# Difference between revisions of "Dieterici equation of state"

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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 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): | + | 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): |

− | :<math>p = \frac{RT}{v} \frac{ 1 + \eta + \eta^2 - \eta^3 }{(1-\eta)^3 } e^{-a/RTv}</math> | + | :<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]]. | where <math> \eta = b/4v </math> is the [[packing fraction]]. | ||

+ | |||

+ | This equation gives: | ||

+ | |||

+ | :<math>a = 2.99679 R T_c v_c</math> | ||

+ | |||

+ | and | ||

+ | |||

+ | :<math>\eta_c = 0.357057</math> | ||

==References== | ==References== |

## Latest revision as of 15:19, 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[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):

where is the packing fraction.

This equation gives:

and

## References[edit]

- ↑ 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)