Interrelation of the Virial Coefficients

An equation of the form F(T, B, C, D, ···) = 0, in which the temperature T is the only independent variable, is presented to interrelate the virial coefficients, B, C, D, ···, which are functions of temperature only. The equation is derived from the experimental observation that temperature and density are linearly related at unit compressibility factor. Further relations are presented according to which the value of any virial coefficient at the Boyle temperature can be found from the temperature derivatives of the previous coefficients at that point. It is shown that the theoretical virial coefficients of the Lennard-Jones potential, which are known through the fifth coefficient E, obey the interrelation closely, and an estimate of the sixth coefficient is made at two temperatures. The coefficients of the Stockmayer potential for polar molecules also appear to conform. These results tend to confirm the validity of the unit compressibility law. Experimental coefficients are considered briefly, and the interrelation is suggested as a guide for estimating and eliminating the errors usually inherent in the determination of experimental virial coefficients from PVT data.