Hansen-Goos hard sphere equation of state
The Hansen-Goos hard sphere equation of state is given by [1] (Eq. 5):
- 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 \rho k_B T \kappa_T = \frac{(1-\eta)^4}{(1+2\eta -\gamma \eta^3 + \delta \eta^4)^2}}
where (Eq. 7)
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \gamma =2(19-{\frac {B_{4}}{V^{3}}})\approx 1.270463}
and (Eq. 8)
- 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 \delta = - \frac{3}{7} + \frac{5\gamma}{8} +\frac{4}{7} \sqrt{1- \frac{21 \gamma}{32} + \frac{105\gamma^2}{1024}} \approx 0.694605}
and 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 \kappa_T} is the isothermal compressibility.