Editing Law of corresponding states
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The '''law of corresponding states''' is an empirical law which encapsulates the finding that the [[equations of state]] for many real gases are remarkably similar when they are expressed in terms of reduced [[temperature]]s (<math>T_r = T/T_c</math>), [[pressure]]s, (<math>p_r = p/p_c</math>) and volumes (<math>V_r = V/V_c</math>), where the subscript <math>c</math> represents the value of the property at the [[Critical points|critical point]]. This law was first described by [[Johannes Diderik van der Waals]] in his 1873 thesis, and forms the subject of a paper by him in 1913 <ref>[http://www.digitallibrary.nl/proceedings/search/detail.cfm?pubid=1493&view=image&startrow=1 Johannes Diderik van der Waals "The law of corresponding states for different substances", Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen '''15 II''' pp. 971-981 (1913)]</ref> | The '''law of corresponding states''' is an empirical law which encapsulates the finding that the [[equations of state]] for many real gases are remarkably similar when they are expressed in terms of reduced [[temperature]]s (<math>T_r = T/T_c</math>), [[pressure]]s, (<math>p_r = p/p_c</math>) and volumes (<math>V_r = V/V_c</math>), where the subscript <math>c</math> represents the value of the property at the [[Critical points|critical point]]. This law was first described by [[Johannes Diderik van der Waals]] in his 1873 thesis, and forms the subject of a paper by him in 1913 <ref>[http://www.digitallibrary.nl/proceedings/search/detail.cfm?pubid=1493&view=image&startrow=1 Johannes Diderik van der Waals "The law of corresponding states for different substances", Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen '''15 II''' pp. 971-981 (1913)]</ref> | ||
==Assumptions== | ==Assumptions== | ||
Pitzer <ref>[http://dx.doi.org/10.1063/1.1750496 Kenneth S. Pitzer "Corresponding States for Perfect Liquids", Journal of Chemical Physics '''7''' pp. 583-590 (1939)]</ref> produced a list of assumptions in order for the law of corresponding states to apply. This list was later modified by Guggenheim <ref name="Guggenheim"> | Pitzer <ref>[http://dx.doi.org/10.1063/1.1750496 Kenneth S. Pitzer "Corresponding States for Perfect Liquids", Journal of Chemical Physics '''7''' pp. 583-590 (1939)]</ref> produced a list of assumptions in order for the law of corresponding states to apply. This list was later modified by Guggenheim <ref name="Guggenheim"> </ref>. These are: | ||
#There is negligible difference between [[Fermi–Dirac statistics]] and [[Bose–Einstein statistics]] for the system (i.e. the system behaves classically). | #There is negligible difference between [[Fermi–Dirac statistics]] and [[Bose–Einstein statistics]] for the system (i.e. the system behaves classically). | ||
#The effect of quantisation of the translational [[Degree of freedom |degrees of freedom]] is negligible (i.e. the system behaves classically). | #The effect of quantisation of the translational [[Degree of freedom |degrees of freedom]] is negligible (i.e. the system behaves classically). | ||
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#The [[Intermolecular pair potential | potential energy for a pair of molecules]] can be written as <math>A\Phi (r/r_0)</math> where <math>r</math> is the intermolecular distance, and <math>A</math> and <math>r_0</math> are characteristic constants, and <math>\Phi</math> is a universal function. | #The [[Intermolecular pair potential | potential energy for a pair of molecules]] can be written as <math>A\Phi (r/r_0)</math> where <math>r</math> is the intermolecular distance, and <math>A</math> and <math>r_0</math> are characteristic constants, and <math>\Phi</math> is a universal function. | ||
==Examples== | ==Examples== | ||
For [[argon]], [[krypton]], [[nitrogen]], [[oxygen]], [[carbon dioxide]] and [[methane]] one has <ref name="Guggenheim"> </ref> | For [[argon]], [[krypton]], [[nitrogen]], [[oxygen]], [[carbon dioxide]] and [[methane]] one has <ref name="Guggenheim"> [http://dx.doi.org/10.1063/1.1724033 E. A. Guggenheim "The Principle of Corresponding States", Journal of Chemical Physics '''13''' pp. 253-261 (1945)]</ref> | ||
:<math>\frac{p_cV_c}{RT_c}\approx 0.292</math> | :<math>\frac{p_cV_c}{RT_c}\approx 0.292</math> | ||
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by Noro and Frenkel | by Noro and Frenkel | ||
<ref>[http://dx.doi.org/10.1063/1.1288684 Massimo G. Noro and Daan Frenkel "Extended corresponding-states behavior for particles with variable range attractions", Journal of Chemical Physics '''113''' 2941-2944 (2000)]</ref>. | <ref>[http://dx.doi.org/10.1063/1.1288684 Massimo G. Noro and Daan Frenkel "Extended corresponding-states behavior for particles with variable range attractions", Journal of Chemical Physics '''113''' 2941-2944 (2000)]</ref>. | ||
==References== | ==References== | ||
<references/> | <references/> | ||
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*[http://dx.doi.org/10.1016/S0031-8914(38)80037-9 J. de Boer and A. Michels "Contribution to the quantum-mechanical theory of the equation of state and the law of corresponding states. Determination of the law of force of helium", Physica '''5''' pp. 945-957 (1938)] | *[http://dx.doi.org/10.1016/S0031-8914(38)80037-9 J. de Boer and A. Michels "Contribution to the quantum-mechanical theory of the equation of state and the law of corresponding states. Determination of the law of force of helium", Physica '''5''' pp. 945-957 (1938)] | ||
*[http://dx.doi.org/10.1063/1.3072156 Patrick Grosfils and James F. Lutsko "Dependence of the liquid-vapor surface tension on the range of interaction: A test of the law of corresponding states", Journal of Chemical Physics '''130''' 054703 (2009)] | *[http://dx.doi.org/10.1063/1.3072156 Patrick Grosfils and James F. Lutsko "Dependence of the liquid-vapor surface tension on the range of interaction: A test of the law of corresponding states", Journal of Chemical Physics '''130''' 054703 (2009)] | ||
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*Hong Wei Xiang "The Corresponding-States Principle and its Practice", Elsevier Science (2005) ISBN 0-444-52062-7 | *Hong Wei Xiang "The Corresponding-States Principle and its Practice", Elsevier Science (2005) ISBN 0-444-52062-7 | ||
[[category: equations of state]] | [[category: equations of state]] |