Brief Discussion on Equation of State

The fluid density plays an important role in fluid mechanics. For an incompressible fluid (e.g., a liquid), the density may often be treated as a constant. For gases, however, one 

While an ideal-gas law serves very well under many circumstances, there are also circumstances in which non-ideal behavior can be significant. A compressibility factor Z is an often-used measure of the extent of nonideality, 

For an ideal gas, Z = 1. In general, the law of corresponding states provides that the compressibility factor depend on the reduced temperature and pressure, 

The critical temperature is defined to be the temperature above which a gas cannot be liquified at any pressure. The pressure at which a substance may exist as a gas in equilibrium with a liquid at the critical temperature is defined to be the critical pressure. Each substance has a critical point, which is at the critical temperature and critical pressure. 

The virial equation of state represents the pressure as a polynomial series in the inverse molar volume as 

---