Editing Clausius equation of state
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where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]], <math> v </math> is the volume per mol, and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points | critical]] temperature and <math>P_c</math> is the [[pressure]] at the critical point, and <math> v_c </math> is the critical volume per mol. | where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]], <math> v </math> is the volume per mol, and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points | critical]] temperature and <math>P_c</math> is the [[pressure]] at the critical point, and <math> v_c </math> is the critical volume per mol. | ||
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 = \frac{27R^2T_c^3}{64P_c}</math> | :<math>a = \frac{27R^2T_c^3}{64P_c}</math> | ||
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and | and | ||
:<math>c= \frac{3RT_c}{8P_c}-v_c</math> | :<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]] |