Pressure equation

From SklogWiki
Revision as of 13:21, 28 June 2007 by Carl McBride (talk | contribs)
Jump to: navigation, search

For particles acting through two-body central forces alone one may use the thermodynamic relation

p = -\left. \frac{\partial A}{\partial V}\right\vert_T

Using this relation, along with the Helmholtz energy function and the canonical partition function, one arrives at the so-called pressure equation (also known as the virial equation):

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

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

References