Virial expansion

The classical virial expansion expresses the pressure P {displaystyle P} of a many-particle system in equilibrium as a power series in the number density: Here the quantity Z ≡ P R T ρ {displaystyle Zequiv {frac {P}{RT ho }}} is the compressibility factor. This is the virial equation of state, the most general function relating PρT properties of fluids, first proposed by Kamerlingh Onnes. The compressibility factor is a dimensionless quantity, indicating how much a real fluid deviates from an ideal gas. A is the first virial coefficient, which has a constant value of 1 and it makes the statement that at low molar density, all fluids behave like ideal gases. Virial coefficients B, C, D, etc., are temperature dependent, and are generally presented as Taylor series in terms of 1/T. The second and third virial coefficients had been studied extensively and tabulated for many fluids for more than a century. The most extensive compilation was in the books by Dymonds. Recently, Thermodynamics Research Center of National Institute of Standards and Technology (NIST/TRC) published a huge amount of thermodynamics data in the forms of Web Thermo Tables (WTT). In the WTT-Lite version, critically reviewed data on 150 fluids are available online. Tables of second and third virial coefficients of many fluids are also included in this compilation. The second and third virial coefficients, as functions of temperature, of argon are shown in the following figure. Reduced temperature and reduced virial coefficients, scaled by respective critical properties, are all dimensionless. Most fluids share the same behavior.