The Virial coefficients are a set of coefficients in the virial equation of state, which describes the relationship between pressure, volume, and temperature for a real gas. The virial equation is often expressed as an expansion in terms of the density of the gas: \[ \frac{P}{kT} = \rho + B(T)\rho^2 + C(T)\rho^3 + \ldots \] Here: - \( P \) is the pressure of the gas.
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A virial coefficient quantifies an interaction correction to the dilute-gas equation of state. In the number-density convention, , where . Thus has units of volume; a molar-density expansion uses differently scaled coefficients.
For classical particles with a pair potential , . Hard spheres of diameter exclude separations below , giving . Attractive interactions can instead contribute negatively. The expansion is a low-density organization of correlations, not a guarantee of convergence near a phase transition.