Clausius theorem
E303521
The Clausius theorem is a fundamental result in thermodynamics that formalizes the second law by relating the cyclic integral of heat transfer over temperature to entropy, showing that this quantity is always less than or equal to zero for any cyclic process.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Clausius inequality | 4 |
| Clausius inequality formulation | 1 |
| Clausius theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2842731 — 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: Clausius theorem Context triple: [Rudolf Clausius, notableFor, Clausius theorem]
-
A.
Kelvin–Planck statement of the second law of thermodynamics
The Kelvin–Planck statement of the second law of thermodynamics asserts that it is impossible to construct a cyclic heat engine that converts all absorbed heat from a single reservoir entirely into work without any other effect.
-
B.
Carathéodory’s formulation of the second law of thermodynamics
Carathéodory’s formulation of the second law of thermodynamics is a mathematically rigorous restatement of the second law based on the inaccessibility of certain thermodynamic states, providing a foundation for the concept of entropy without relying on cyclic processes or heat engines.
-
C.
Carnot efficiency
Carnot efficiency is the theoretical maximum efficiency that any heat engine can achieve when operating between two temperatures, serving as a fundamental limit in thermodynamics.
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D.
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.
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E.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
- 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: Clausius theorem Target entity description: The Clausius theorem is a fundamental result in thermodynamics that formalizes the second law by relating the cyclic integral of heat transfer over temperature to entropy, showing that this quantity is always less than or equal to zero for any cyclic process.
-
A.
Kelvin–Planck statement of the second law of thermodynamics
The Kelvin–Planck statement of the second law of thermodynamics asserts that it is impossible to construct a cyclic heat engine that converts all absorbed heat from a single reservoir entirely into work without any other effect.
-
B.
Carathéodory’s formulation of the second law of thermodynamics
Carathéodory’s formulation of the second law of thermodynamics is a mathematically rigorous restatement of the second law based on the inaccessibility of certain thermodynamic states, providing a foundation for the concept of entropy without relying on cyclic processes or heat engines.
-
C.
Carnot efficiency
Carnot efficiency is the theoretical maximum efficiency that any heat engine can achieve when operating between two temperatures, serving as a fundamental limit in thermodynamics.
-
D.
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.
-
E.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
result in classical thermodynamics
ⓘ
thermodynamic theorem ⓘ |
| appliesTo | cyclic thermodynamic processes ⓘ |
| assumes |
macroscopic equilibrium states
ⓘ
quasi-static reversible paths for equality case ⓘ |
| concernsQuantity | cyclic integral of δQ/T ⓘ |
| consequence | entropy increase in spontaneous processes ⓘ |
| distinguishes |
irreversible processes
ⓘ
reversible processes ⓘ |
| domainOfValidity | macroscopic thermodynamic systems ⓘ |
| equalityCondition | reversible cyclic process ⓘ |
| field | physics ⓘ |
| formalizes | second law of thermodynamics ⓘ |
| framework | classical thermodynamics ⓘ |
| historicalPeriod | 19th century ⓘ |
| implies |
entropy is a state function
ⓘ
entropy of isolated system does not decrease ⓘ existence of entropy state function ⓘ |
| inequalityDirection | less than or equal to zero ⓘ |
| involves | cyclic integral over closed path in state space ⓘ |
| isFormulationOf | Clausius statement of the second law ⓘ |
| mathematicalForm | ∮ (δQ_rev/T) = 0 for reversible cycles ⓘ |
| mathematicalNature | integral inequality ⓘ |
| namedAfter | Rudolf Clausius ⓘ |
| relatedConcept |
Carnot cycle
ⓘ
Kelvin–Planck statement of the second law ⓘ entropy production ⓘ thermodynamic reversibility ⓘ |
| relates |
entropy
ⓘ
heat transfer ⓘ temperature ⓘ |
| shows |
δQ is not an exact differential
ⓘ
δQ/T is an exact differential for reversible processes ⓘ |
| statesInequality | ∮ δQ/T ≤ 0 ⓘ |
| strictInequalityCondition | irreversible cyclic process ⓘ |
| subfield | thermodynamics ⓘ |
| supports |
Clausius inequality
ⓘ
linked to:
Clausius theorem
|
| usedFor | defining integrating factor 1/T for heat ⓘ |
| usedIn |
analysis of heat engine cycles
ⓘ
analysis of refrigeration cycles ⓘ derivation of entropy for general thermodynamic systems ⓘ derivation of entropy for ideal gases ⓘ proofs of maximum efficiency of heat engines ⓘ |
| usedToDefine | entropy change ⓘ |
| usesSymbol |
T
ⓘ
δQ ⓘ ∮ ⓘ |
| validFor | any cyclic process ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Clausius theorem Description of subject: The Clausius theorem is a fundamental result in thermodynamics that formalizes the second law by relating the cyclic integral of heat transfer over temperature to entropy, showing that this quantity is always less than or equal to zero for any cyclic process.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Clausius theorem
linked to: Clausius theorem
linked to: Clausius theorem
linked to: Clausius theorem
linked to: Clausius theorem