Practical determination of gas densities from the speed of sound using square-well potentials

Abstract

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 ande a are rederived and a published error relatingD toδ a is corrected. We observe that even it thenth and higher-density virial coefficients of a hypothetical gas are identifically zero, thenth 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 preciously 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 be a few tenths of a percent in an important range of conditions, These estimates require nop p T data whatsoever.