Clausius equation of state: Difference between revisions
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Carl McBride (talk | contribs) m (Changed comment to be a reference.) |
Carl McBride (talk | contribs) (Corrected T_c to be T_c^3 not T_c^2) |
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At the [[critical points | critical point]] one has <math>\left.\frac{\partial p}{\partial v}\right|_{T=T_c}=0 </math>, and <math>\left.\frac{\partial^2 p}{\partial v^2}\right|_{T=T_c}=0 </math>, which leads to <ref>For details see the [[Mathematica]] [http://urey.uoregon.edu/~pchemlab/CH417/Lect2009/Clausius%20equation%20of%20state%20to%20evaluate%20a%20b%20c.pdf printout] produced by [http://www.uoregon.edu/~chem/hardwick.html Dr. John L. Hardwick].</ref> | At the [[critical points | critical point]] one has <math>\left.\frac{\partial p}{\partial v}\right|_{T=T_c}=0 </math>, and <math>\left.\frac{\partial^2 p}{\partial v^2}\right|_{T=T_c}=0 </math>, which leads to <ref>For details see the [[Mathematica]] [http://urey.uoregon.edu/~pchemlab/CH417/Lect2009/Clausius%20equation%20of%20state%20to%20evaluate%20a%20b%20c.pdf printout] produced by [http://www.uoregon.edu/~chem/hardwick.html Dr. John L. Hardwick].</ref> | ||
:<math>a = \frac{27R^2T_c^ | :<math>a = \frac{27R^2T_c^3}{64P_c}</math> | ||
:<math>b= v_c - \frac{RT_c}{4P_c}</math> | :<math>b= v_c - \frac{RT_c}{4P_c}</math> | ||
Latest revision as of 08:52, 7 September 2012
The Clausius equation of state, proposed in 1880 by Rudolf Julius Emanuel Clausius [1] [2] is given by (Eq. 1 [3])
=RT.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f02e21ed2347a97172552cb26efb9eeb9920888)
where is the pressure, is the temperature, is the volume per mol, and is the molar gas constant. is the critical temperature and is the pressure at the critical point, and is the critical volume per mol.
At the critical point one has , and , which leads to [4]
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a = \frac{27R^2T_c^3}{64P_c}}
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b= v_c - \frac{RT_c}{4P_c}}
and
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c= \frac{3RT_c}{8P_c}-v_c}
References[edit]
- ↑ R. Clausius "Über das Verhalten der Kohlensäure in Bezug auf Druck, Volumen und Temperatur", Annalen der Physik und Chemie 9 pp. 337-357 (1880)
- ↑ R. Clausius "Ueber die theoretische Bestimmung des Dampfdruckes und der Volumina des Dampfes und der Flüssigkeit", Annalen der Physik und Chemie 14 pp. 279-290 (1881)
- ↑ E. Sarrau "Sur la compressibilité des fluides", Comptes Rendus des Séances de l'Académie des Sciences. Paris 101 pp. 941-944 (1885)
- ↑ For details see the Mathematica printout produced by Dr. John L. Hardwick.