Pressure equation: Difference between revisions

Revision as of 14:39, 25 June 2007

The pressure equation, also known as the virial equation is given by

p^{*}={\frac {\beta p}{\rho }}={\frac {pV}{Nk_{B}T}}=1-\beta {\frac {2}{3}}\pi \rho \int _{0}^{\infty }\left({\frac {{\rm {d}}\Phi (r)}{{\rm {d}}r}}~r\right)~{\rm {g}}(r)r^{3}~{\rm {d}}r

where $\beta =1/k_{B}T$ , $\Phi (r)$ is a central potential and ${\rm {g}}(r)$ is the pair distribution function.

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 The '''pressure equation''', also known as the '''virial equation''' is given by
-:<math>P^*=\frac{\beta P}{\rho}= \frac{PV}{NkT} = 1 - \beta \frac{2}{3} \pi  \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^2~{\rm d}r</math>
+:<math>p^*=\frac{\beta p}{\rho}= \frac{pV}{Nk_BT} = 1 - \beta \frac{2}{3} \pi  \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^3~{\rm d}r</math>
-where <math>\Phi(r)</math> is a ''central'' [[Intermolecular pair potential | potential]] and <math>{\rm g}(r)</math> is the [[pair distribution function]].
+where <math>\beta = 1/k_BT</math>,
+<math>\Phi(r)</math> is a ''central'' [[Intermolecular pair potential | potential]] and <math>{\rm g}(r)</math> is the [[pair distribution function]].
+==References==
 [[category: statistical mechanics]]