Pressure equation: Difference between revisions

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The '''pressure equation''', also known as the '''virial equation''' is given by
For particles acting through two-body central forces alone one may use the [[Thermodynamic relations | thermodynamic relation]]
:<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>
 
:<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>,
where <math>\beta = 1/k_BT</math>,

Revision as of 13:21, 28 June 2007

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

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):

where , is a central potential and is the pair distribution function.

References