Editing Phase rule (section)

{{Short description|General principle in thermodynamics regarding pVT systems in equilibrium}}
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{{Redirect-distinguish|Gibbs rule|Antony Gibbs & Sons v La Societe Industrielle et Commerciale des Metaux}}
In [[thermodynamics]], the '''phase rule''' is a general principle governing multi-component, multi-phase systems in [[thermodynamic equilibrium]]. For a system without [[chemical reaction]]s, it relates the number of freely varying [[intensive properties]] ({{mvar|F}}) to the number of [[Component (thermodynamics)|components]] ({{mvar|C}}), the number of [[Phase (matter)|phases]] ({{mvar|P}}), and number of ways of performing work on the system ({{mvar|N}}):<ref name="Kardar">{{cite book | last=Kardar | first=Mehran | title=Statistical Physics of Particles | publisher=Cambridge University Press | publication-place=Cambridge | date=2007-06-07 | isbn=978-0-521-87342-0 | page=22}}</ref><ref name="Ness">{{Cite book |last1=Ness |first1=Hendrick C. Van |url=https://books.google.com/books?id=PV07vgAACAAJ |title=Introduction to Chemical Engineering Thermodynamics |last2=Abbott |first2=Michael |last3=Swihart |first3=Mark |last4=Smith |first4=J. M. |date=March 20, 2017 |publisher=[[McGraw Hill Education]] |isbn=9781259696527 |location=Dubuque, Iowa |pages=422 |oclc=1001316575}}</ref><ref name="Atkins">{{Cite book |last1=Atkins |first1=Peter William |url=https://books.google.com/books?id=3QpDDwAAQBAJ |title=Atkins' Physical Chemistry |last2=De Paula |first2=Julio |last3=Keeler |first3=James |publisher=[[Oxford University Press]] |year=2018 |isbn=9780198769866|oclc=1013164457 |author-link=Peter Atkins|edition=11th }}</ref>{{rp|123–125}}
:<math>F = N + C - P + 1</math>
Examples of intensive properties that count toward {{mvar|F}} are the temperature and pressure. For simple liquids and gases, [[pressure-volume work]] is the only type of work, in which case {{math|''N'' {{=}} 1}}.

The rule was derived by American physicist [[Josiah Willard Gibbs]] in his landmark paper titled ''[[On the Equilibrium of Heterogeneous Substances]]'', published in parts between 1875 and 1878.<ref name="Gibbs">{{Cite book |last=Gibbs |first=Josiah W. |url=https://books.google.com/books?id=gx8zAQAAMAAJ |title=Scientific Papers of J. Willard Gibbs |publisher=[[Longman]]s, Green and Co. |year=1906 |oclc=1136910263 |author-link=Josiah Willard Gibbs}}</ref>

The number of degrees of freedom {{mvar|F}} (also called the ''variance'') is the number of independent intensive properties, ''i.e.'', the largest number of thermodynamic parameters such as temperature or pressure that can be varied simultaneously and independently of each other.<ref>{{cite book |last1=Atkins |first1=Peter |last2=de Paula |first2=Julio |title=Physical Chemistry |date=2002 |publisher=W. H. Freeman |isbn=0-7167-3539-3 |page=195 |edition=7th}}</ref>

An example of a one-component system ({{math|''C'' {{=}} 1}}) is a pure chemical. A two-component system ({{math|''C'' {{=}} 2}}) has two chemically independent components, like a mixture of water and ethanol. Examples of phases that count toward {{mvar|P}} are [[solid]]s, [[liquid]]s and [[gas]]es.