Ka. Gillis et Mr. Moldover, PRACTICAL DETERMINATION OF GAS DENSITIES FROM THE SPEED OF SOUND USING SQUARE-WELL POTENTIALS, International journal of thermophysics, 17(6), 1996, pp. 1305-1324
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.