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 :

$Z=\frac{1+\eta +{\eta }^2-\frac{8}{13}{\eta }^3-{\eta }^4+\frac{1}{2}{\eta }^5}{(1-\eta {)}^3}.$

The conjugate virial coefficient correlation is given by:

$B_n=0.9423n^2+1.28846n-1.84615,n>3.$

The excess entropy is given by:

$S^{ex}=\frac{S-S^{id}}{N{k}_b}=\frac{188\eta -126{\eta }^2-13{\eta }^4}{52(1-\eta {)}^2}-\frac{5}{13}ln(1-\eta ).$