Virial expansion

The classical virial expansion expresses the pressure of a many-particle system in equilibrium as a power series in the number 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 ${\displaystyle N}$ atoms or molecules,

where ${\displaystyle p}$ is the pressure, ${\displaystyle k_{B}}$ is the Boltzmann constant, ${\displaystyle T}$ is the absolute temperature, and ${\displaystyle \rho \equiv N/V}$ is the number density of the gas. Note that for a gas containing a fraction ${\displaystyle n}$ of ${\displaystyle N_{A}}$ (Avogadro's number) molecules, truncation of the virial expansion after the first term leads to ${\displaystyle pV=nN_{A}k_{B}T=nRT}$, which is the ideal gas law.

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