# Difference between revisions of "Pressure equation"

Carl McBride (talk | contribs) |
Carl McBride (talk | contribs) |
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− | + | 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^ | + | |

+ | :<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.