elements have approximately the same molar heat capacity at high temperature
status approximate law
superseded in detail by quantum models of specific heat
typeOf specific heat law
unitContext joules per mole kelvin
usedFor estimating atomic weights of elements (historically)
validAt high temperatures
yearProposed 1819

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equipartition theorem relatedTo Dulong–Petit law