Real Gases
Gases (or vapors) at relatively high pressures or relatively low temperatures do not obey the ideal gas law. To understand why that is the case, it is helpful to know a little bit about the derivation of the ideal gas law with the tools of Statistical Thermodynamics, which relies on two assumptions: (a) Gas particles are mass points, that is their volume can be ignored. (b) There are no long-distance forces between the particles, they only interact in short collisions, and travel most distance between collisions in free flight.
J. D. van der Waals (1837-1923) derived an equation that modifies the ideal gas equation to address both points. The van der Waals equation reads
The constant b accounts for the volume of the particles, where v − b is the volume accessible to an individual particle. The constant a accounts for long- range attractive forces between the particles, which reduce the pressure. The constants a, b can be obtained from fitting to critical point data. For large values of the specific volume v the equation reduces to the ideal gas law. A deeper discussion of the van der Waals equation can be found in Sec. 16.8, where it will be seen that the equation gives a good qualitative description of real gas effects and liquid-vapor phase change. However, its quantitative agreement with gas behavior is not so good. Therefore, the equation is mainly used as an educational example, but not for simulation of real processes.
Since explicit equations for real gas behavior are useful for simulations and calculations, there exist a wide variety of real gas equations, which can be found in the technical literature (Redlich Kwong equation, Beattie- Bridgeman equation, virial expansions, etc.).