# Difference between revisions of "Dieterici equation of state"

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

− | :<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>): | ||

− | |||

:<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== | ||

− | + | <references/> | |

− | + | ||

− | + | ||

[[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

- ↑ C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)
- ↑ K. K. Shah and G. Thodos "A Comparison of Equations of State", Industrial & Engineering Chemistry
**57**pp. 30-37 (1965) - ↑ Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics
**115**pp. 1460-1462 (2001)