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The classical '''virial expansion''' expresses the [[pressure]] of a [[many-particle system]] in [[Thermodynamic equilibrium|equilibrium]] as a [[power series]] in the [[density]].
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The [[virial]] expansion, introduced in 1901 by [[Heike Kamerlingh Onnes]], is a generalization of the [[ideal gas]] law. He wrote that for a gas containing <math>N</math> atoms
or molecules,
 
:<math>
  \frac{p}{k_BT} = \rho + B_2(T) \rho^2 +B_3(T) \rho^3+ \cdots,
</math>
 
where <math>p</math> is the pressure, <math>k_B</math> is the [[Boltzmann constant]], <math>T </math> is the absolute temperature, and
<math>\rho \equiv N/V</math> is the [[number density]] of the
gas.
Note that for a gas containing a fraction <math>n</math> of <math>N_A</math> ([[Avogadros_Number|Avogadro's number]]) molecules, truncation of the virial expansion after the
first term leads to <math>pV = n N_A k_B T = nRT</math>, which is the [[ideal gas law]].  
 
Writing <math>\beta=(k_{B}T)^{-1}</math>,  the virial expansion can be written in closed form as
 
:<math>\frac{\beta p}{\rho}=1+\sum_{i=1}^{\infty}B_{i+1}(T)\rho^{i}</math>.
 
The [[virial coefficient]]s <math>B_i(T)</math> are characteristic of the interactions between the particles in the system and in general depend on the temperature <math>T</math>.
 
== See also ==
*[[Virial theorem]]
*[[Statistical mechanics]]
 
[[Category:Statistical mechanics]]
 
{{physical-chemistry-stub}}

Latest revision as of 03:04, 23 September 2014

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