The classical virial expansion expresses the pressure of a many-particle system in equilibrium as a power series in the density. 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 atoms or molecules,
where is the pressure, is the Boltzmann constant, is the absolute temperature, and is the number density of the gas. Note that for a gas containing a fraction of (Avogadro's number) molecules, truncation of the virial expansion after the first term leads to , which is the ideal gas law.
Writing , the virial expansion can be written as
The virial coefficients are characteristic of the interactions between the particles in the system and in general depend on the temperature . Virial expansion can also be applied to aqueous ionic solutions, as shown by Harold Friedman.
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