third virial coefficients against reduced temperature according to Starling: The exponential terms in the last two equations correct the third virial coefficient so that the isotherms in the liquid phase can be represented correctly. The exponential term converges rapidly as ρ increases, and if we took only the first two terms in its Taylor expansion series, , and multiply it with , the result is . It thus contributes a term to the third virial coefficient, and one term to the eighth virial coefficient, which can be ignored. After the expansion of the exponential terms, the Benedict-Webb-Rubin and Starling equations of state have this form: The fourth and fifth virial coefficients are zero. After the third virial term, the next significant term is the sixth virial coefficient. It seems that the first three virial terms dominate the compressibility factor for fluids, down to , and up to . Re-analysis of the data by Starling Re-analyzing the data reported by Starling, the virial coefficients are best represented by and could be determined using simple second order regression analysis from experimental PρT isotherms. and could then be determined using third order regression analysis on and . could then be determined by analyzing residues in compressibility factor after the first three virial terms are removed from the virial equation. The data by Starling are re-analyzed and the results are shown in the following table. These coefficients are all dimensionless, they are all scaled with critical molar volumes and critical temperature. Cubic virial equation of state The three-term virial equation or a cubic virial equation of state has the simplicity of the Van der Waals equation of state without its singularity at . Theoretically, the second virial coefficient represents bimolecular attraction forces, and the third virial term represents the repulsive forces among three molecules in close contact. Intuitively, we should expect to become negative at low temperature, while would remain positive to counterbalance the effect of and pushes and hence the pressure to high values as increases. With this cubic virial equation, the coefficients B and C can be solved in closed form. Imposing the critical conditions: the cubic virial equation can be solved to yield: and is therefore 0.333, comparing to 0.375 from Van der Waals equation of state. Between the critical point and the triple point is the saturation region of fluids. In this region, the gaseous phase coexists with the liquid