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Section 9-354 entries

9-35.1microcanonical partition function 9-35.2canonical partition function 9-35.3grand-canonical partition function, grand partition function 9-35.4molecular partition function, partition function of a molecule

9-35.3

grand-canonical partition function, grand partition function

URNurn:iso:std:iso:80000:-9:ed-2:en:item:9-35.3

Download RDF.jsonld .ttl

https://metanorma.github.io/isq-smart/quantities/part-9/t9-35.3
urn:iso:std:iso:80000:-9:ed-2:en:item:9-35.3

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-9:ed-2:en:item:9-35.3

IEC

urn:iec:std:iec:80000-9:2019:::item:9-35.3

Designations

ENgrand-canonical partition function

FRfonction de partition grand-canonique

ENgrand partition function

FRfonction de partition grand canonique

Symbol

Ξ

Notation systems

Rendered

Ξ

AsciiMath

ii(Xi)

LaTeX

\mathit{\Xi}

Definition

sum of canonical partition function $Z (N_{A}, N_{B}, \dots)$ for the given number of particles $A, B$ multiplied by absolute activities (absolute activity) $λ_{A}, λ_{B}, \dots$ of particles $A, B$ :

Ξ = \sum_{N_{A}, N_{B}, \dots} Z (N_{A}, N_{B}, \dots) \cdot λ_{A}^{N_{A}} \cdot λ_{B}^{N_{B}} \cdot \dots

somme regroupant les produits de la fonction de partition canonique $Z (N_{A}, N_{B}, \dots)$ , pour les nombres donnés de particules $A, B$ , et des activités absolues(absolute activity) $λ_{A}, λ_{B}, \dots$ des particules $A, B$ :

Ξ = \sum_{N_{A}, N_{B}, \dots} Z (N_{A}, N_{B}, \dots) \cdot λ_{A}^{N_{A}} \cdot λ_{B}^{N_{B}} \cdot \dots

Units

1

one

View related quantities →

Notes

A - \sum μ_{B} n_{B} = - k T ln Ξ

where $A$ is Helmholtz energy (ISO 80000-5: Thermodynamics), $μ_{B}$ is the chemical potential of substance $B$ , and $n_{B}$ is the amount of substance $B$ .

A - \sum μ_{B} n_{B} = - k T ln Ξ

où $A$ est l'énergie libre (ISO 80000-5: Thermodynamics), $μ_{B}$ est le potentiel chimique du constituant $B$ et $n_{B}$ est la quantité de matière du constituant $B$ .

Concept HierarchyPendrill (2024)

1dimensionless quantitiesLevel 0 · Kind

Broader concepts

◇ dimensionless quantities

Characterizes

● substance

Ontology
isq:Quantity smart:TermEntry

Class Hierarchy

smart:Entity smart:TermEntryisq:Quantity

A physical quantity as defined in ISO/IEC 80000, with associated symbols, definitions, and units of measurement.

Instance IRI

isq:t9-35.3

Properties

isq:QuantityShape

Property	Value
rdf:type	isq:Quantity smart:TermEntry
dcterms:identifier	9-35.3
skosxl:prefLabel	"grand-canonical partition function"@en
skosxl:altLabel	"grand partition function"@en"ii(Xi)"@en
skos:definition	sum of canonical partition function stem:[Z (N_"A",N_"B",...)] for the given number of particles stem:["A", "B"] multipl…
skos:note	[stem%unnumbered] ++++ A - sum mu_"B" n_"B" = - kT "ln" ii(Xi) ++++ where stem:[A] is Helmholtz energy (<<iso80000-5>>)…
isq:hasUnit	1 (one)
isq:hasDimension	isq:Dimension
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-9

Related Entities

isq:QuantityShape isq:part-9 isq:Unit isq:Dimension isq:hasDimension smart:TermEntry