PRACTICAL DETERMINATION OF GAS DENSITIES FROM THE SPEED OF SOUND USING SQUARE-WELL POTENTIALS

The relationships between the first three density virial coefficients (B, C, and D) and the first four acoustic virial coefficients (beta(a) , gamma(a), delta(a), and epsilon(a)) are rederived and a published er ror relating D to delta(a) is corrected. We observe that even if the n th and higher-density virial coefficients of a hypothetical gas are id entically zero, the nth and higher acoustic virial coefficients are no t zero; they depend on the temperature derivatives of the 1st through (n-1)th density virial coefficients. Thus, two density virial coeffici ents may suffice for a fit to acoustic data with a cubic pressure depe ndence. These results are exploited by extending the pressure range of fits to previously published speed-of-sound data without either intro ducing additional parameters or degrading the fits. We deduce gas dens ities from fits to speed-of-sound data with acoustic virial coefficien ts having the temperature dependencies calculated from square-well pot entials. The estimated densities differ from independent measurements by a few tenths of a percent in an important range of conditions. Thes e estimates require no p-p-T data whatsoever.