Berthelot equation of state: Difference between revisions
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The '''Berthelot equation of state''' <ref>[http://dx.doi.org/10.1051/jphystap:018990080026300 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)]</ref> can be written as | The '''Berthelot equation of state''' <ref>[http://dx.doi.org/10.1051/jphystap:018990080026300 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)]</ref><ref>D. Berthelot "", Travaux et Mémoires du Bureau international des Poids et Mesures '''Tome XIII''' (Paris: Gauthier-Villars, 1907)</ref> | ||
can be written as | |||
:<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>. | ||
| Line 8: | Line 9: | ||
:<math>a = | :<math>a = 3 T_c p_c v_c^2</math> | ||
:<math>b= \frac{ | :<math>b= \frac{v_c}{3}</math> | ||
and | and | ||
:<math> | :<math>\frac{RT_c}{p_cv_c} = \frac{8}{3} \approx 2.667 </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, <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, <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 14:40, 21 September 2010
The Berthelot equation of state [1][2] can be written as
- .
At the critical point one has , and ,
which leads to (Eqs. 4.1 - 4.3 [3][4])
and
where is the pressure, is the temperature and is the molar gas constant. is the critical temperature, is the pressure and 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)
- ↑ D. Berthelot "", Travaux et Mémoires du Bureau international des Poids et Mesures Tome XIII (Paris: Gauthier-Villars, 1907)
- ↑ 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