Virial expansion

A low-density expansion of a gas’s equation of state in powers of number density. Its coefficients encode two-particle and higher-order interactions.

Virial equation of state: An equation of state that expresses pressure as an ideal-gas term multiplied by a series in density. It is the thermodynamic form of the expansion, relating its coefficients directly to pressure.
Equation of state: A relation among a system’s thermodynamic state variables, such as pressure, volume, temperature, and particle number. The virial expansion is one particular representation of a gas equation of state.
Boyle temperature: The temperature at which a gas’s second virial coefficient vanishes, making its low-pressure behavior approximately ideal. At this temperature the expansion’s leading nonideal correction disappears.
Ideal gas law: The equation pV=nRT, which assumes particles have negligible volume and no intermolecular interactions. It is the zero-density limit recovered when all virial corrections vanish.
Virial coefficient: A coefficient in a virial expansion that quantifies a contribution from particle interactions at a given order. Each coefficient supplies one density-dependent correction to the ideal-gas equation.
Number density: The number of particles per unit volume in a system. It is the expansion variable whose powers organize the virial corrections.
Pitzer acentric factor: A dimensionless measure of how much a fluid’s vapor-pressure curve departs from that of a simple spherical fluid. It helps estimate corresponding-states correlations for virial behavior across different substances.
Van der Waals equation: A cubic equation of state that approximates finite molecular size and attractive interactions with two parameters. Unlike the virial series, it packages nonideality into a compact equation with a broader intended range.
Mayer cluster expansion: A statistical-mechanical expansion of a gas’s partition function into connected clusters of interacting particles. It derives virial coefficients by organizing interactions into connected particle clusters.
Compressibility factor: The ratio of a gas’s pressure to the pressure predicted for an ideal gas at the same temperature and density. The virial series expresses this dimensionless departure from ideal behavior in density powers.

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