Tetrahedral hard sphere model

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The tetrahedral hard sphere model consists of four hard spheres located on the vertices of a regular tetrahedron.

Second virial coefficient

The second virial coefficient is given by ([1] Eq.5):

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {B_{2}^{*}}{4V_{m}^{*}}}=1+{\frac {UL^{*}+VL^{*3}}{4}}}

where is the reduced elongation, is the corresponding reduced volume, Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle U=0.72477} and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle V=4.730} .

Equation of state

The equation of state is given by ([1] Eq. 17):


Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {\beta P}{\rho }}={\frac {1+(1+UL^{*}+VL^{*3})y+(1+WL^{*}+XL^{*4})y^{2}-(1+ZL^{*3})y^{3}}{(1-y)^{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 U=0.72477} , 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=4.730} , 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 W=1.3926} , 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 X=24.78} 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 Z=7.69} .

References