Difference between revisions of "Dieterici equation of state"

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The Dieterici equation of state, proposed in 1899 (Ref. 1) is given by
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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.= kT e^{-a/kTv}</math>
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:<math>p =  \frac{RT}{v-b} e^{-a/RTv}</math>
  
where <math>a</math> is an empirical constant.
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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>):
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:<math>a = \frac{4R^2T_c^2}{P_ce^2}</math>
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and
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:<math>b=\frac{RT_c}{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.
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==Sadus modification==
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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]], which is often used to describe the equation of state of the [[hard sphere model]], resulting in (Eq. 5):
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:<math>p = \frac{RT}{v} \frac{(1 + \eta + \eta^2 - \eta^3)}{(1-\eta)^3 }  e^{-a/RTv}</math>
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where <math> \eta = b/4v </math> is the [[packing fraction]].
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This equation gives:
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:<math>a = 2.99679 R T_c  v_c</math>
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and
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:<math>\eta_c = 0.357057</math>
  
 
==References==
 
==References==
# C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)
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<references/>
#[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)]
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[[category: equations of state]]
 
[[category: equations of state]]

Latest revision as of 15:19, 22 September 2010

The Dieterici equation of state [1] is given by

p =  \frac{RT}{v-b} e^{-a/RTv}

where (Eq. 8 in [2]):


a = \frac{4R^2T_c^2}{P_ce^2}

and

b=\frac{RT_c}{P_ce^2}

where p is the pressure, T is the temperature and R is the molar gas constant. T_c is the critical temperature and P_c is the pressure at the critical point.

Sadus modification[edit]

Sadus [3] proposed replacing the repulsive section of the Dieterici equation with the Carnahan-Starling equation of state, which is often used to describe the equation of state of the hard sphere model, resulting in (Eq. 5):

p = \frac{RT}{v} \frac{(1 + \eta + \eta^2 - \eta^3)}{(1-\eta)^3 }  e^{-a/RTv}

where  \eta = b/4v is the packing fraction.

This equation gives:

a = 2.99679 R T_c  v_c

and

\eta_c = 0.357057

References[edit]