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.

Isihara-Hadwiger formula

The Isihara-Hadwiger formula was discovered simultaneously and independently by Isihara [1] [2] [3] and the Swiss mathematician Hadwiger in 1950 [4] [5] [6] The second virial coefficient for any hard convex body is given by the exact relation

or

where

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

Hard spheres

For the hard sphere model one has [7]

leading to

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

Van der Waals equation of state

For the Van der Waals equation of state one has:

For the derivation click here.

Excluded volume

The second virial coefficient can be computed from the expression

where is the excluded volume.

See also

References

Related reading