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Virial expansion

The classical virial expansion expresses the pressure of a many-particle system in equilibrium as a power series in the density. The virial expansion was introduced in 1901 by Heike Kamerlingh Onnes as a generalization of the ideal gas law. He wrote for a gas containing N atoms or molecules,

\frac{p}{k_BT} = \rho + B_2(T) \rho^2 +B_3(T) \rho^3+ \cdots,

where kB is the Boltzmann constant, T the absolute temperature, and \rho \equiv N/V is the number density of the gas. Note that for a gas containing NA (Avogadro's number) molecules truncation of the virial expansion after the first term leads to pV = NAkBT = RT, which is the ideal gas law.

Writing β = (kBT) − 1, the virial expansion can be written in closed form as

\frac{\beta p}{\rho}=1+\sum_{i=1}^{\infty}B_{i+1}(T)\rho^{i}.

The virial coefficients Bi(T) are characteristic of the interactions between the particles in the system and in general depend on the temperature T.

See also

Statistical mechanics

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Virial_expansion". A list of authors is available in Wikipedia.
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