Difference between revisions of "Pressure equation"

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For particles acting through two-body central forces alone one may use the [[Thermodynamic relations | thermodynamic relation]]
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#REDIRECT[[Pressure#Pressure equation]]
 
 
:<math>p = -\left. \frac{\partial A}{\partial V}\right\vert_T </math>
 
 
 
Using this relation, along with the [[Helmholtz energy function]] and the [[partition function | canonical partition function]], one
 
arrives at the so-called
 
'''pressure equation''' (also known as the '''virial equation'''):
 
:<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^2~{\rm d}r</math>
 
 
 
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]].
 
==See also==
 
*[[Virial pressure]]
 
==References==
 
[[category: statistical mechanics]]
 

Latest revision as of 15:12, 14 March 2012