virial equation of state

The virial equation of state is a theoretical result used to describe the behavior of real gases, especially at high densities where the ideal gas law breaks down. It expresses the relationship between pressure (P), volume (V), and temperature (T) as an infinite series expansion in powers of 1/V.1

The equation is written as:
[PV = A + \frac{B}{v} + \frac{C}{v^2} + \dots]
where A, B, C, and so on, are called virial coefficients. These coefficients are functions of temperature and are directly related to the intermolecular forces between gas particles. The first virial coefficient, A, is equivalent to nRT for an ideal gas. The second virial coefficient, B(T), provides quantitative information about these forces.213

While theoretically rigorous, the virial equation becomes less practical at very high densities, as it is an infinite series and does not predict phenomena like condensation.1