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,

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where k_B is the Boltzmann constant, T the absolute temperature, and is the number density of the gas. Note that for a gas containing N_A (Avogadro's number) molecules truncation of the virial expansion after the first term leads to pV = N_Ak_BT = RT, which is the ideal gas law.

Writing β = (k_BT) ^{− 1}, 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