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 $N$ atomsor molecules,

:$frac\{p\}\{k\_BT\}\; =\; ho\; +\; B\_2(T)\; ho^2\; +B\_3(T)\; ho^3+\; cdots,$

where $p$ is the pressure, $k\_B$ is the Boltzmann constant, $T$ the absolute temperature, and$ho\; equiv\; N/V$ is the number density of thegas.Note that for a gas containing a fraction $n$ of $N\_A$ (Avogadro's number) of molecules truncation of the virial expansion after thefirst term leads to $pV\; =\; n\; N\_A\; k\_B\; T\; =\; nRT$, which is the ideal gas law.

Writing , the virial expansion can be written in closed form as

:.

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

See also

Statistical mechanics