AN EMPIRICAL THREE-CONSTANT EQUATION OF STATE FOR GASES

In this article it is pointed out that the semi-empirical van der Waals' equation of state for gases is particularly unsatisfactory in the neighborhood of the critical point, as indicated by the fact that the experimental values of the critical ratio (?) seldom agree with the theoretical constant value 8/3. It is also noted that this τ value may serve as a satisfactory measure (at least to a first approximation) of the deviation of the law of corresponding states when applied to gases at high densities. We have therefore proposed in this communication a rather straightforward modification of the van der Waals' equation which leads to an empirical three-constant equation of state for gases involving this τ value as an adjustable parameter and thus requiring only critical data for the determination of the three constants. This equation is made to fit the p-V-T data at the critical point, but reduces itself to the simpler forms of the van der Waals' equation and the ideal gas equation for lower values of gas densities. Numerical calculations made for gases of widely different τ values show that this rather simple equation of state is fairly satisfactory even at high densities. The plausibility of using the τ value as an adjustable parameter both for the equation of state and for the law of corresponding states is also briefly discussed.