Santos-Lopez de Haro-Yuste hard disk equation of state: Difference between revisions
Jump to navigation
Jump to search
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) |
||
Line 1: | Line 1: | ||
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 13:47, 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)