Dieterici equation of state: Difference between revisions

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The Dieterici equation of state, proposed in 1899 (Ref. 1) is given by
The '''Dieterici''' [[Equations of state |equation of state]] <ref>C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)</ref> is given by


:<math>\left. p(v-b) \right.= RT e^{-a/RTv}</math>
:<math>p =  \frac{RT}{v-b} e^{-a/RTv}</math>
 
where (Eq. 8 in <ref>[http://dx.doi.org/10.1021/ie50663a005 K. K. Shah and G. Thodos "A Comparison of Equations of State", Industrial & Engineering Chemistry '''57''' pp. 30-37 (1965)]</ref>):


where


:<math>a = \frac{4R^2T_c^2}{P_ce^2}</math>
:<math>a = \frac{4R^2T_c^2}{P_ce^2}</math>
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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 and <math>P_c</math> is the [[pressure]] 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 and <math>P_c</math> is the [[pressure]] at the critical point.
==Sadus modification==
Sadus <ref>[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]</ref> proposed replacing the repulsive section of the Dieterici equation with the [[Carnahan-Starling equation of state]], resulting in (Eq. 5):
:<math>p = \frac{RT}{v} \frac{ 1 + \eta + \eta^2 - \eta^3 }{(1-\eta)^3 }  e^{-a/RTv}</math>
where <math> \eta = b/4v </math> is the [[packing fraction]].
==References==
==References==
# C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)
<references/>
#[http://dx.doi.org/10.1021/ie50663a005 K. K. Shah and G. Thodos "A Comparison of Equations of State", Industrial & Engineering Chemistry '''57''' pp. 30 - 37 (1965)]
 
#[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]
 
[[category: equations of state]]
[[category: equations of state]]

Revision as of 15:00, 22 September 2010

The Dieterici equation of state [1] is given by

where (Eq. 8 in [2]):


and

where is the pressure, is the temperature and is the molar gas constant. is the critical temperature and is the pressure at the critical point.

Sadus modification

Sadus [3] proposed replacing the repulsive section of the Dieterici equation with the Carnahan-Starling equation of state, resulting in (Eq. 5):

where is the packing fraction.

References