Liu hard sphere equation of state
Hongqin Liu proposed a correction to the C-S EOS which improved accuracy by almost two order of magnitude [1]:
- 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 = \frac{ 1 + \eta + \eta^2 - \frac{8}{13}\eta^3 - \eta^4 + \frac{1}{2}\eta^5 }{(1-\eta)^3 }. }
The conjugate virial coefficient correlation is given by:
- 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 B_n = 0.9423n^2 + 1.28846n - 1.84615, n > 3. }
The excess entropy is given by:
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle S^{ex}={\frac {S-S^{id}}{Nk_{b}}}={\frac {188\eta -126\eta ^{2}-13\eta ^{4}-\eta ^{4}}{52(1-\eta )^{2}-{\frac {5}{13}}ln(1-\eta )}}.}