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# Liu hard sphere equation of state

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Hongqin Liu proposed a correction to the C-S EOS which improved accuracy by almost two order of magnitude [1]:

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

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:

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