Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in or
create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision |
Your text |
Line 39: |
Line 39: |
|
| |
|
| :<math>P=nk_BT\frac{(1+\eta+\eta^2)}{(1-\eta)^3}</math> | | :<math>P=nk_BT\frac{(1+\eta+\eta^2)}{(1-\eta)^3}</math> |
|
| |
| ==A derivation of the Carnahan-Starling equation of state==
| |
| It is interesting to note (Ref <ref> [http://dx.doi.org/10.1063/1.1675048 G. A. Mansoori, N. F. Carnahan, K. E. Starling, and T. W. Leland, Jr. "Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres", Journal of Chemical Physics '''54''' pp. 1523-1525 (1971)] </ref> Eq. 6) that one can arrive at the [[Carnahan-Starling equation of state]] by adding two thirds of the exact solution via the compressibility route, to one third via the pressure route, i.e.
| |
|
| |
| :<math>Z = \frac{ p V}{N k_B T} = \frac{2}{3} \left[ \frac{(1+\eta+\eta^2)}{(1-\eta)^3} \right] + \frac{1}{3} \left[ \frac{(1+2\eta+3\eta^2)}{(1-\eta)^2} \right] = \frac{ 1 + \eta + \eta^2 - \eta^3 }{(1-\eta)^3 }</math>
| |
|
| |
| The reason for this seems to be a slight mystery (see discussion in Ref. <ref>[http://dx.doi.org/10.1021/j100356a008 Yuhua Song, E. A. Mason, and Richard M. Stratt "Why does the Carnahan-Starling equation work so well?", Journal of Physical Chemistry '''93''' pp. 6916-6919 (1989)]</ref> ).
| |
|
| |
|
| ==References== | | ==References== |