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

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

Revision as of 21:19, 25 February 2021

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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:

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

where:

Z_{hs} is the compressibility factor of the hard sphere fluid;
p_{hs} is the pressure of the fluid;
V_m is the molar volume of the fluid;
T is the absolute temperature of the fluid;
R is the gas constant; and
\eta is the packing fraction of the fluid.

In terms of accuracy, the Thiele equation is superseded by the Carnahan-Starling equation of state

References