Editing Berthelot equation of state

:<math>RT = \left( p + \frac{a}{Tv^2} \right) \left( v - b\right)</math>

where 

:<math>a= \frac{27}{64}R \frac{T_c^3}{P_c}</math>

and

:<math>b=\frac{RT_c}{8P_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 and <math>P_c</math> is the pressure at the critical point.
==References==
# D. J. Berthelot "", J. Phys., '''8''' pp. 263- (1899)
[[category: equations of state]]
@@ Line 1: / Line 1: @@
-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>
+:<math>RT = \left( p + \frac{a}{Tv^2} \right) \left( v - b\right)</math>
-can be written as
-:<math>RT = \left( p + \frac{a}{Tv^2} \right) \left( v - b\right)</math>.
+where
-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>,
+:<math>a= \frac{27}{64}R \frac{T_c^3}{P_c}</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 open-source mathematics software [http://www.sagemath.org/ SAGE]</ref>)
+and
+:<math>b=\frac{RT_c}{8P_c}</math>
-:<math>a = 3 T_c p_c v_c^2</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 and <math>P_c</math> is the pressure at the critical point.
-:<math>b= \frac{v_c}{3}</math>
-and giving a critical [[compressibility factor]] of
-:<math>Z_c = \frac{p_cv_c}{RT_c} = \frac{3}{8} = 0.375 </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.
-==Low pressure variant==
-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>
 ==References==
-<references/>
+# D. J. Berthelot "", J. Phys., '''8''' pp. 263- (1899)
 [[category: equations of state]]