IC 8437 On Estimating Virial Coefficients From Experimental Data

The polynomial method for estimating virial coefficients from experimental data suffers from three serious defects: (1) There is no known relationship between the polynomial coefficients and the virial coefficients, (2) the values of the estimates depend upon the degree of the polynomial and the particular set of values used for the independent variable, as well as the random errors in the dependent variable, and (3) the variances calculated for the estimates do not represent the mean square errors of estimation. Attempts to overcome these defects have thus far been unsuccessful; these attempts have also failed to account for the fact that none of the virial coefficients are uniquely determined by the values of the dependent variable for a finite set of values of the independent variable. The conclusion is that virial coefficients cannot be reliably estimated from experimental data unless additional information about the virial expansion itself, such as its rate of convergence, is available.