Clausius equation of state: Difference between revisions
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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 | 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 | ||
:<math>a = | :<math>a = \frac{27R^2T_c^2}{64P_c}</math> | ||
:<math>b= \frac{ | :<math>b= v_c - \frac{RT_c}{4P_c}</math> | ||
and | and | ||
:<math>c= \frac{ | :<math>c= \frac{3RT_c}{8P_c}-v_c</math> | ||
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]. | |||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: equations of state]] | [[category: equations of state]] | ||
Revision as of 12:36, 20 November 2009
The Clausius equation of state, proposed in 1880 by Rudolf Julius Emanuel Clausius [1] is given by (Equations 3 and 4 in [2])
=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
and
For details see the Mathematica printout produced by Dr. John L. Hardwick.