where:
- a is the interaction energy between molecules;
- b is the occupied volume by the molecules.
This equation gives a much better prediction of real gas behaviour in practice. Each gas (or mixture) has different a en b coefficient. When the molecules do not interact (a=0) and do not occupy space (b=0), the result is again the ideal gas law.
The equation of state used in Fluidat is based on a more advanced virial equation of state (an expression of a system derived from statistical mechanics, usually describing a system in equilibrium as a power series of particle interactions). It is called the Benedict-Webb-Rubin equation, named after the three researchers (M. Benedict, G.B. Webb and L.C. Rubin) working at the research laboratory of M. W. Kellogg Limited who determined the model. From this equation of state the non-ideal behaviour of fluids can be derived, a required input for the calculation of physical properties like:
- density
- heat capacity
- thermal conduction
- viscosity
- and vapour pressure
The Benedict-Webb-Rubin equations are calculated using intrinsic properties, like molar mass, critical properties, polarity, accentric factor and other parameters. These intrinsic properties characterize the fluid, taken into account effects like compressibility, variable specific heat capacity, and Van der Waals forces. These properties will influence the physical properties of a fluid.
For example the accentric factor (the shape of the molecule) will influence the viscosity for large hydrocarbon molecules. And the critical properties are most important to calculate the reduced (or normalized) properties; all calculations perfomed in the Benedict-Webb-Rubin equations are based on reduced properties, thus resulting in a universal gas model . The reduced properties are calculated by deviding the actual state properties by the critical properties (for example P_r=P/P_c, where P_r is the reduced pressure and P_c is the critical pressure).
Basically, the Benedict-Webb-Rubin equation is a model to derive the compressibility factor (the deviation from ideality) of fluids: