# Difference between revisions of "Santos-Lopez de Haro-Yuste hard disk equation of state"

Carl McBride (talk | contribs) (New page: The '''Santos-Lopez de Haro-Yuste''' equation of state for hard disks (2-dimensional hard spheres) is given by (Eq. 2 Ref. 1, Eq. 5 Ref...) |
Carl McBride (talk | contribs) m (Corrected the equation, now as in Ref. 3) |
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The '''Santos-Lopez de Haro-Yuste''' [[Equations of state | equation of state]] for [[hard disks]] (2-dimensional [[hard sphere model | hard spheres]]) is given by (Eq. 2 Ref. 1, Eq. 5 Ref. 2, Eq. 1 Ref. 3): | The '''Santos-Lopez de Haro-Yuste''' [[Equations of state | equation of state]] for [[hard disks]] (2-dimensional [[hard sphere model | hard spheres]]) is given by (Eq. 2 Ref. 1, Eq. 5 Ref. 2, Eq. 1 Ref. 3): | ||

− | :<math>\frac{p}{\rho k_B T} = \left[ 1- b_2 \eta - \frac{(b_2 \eta_{\mathrm{max}} | + | :<math>\frac{p}{\rho k_B T} = \left[ 1- b_2 \eta - \frac{(1-b_2 \eta_{\mathrm{max}}) \eta^2}{\eta^2_{\mathrm{max}}} \right]^{-1}</math> |

where <math>p</math> is the [[pressure]], <math>\rho</math> is the number density, <math>k_B</math> is the [[Boltzmann constant]], <math>T</math> is the [[temperature]], <math>b_2=2</math> is the reduced [[second virial coefficient]], <math>\eta = a_0(\sigma)\rho</math> is the [[packing fraction]], with <math>a_0(\sigma) = (\pi/4)\sigma^2</math> the area of a hard disk with diameter <math>\sigma</math>, and <math>\eta_{\mathrm{max}} = \pi \sqrt3 /6 </math> | where <math>p</math> is the [[pressure]], <math>\rho</math> is the number density, <math>k_B</math> is the [[Boltzmann constant]], <math>T</math> is the [[temperature]], <math>b_2=2</math> is the reduced [[second virial coefficient]], <math>\eta = a_0(\sigma)\rho</math> is the [[packing fraction]], with <math>a_0(\sigma) = (\pi/4)\sigma^2</math> the area of a hard disk with diameter <math>\sigma</math>, and <math>\eta_{\mathrm{max}} = \pi \sqrt3 /6 </math> |

## Latest revision as of 12:47, 18 September 2008

The **Santos-Lopez de Haro-Yuste** equation of state for hard disks (2-dimensional hard spheres) is given by (Eq. 2 Ref. 1, Eq. 5 Ref. 2, Eq. 1 Ref. 3):

where is the pressure, is the number density, is the Boltzmann constant, is the temperature, is the reduced second virial coefficient, is the packing fraction, with the area of a hard disk with diameter , and

## References[edit]

- A. Santos, M. López de Haro, and S. Bravo Yuste "An accurate and simple equation of state for hard disks", Journal of Chemical Physics
**103**4622 (1995) - Mariano López de Haro, Andrés Santos and Santos Bravo Yuste "A student-oriented derivation of a reliable equation of state for a hard-disc fluid", European Journal of Physics
**19**pp. 281-286 (1998) - Mariano López de Haro, Andrés Santos, and Santos B. Yuste "Simple equation of state for hard disks on the hyperbolic plane", Journal of Chemical Physics
**129**116101 (2008)