**2022: SklogWiki celebrates 15 years on-line**

# Difference between revisions of "Liu hard sphere equation of state"

Carl McBride (talk | contribs) m (Slight tidy) |
|||

(7 intermediate revisions by one other user not shown) | |||

Line 1: | Line 1: | ||

− | Hongqin Liu proposed a correction to the | + | 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>: |

: <math> | : <math> | ||

Line 5: | Line 5: | ||

</math> | </math> | ||

− | The conjugate virial coefficient correlation is given by: | + | The conjugate [[Virial equation of state | virial coefficient]] correlation is given by: |

: <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> | ||

+ | |||

+ | The excess [[Helmholtz energy function]] is given by: | ||

+ | |||

+ | : <math> | ||

+ | 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> | ||

+ | |||

+ | The isothermal [[compressibility]] is given by: | ||

+ | |||

+ | : <math> | ||

+ | k_T = (\eta\frac{ dZ}{d\eta} + Z)^{-1} \rho^{-1}. | ||

+ | </math> | ||

+ | |||

+ | where | ||

+ | |||

+ | : <math> | ||

+ | \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> | ||

+ | == References == | ||

+ | <references/> | ||

+ | [[Category: Equations of state]] | ||

+ | [[category: hard sphere]] |

## Latest revision as of 11:21, 10 November 2020

Hongqin Liu proposed a correction to the Carnahan-Starling equation of state which improved accuracy by almost two orders of magnitude ^{[1]}:

The conjugate virial coefficient correlation is given by:

The excess Helmholtz energy function is given by:

The isothermal compressibility is given by:

where