Dulong–Petit law for molar heat capacity of many solids at high temperature

E287399

empirical law law of solid-state physics thermodynamic law

The Dulong–Petit law states that many crystalline solids have an approximately constant molar heat capacity of about 3R at sufficiently high temperatures, reflecting classical equipartition of energy among atomic vibrations.

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All labels observed (1)

Label	Occurrences
Dulong–Petit law for molar heat capacity of many solids at high temperature canonical	1

Statements (47)

Predicate	Object
instanceOf	empirical law ⓘ law of solid-state physics ⓘ thermodynamic law ⓘ
appliesTo	many crystalline solids ⓘ monatomic crystalline solids ⓘ
approachedAsLimit	high-temperature limit of the Debye model ⓘ high-temperature limit of the Einstein model ⓘ
assumes	classical behavior of atomic vibrations ⓘ each atom in a solid has three translational degrees of freedom ⓘ each vibrational degree of freedom contributes kB to energy per atom ⓘ harmonic approximation for atomic vibrations ⓘ
basedOn	equipartition theorem ⓘ surface form: classical equipartition theorem
concerns	heat capacity of solids ⓘ lattice vibrations ⓘ
explains	approximate constancy of molar heat capacity of many solids at high temperature ⓘ
failsAt	low temperatures ⓘ
field	solid-state physics ⓘ statistical mechanics ⓘ thermodynamics ⓘ
historicalContext	formulated in the early 19th century ⓘ
holdsBestFor	heavy metallic elements ⓘ simple monatomic metals ⓘ
impliesPerAtomHeatCapacity	3kB ⓘ
involvesConstant	Boltzmann constant ⓘ surface form: Boltzmann constant kB universal gas constant R ⓘ
isClassicalApproximationOf	quantum theory of lattice vibrations ⓘ
limitationsInclude	deviations for covalent crystals like diamond ⓘ deviations for light-element solids ⓘ deviations for solids with low Debye temperature ⓘ
mathematicalForm	Cv,m ≈ 3R ⓘ
molarHeatCapacityApproximateNumericalValue	24.9 J mol−1 K−1 ⓘ 25 J mol−1 K−1 ⓘ
molarHeatCapacityValue	3R ⓘ
namedAfter	Alexis Thérèse Petit ⓘ Pierre Louis Dulong ⓘ
predicts	constant molar heat capacity for many solids at high temperature ⓘ
relatedConcept	Debye model ⓘ surface form: Debye model of solids Debye model ⓘ surface form: Einstein model of solids
relatesQuantity	gas constant R ⓘ molar heat capacity at constant volume ⓘ
states	the molar heat capacity at constant volume is approximately 3R ⓘ
temperatureRegime	high temperature ⓘ
usedFor	estimating atomic weights of elements historically ⓘ
usedIn	introductory solid-state physics ⓘ introductory thermodynamics education ⓘ
validWhen	thermal energy kBT is large compared to vibrational quantum energies ⓘ
yearProposed	1819 ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

equipartition theorem → implies → Dulong–Petit law for molar heat capacity of many solids at high temperature ⓘ