Berthelot equation of state: Difference between revisions
Carl McBride (talk | contribs) m (Recalculated a, b, and R) |
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:<math>RT = \left( p + \frac{a}{Tv^2} \right) \left( v - b\right)</math>. | :<math>RT = \left( p + \frac{a}{Tv^2} \right) \left( v - b\right)</math>. | ||
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>, | 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 (Eqs. 4.1 - 4.3 <ref>[http://dx.doi.org/10.1021/ed039p464 Antony F. Saturno "Daniel Berthelot's equation of state", Journal of Chemical Education '''39''' (9) pp. 464-465 (1962)]</ref><ref> [http://www.ucm.es/info/molecsim/Berthelot_EOS.sws SAGE Notebook Worksheet] for use in the mathematics program [http://www.sagemath.org/ SAGE]</ref>) | ||
:<math>b= \frac{ | :<math>a = 3T_cP_cV_c^2</math> | ||
:<math>b= \frac{V_c}{3}</math> | |||
and | and | ||
:<math>R = \frac{ | :<math>R = \frac{8P_cV_c}{3T_c}</math> | ||
where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points | critical]] temperature | where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points | critical]] temperature, <math>P_c</math> is the pressure and <math>V_c</math> is the volume at the critical point. | ||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: equations of state]] | [[category: equations of state]] | ||
Revision as of 13:00, 21 September 2010
The Berthelot equation of state [1] can be written as
- .
At the critical point one has , and ,
which leads to (Eqs. 4.1 - 4.3 [2][3])
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle a=3T_{c}P_{c}V_{c}^{2}}
- 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= \frac{V_c}{3}}
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 R = \frac{8P_cV_c}{3T_c}}
where 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 p}
is the pressure, 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 T}
is the temperature 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 R}
is the molar gas constant. 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 T_c}
is the critical temperature, 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 P_c}
is the pressure 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 V_c}
is the volume at the critical point.
References
- ↑ D. J. Berthelot "Sur Une Méthode Purement Physique Pour La Détermination des Poids Moléculaires des Gaz et des Poids Atomiques de Leurs Éléments", J. Phys., 8 pp. 263-274 (1899)
- ↑ Antony F. Saturno "Daniel Berthelot's equation of state", Journal of Chemical Education 39 (9) pp. 464-465 (1962)
- ↑ SAGE Notebook Worksheet for use in the mathematics program SAGE