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| Hongqin Liu proposed a correction to the [[Carnahan-Starling equation of state]] which improved accuracy by almost two orders of magnitude <ref>[https://arxiv.org/abs/2010.14357 Hongqin Liu "Carnahan Starling type equations of state for stable hard disk and hard sphere fluids", arXiv:2010.14357]</ref>: | | 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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| : <math> | | : <math> |
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| </math> | | </math> |
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| The conjugate [[Virial equation of state | virial coefficient]] correlation is given by: | | The conjugate virial coefficient correlation is given by: |
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| : <math> | | : <math> |
| B_n = 0.9423n^2 + 1.28846n - 1.84615, n > 3. | | B_n = 0.9423n^2 + 1.28846n - 1.84615, n > 3. |
| </math> | | </math> |
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| The excess [[Helmholtz energy function]] is given by:
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| : <math>
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| 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).
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| </math>
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| The isothermal [[compressibility]] is given by:
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| : <math>
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| k_T = (\eta\frac{ dZ}{d\eta} + Z)^{-1} \rho^{-1}.
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| </math>
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| where
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| : <math>
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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 }.
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| </math>
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| == References ==
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| <references/>
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| [[Category: Equations of state]]
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| [[category: hard sphere]]
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