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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 | | The Dieterici equation of state, proposed in 1899 (Ref. 1) is given by |
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| :<math>p = \frac{RT}{v-b} e^{-a/RTv}</math> | | :<math>\left. p(v-b) \right.= kT e^{-a/kTv}</math> |
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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>): | | where <math>a</math> is an empirical constant. |
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| :<math>a = \frac{4R^2T_c^2}{P_ce^2}</math>
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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>
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| ==References== | | ==References== |
| <references/>
| | # C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899) |
| | | #[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]] |