Berthelot equation of state: Difference between revisions
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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. | 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. | ||
==Low pressure variant== | ==Low pressure variant== | ||
Berthelot also proposed an [[Equations of state |equation of state]] for use at low pressures: | Berthelot also proposed an [[Equations of state |equation of state]] for use at low pressures{{reference needed}}: | ||
:<math>p = \frac{RT}{v} \left( 1 + \frac{9}{128} \frac{pT_c}{p_c T} \left( 1- \frac{6T_c^2}{T^2} \right) \right)</math> | :<math>p = \frac{RT}{v} \left( 1 + \frac{9}{128} \frac{pT_c}{p_c T} \left( 1- \frac{6T_c^2}{T^2} \right) \right)</math> | ||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: equations of state]] | [[category: equations of state]] | ||
Revision as of 17:41, 29 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 giving a critical compressibility factor of
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.
Low pressure variant
Berthelot also proposed an equation of state for use at low pressures[?]
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 open-source mathematics software SAGE