# Editing Pressure equation

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β | + | For particles acting through two-body central forces alone one may use the [[Thermodynamic relations | thermodynamic relation]] | |

+ | |||

+ | :<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]] |