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| {{Thermodynamics|cTopic=[[List of thermodynamic properties|System properties]]}}
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| According to van der Waals, the '''theorem of corresponding states''' (or '''principle of corresponding states''') indicates that all [[fluid]]s, when compared at the same [[reduced temperature]] and [[reduced pressure]], have approximately the same [[compressibility factor]] and all deviate from ideal gas behavior to about the same degree.<ref>{{cite book |author=Tester, Jefferson W. and Modell, Michael |title=Thermodynamics and its applications |publisher=Prentice Hall |year=1997 |isbn=0-13-915356-X}}</ref><ref>{{cite book|author=Çengel Y.A., Boles M.A.|title=Thermodynamics: An Engineering Approach|edition=Sixth Edition|publisher=McGraw Hill|year= 2007|isbn=9780071257718}} page 141</ref>
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| [[Material constant]]s that vary for each type of material are eliminated, in a recast reduced form of a [[constitutive equation]]. The reduced variables are defined in terms of [[critical variables]].
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| It originated with the work of [[Johannes Diderik van der Waals]] in about 1873<ref>[http://digital.library.okstate.edu/oas/oas_pdf/v56/p125_132.pdf ''A Four-Parameter Corresponding States Correlation for Fluid Compressibility Factors''] by Walter M. Kalback and Kenneth E. Starling, Chemical Engineering Department, [[University of Oklahoma]].</ref> when he used the [[critical temperature]] and [[critical pressure]] to characterize a fluid.
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| The most prominent example is the [[van der Waals equation]] of state, the reduced form of which applies to all fluids.
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| ==Compressibility factor at the critical point==
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| The compressibility factor at the critical point, which is defined as <math>Z_c=\frac{p_c}{n_c k_B T_c}</math>, where the subscript <math>c</math> indicates the [[Critical point (thermodynamics)|critical point]] is predicted to be a constant independent of substance by many equations of state; the [[Van der Waals equation]] e.g. predicts a value of <math>3/8 = 0.375</math>.
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| {| class="wikitable sortable" border="1"
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| ! Substance
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| ! Value
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| | [[Properties of water|H<sub>2</sub>O]]
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| | 0.23<ref name="Goodstein">{{cite book|last=Goodstein|first=David|title=States of Matter|edition=1st|origyear=1975|year=1985|publisher=[[General Publishing Company, Ltd.]]|location=[[Toronto]], [[Canada]]|isbn=0-486-64927-X|page=452|chapter=6|trans_chapter=Critical Phenomena and Phase Transitions}}</ref>
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| | [[Helium-4|<sup>4</sup>He]]
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| | 0.31<ref name="Goodstein"/>
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| |[[Helium|He]]
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| | 0.30<ref name="Boer">{{cite journal| last = de Boer| first = J.|date=April 1948| title = Quantum theory of condensed permanent gases I the law of corresponding states| journal = [[Physica (journal)|Physica]]| volume = 14| pages = 139–148| publisher = [[Elsevier]]| location = [[Utrecht (city)|Utrecht]], [[Netherlands]]| doi =10.1016/0031-8914(48)90032-9 | accessdate = 2009-12-08|bibcode = 1948Phy....14..139D }}</ref>
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| |-
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| |[[Hydrogen|H<sub>2</sub>]]
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| |0.30<ref name="Boer"/>
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| |-
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| |[[Neon|Ne]]
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| |0.29<ref name="Boer"/>
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| |-
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| |[[Nitrogen|N<sub>2</sub>]]
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| |0.29<ref name="Boer"/>
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| |-
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| |[[Argon|Ar]]
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| |0.29<ref name="Boer"/>
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| |}
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| ==See also==
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| *[[Van der Waals equation]]
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| *[[Equation of state]]s
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| *[[Compressibility factor]]s
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| *[[Johannes Diderik van der Waals]]
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| *[[Noro-Frenkel law of corresponding states]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| * [http://iptibm1.ipt.ntnu.no/~jsg/undervisning/naturgass/parlaktuna/Chap3.pdf Properties of Natural Gases]. Includes a chart of compressibility factors versus reduced pressure and reduced temperature (on last page of the PDF document)
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| *[http://www.sklogwiki.org/SklogWiki/index.php/Law_of_corresponding_states Theorem of corresponding states] on [http://www.sklogwiki.org/ SklogWiki].
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| <br>
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| [[Category:Thermodynamics]]
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| [[Category:Chemical engineering]]
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| [[Category:Continuum mechanics]]
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| {{thermodynamics-stub}}
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