Second virial coefficient

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The second virial coefficient is usually written as B or as . The second virial coefficient represents the initial departure from ideal-gas behaviour. The second virial coefficient, in three dimensions, is given by

where is the intermolecular pair potential, T is the temperature and is the Boltzmann constant. Notice that the expression within the parenthesis of the integral is the Mayer f-function.

In practice the integral is often very hard to integrate analytically for anything other than, say, the hard sphere model, thus one numerically evaluates


for each using the numerical integration scheme proposed by Harold Conroy [1][2].

Isihara-Hadwiger formula[edit]

The Isihara-Hadwiger formula was discovered simultaneously and independently by Isihara [3] [4] [5] and the Swiss mathematician Hadwiger in 1950 [6] [7] [8] The second virial coefficient for any hard convex body is given by the exact relation



where is the volume, , the surface area, and the mean radius of curvature.

Hard spheres[edit]

For the hard sphere model one has [9]

leading to

Note that for the hard sphere is independent of temperature. See also: Hard sphere: virial coefficients.

Van der Waals equation of state[edit]

For the Van der Waals equation of state one has:

For the derivation click here.

Excluded volume[edit]

The second virial coefficient can be computed from the expression

where is the excluded volume.

Admur and Mason mixing rule[edit]

The second virial coefficient for a mixture of components is given by (Eq. 11 in [10])

where and are the mole fractions of the th and th component gasses of the mixture.



See also[edit]


Related reading