# Difference between revisions of "Pressure equation"

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:<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> | :<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>, |

<math>\Phi(r)</math> is a ''central'' [[Intermolecular pair potential | potential]] and <math>{\rm g}(r)</math> is the [[pair distribution function]]. | <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== | ==References== | ||

[[category: statistical mechanics]] | [[category: statistical mechanics]] |

## Revision as of 18:04, 27 February 2008

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.