Dulong–Petit law for molar heat capacity of many solids at high temperature
E287399
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Dulong–Petit law for molar heat capacity of many solids at high temperature canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2682918 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dulong–Petit law for molar heat capacity of many solids at high temperature Context triple: [equipartition theorem, implies, Dulong–Petit law for molar heat capacity of many solids at high temperature]
-
A.
Onsager reciprocal relations
Onsager reciprocal relations are fundamental symmetry relations in nonequilibrium thermodynamics that link pairs of coupled fluxes and forces, showing that certain transport coefficients are equal.
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B.
Kirchhoff's law of thermal radiation
Kirchhoff's law of thermal radiation is a fundamental principle in thermodynamics stating that, for a body in thermal equilibrium, its emissivity equals its absorptivity at each wavelength.
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C.
Langevin theory of paramagnetism
The Langevin theory of paramagnetism is a classical statistical model that explains how the magnetization of paramagnetic materials depends on temperature and applied magnetic field by treating atomic magnetic moments as non-interacting dipoles subject to thermal agitation.
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D.
Curie law of magnetization
The Curie law of magnetization is a fundamental principle in magnetism stating that the magnetic susceptibility of a paramagnetic material is inversely proportional to its absolute temperature.
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E.
Sackur–Tetrode equation
The Sackur–Tetrode equation is a fundamental formula in statistical mechanics that gives the absolute entropy of an ideal monatomic gas in terms of its volume, temperature, and particle number.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Dulong–Petit law for molar heat capacity of many solids at high temperature Target entity description: 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.
-
A.
Onsager reciprocal relations
Onsager reciprocal relations are fundamental symmetry relations in nonequilibrium thermodynamics that link pairs of coupled fluxes and forces, showing that certain transport coefficients are equal.
-
B.
Kirchhoff's law of thermal radiation
Kirchhoff's law of thermal radiation is a fundamental principle in thermodynamics stating that, for a body in thermal equilibrium, its emissivity equals its absorptivity at each wavelength.
-
C.
Langevin theory of paramagnetism
The Langevin theory of paramagnetism is a classical statistical model that explains how the magnetization of paramagnetic materials depends on temperature and applied magnetic field by treating atomic magnetic moments as non-interacting dipoles subject to thermal agitation.
-
D.
Curie law of magnetization
The Curie law of magnetization is a fundamental principle in magnetism stating that the magnetic susceptibility of a paramagnetic material is inversely proportional to its absolute temperature.
-
E.
Sackur–Tetrode equation
The Sackur–Tetrode equation is a fundamental formula in statistical mechanics that gives the absolute entropy of an ideal monatomic gas in terms of its volume, temperature, and particle number.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Dulong–Petit law for molar heat capacity of many solids at high temperature Description of subject: 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.
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
ⓘ