Practical Determination of Gas Densities from the Speed of Sound Using Square-Well Potentials

摘要

The relationships between the first three density virial coefficients (B, C, and D) and the first four acoustic virial coefficients (β_a, γ_a, δ_a, and ε_a) are rederived and a published error relating D to δ_a is corrected. We observe that even if the nth and higher-density virial coefficients of a hypothetical gas are identically zero, the nth and higher acoustic virial coefficients are not zero; they depend on the temperature derivatives of the 1st through (n — 1)th density virial coefficients. Thus, two density virial coefficients may suffice for a fit to acoustic data with a cubic pressure dependence. These results are exploited by extending the pressure range of fits to previously published speed-of-sound data without either introducing additional parameters or degrading the fits. We deduce gas densities from fits to speed-of-sound data with acoustic virial coefficients having the temperature dependencies calculated from square-well potentials. The estimated densities differ from independent measurements by a few tenths of a percent in an important range of conditions. These estimates require no p-ρ—T data whatsoever.