Thiele hard sphere equation of state: Difference between revisions
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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 '''Thiele hard sphere equation of state''' is an [[equations of state|equation of state]] for modeling a [[hard sphere model|hard sphere]] fluid developed by Everett 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>. | <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: | 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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where: | where: | ||
:<math>Z_{hs}</math> is the compressibility factor of the hard sphere fluid; | :<math>Z_{hs}</math> is the [[compressibility factor]] of the hard sphere fluid; | ||
:<math>p_{hs}</math> is the pressure of the fluid; | :<math>p_{hs}</math> is the [[pressure]] of the fluid; | ||
:<math>V_m</math> is the molar volume of the fluid; | :<math>V_m</math> is the molar volume of the fluid; | ||
:<math>T</math> is the absolute temperature of the fluid; | :<math>T</math> is the absolute [[temperature]] of the fluid; | ||
:<math>R</math> is the gas constant; and | :<math>R</math> is the [[molar gas constant]]; and | ||
:<math>\eta</math> is the [[packing fraction]] of the fluid. | :<math>\eta</math> is the [[packing fraction]] of the fluid. | ||
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==References== | ==References== | ||
<references/> | <references/> | ||
Latest revision as of 23:20, 12 June 2024
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The Thiele hard sphere equation of state is an equation of state for modeling a hard sphere fluid developed by Everett 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:
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z_{hs} = \frac{p_{hs}V_m}{RT} = \frac{1 - \eta^3}{(1-\eta)^4} = \frac{1 + \eta + \eta^2}{(1-\eta)^3} } ,
where:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z_{hs}} is the compressibility factor of the hard sphere fluid;
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_{hs}} is the pressure of the fluid;
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_m} is the molar volume of the fluid;
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} is the absolute temperature of the fluid;
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} is the molar gas constant; and
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \eta} is the packing fraction of the fluid.
In terms of accuracy, the Thiele equation is superseded by the Carnahan-Starling equation of state