Clausius theorem

E303521

result in classical thermodynamics thermodynamic theorem

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.

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All labels observed (2)

Label	Occurrences
Clausius inequality	3
Clausius theorem canonical	1

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 of thermodynamics ⓘ surface form: 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 theorem self-linksurface differs ⓘ surface form: Clausius inequality
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 ⓘ

Referenced by (4)

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

Rudolf Clausius → notableFor → Clausius theorem ⓘ

Carnot efficiency → relatedTo → Clausius theorem ⓘ

this entity surface form: Clausius inequality

Clausius theorem → supports → Clausius theorem self-linksurface differs ⓘ

this entity surface form: Clausius inequality

Clausius statement of the second law of thermodynamics → foundationFor → Clausius theorem ⓘ

this entity surface form: Clausius inequality