Difference between revisions of "Pressure equation"

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The '''pressure equation''', also known as the '''virial equation''' is given by
 
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]]
 
[[category: statistical mechanics]]

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_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

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

References