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| For particles acting through two-body central forces alone one may use the [[Thermodynamic relations | thermodynamic relation]]
| | #REDIRECT[[Pressure#Pressure equation]] |
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| :<math>p = -\left. \frac{\partial A}{\partial V}\right\vert_T </math>
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| Using this relation, along with the [[Helmholtz energy function]] and the [[partition function | canonical partition function]], one
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| arrives at the so-called
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| '''pressure equation''' (also known as the '''virial 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>
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| where <math>\beta = 1/k_BT</math>,
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| <math>\Phi(r)</math> is a ''central'' [[Intermolecular pair potential | potential]] and <math>{\rm g}(r)</math> is the [[pair distribution function]].
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| ==References==
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| [[category: statistical mechanics]]
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