# Second Virial Coefficients for the Lennard-Jones (2*n*-*n*) Potential

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The Lennard–Jones interaction potential is defined as , where is the minimum, is the distance at which the potential changes sign, and is an exponent that defines the shape of the potential. The conventional Lennard–Jones potential uses . In this Demonstration, you can control the exponent to plot the second virial coefficient , relative to the hard-sphere value , as a function of the reduced temperature . The value of the Boyle temperature (at which ) is also calculated. You can control the temperature range of the plot in units of the Boyle temperature.

Contributed by: Andrés Santos (March 2012)

Open content licensed under CC BY-NC-SA

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The classical second virial coefficient of a gas of particles interacting via a potential is . In the particular case of the Lennard–Jones potential , it is possible to prove that . Here, , where is the second virial coefficient of a gas of hard spheres of diameter , is the reduced temperature, and is a parabolic cylinder function.

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