# Difference between revisions of "Thiele hard sphere equation of state"

(Mentioned the Carnahan-Starling equation) |
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− | The '''Thiele hard sphere equation of state''' is an [[equations of state|equation of state]] for a [[hard sphere model|hard sphere]] fluid developed by Thiele in 1963. The equation provides a better approximation of the repulsive forces between molecules than the [[Van der Waals equation of state|Van der Waals repulsive term]]. The equation is given below: | + | The '''Thiele hard sphere equation of state''' is an [[equations of state|equation of state]] for a [[hard sphere model|hard sphere]] fluid developed by Thiele in 1963 |

+ | <ref>[https://doi.org/10.1063/1.1734272 Everett Thiele "Equation of State for Hard Spheres", Journal of Chemical Physics '''39''' 474 (1963)]</ref>. | ||

+ | The equation provides a better approximation of the repulsive forces between molecules than the [[Van der Waals equation of state|Van der Waals repulsive term]]. The equation is given below: | ||

<math> Z_{hs} = \frac{p_{hs}V_m}{RT} = \frac{1 - \eta^3}{(1-\eta)^4} = \frac{1 + \eta + \eta^2}{(1-\eta)^3} </math>, | <math> Z_{hs} = \frac{p_{hs}V_m}{RT} = \frac{1 - \eta^3}{(1-\eta)^4} = \frac{1 + \eta + \eta^2}{(1-\eta)^3} </math>, | ||

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[[category: Equations of state]] | [[category: Equations of state]] | ||

[[category: hard sphere]] | [[category: hard sphere]] | ||

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+ | ==References== | ||

+ | <references/> |

## Revision as of 21:19, 25 February 2021

The **Thiele hard sphere equation of state** is an equation of state for a hard sphere fluid developed by Thiele in 1963
^{[1]}.
The equation provides a better approximation of the repulsive forces between molecules than the Van der Waals repulsive term. The equation is given below:

,

where:

- is the compressibility factor of the hard sphere fluid;
- is the pressure of the fluid;
- is the molar volume of the fluid;
- is the absolute temperature of the fluid;
- is the gas constant; and
- is the packing fraction of the fluid.

In terms of accuracy, the Thiele equation is superseded by the Carnahan-Starling equation of state