Editing Liu hard sphere equation of state
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Hongqin Liu proposed a correction to the | Hongqin Liu proposed a correction to the C-S EOS which improved accuracy by almost two order of magnitude <ref>[https://arxiv.org/abs/2010.14357]</ref>: | ||
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The conjugate | The conjugate virial coefficient correlation is given by: | ||
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The excess | The excess Helmholtz free energy is given by: | ||
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A^{ex} = \frac{ A - A^{id}}{ | A^{ex} = \frac{ A - A^{id}}{Nk_b}= \frac{ 188\eta - 126\eta^2 - 13\eta^4 }{52(1-\eta)^2} - \frac{5}{13} ln(1-\eta). | ||
</math> | </math> | ||
The isothermal | The isothermal compressibility is given by: | ||
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\frac{ dZ}{d\eta} = \frac{ 4 + 4\eta - \frac {11}{13} \eta^2 - \frac{52}{13}\eta^3 + \frac {7}{2}\eta^4 - \eta^5 }{(1-\eta)^4 }. | \frac{ dZ}{d\eta} = \frac{ 4 + 4\eta - \frac {11}{13} \eta^2 - \frac{52}{13}\eta^3 + \frac {7}{2}\eta^4 - \eta^5 }{(1-\eta)^4 }. | ||
</math> | </math> | ||