# Editing Santos-Lopez de Haro-Yuste hard disk equation of state

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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{( | + | :<math>\frac{p}{\rho k_B T} = \left[ 1- b_2 \eta - \frac{(b_2 \eta_{\mathrm{max}}-1) \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> |