Speed of Sound in Helium-4 from Ab Initio Acoustic Virial Coefficients

We present values for 4He of temperature-dependent acoustic virial coefficients that appear in series expansions for the speed of sound in the gas (AVEOS). Coefficients are computed from first-principles molecular models from the literature and are presented for expansions both in density and in pressure. These coefficients, labeled here as ωn and ωn, respectively, are determined from previously reported values of the pressure virials Bn as a function of temperature T. Data are provided for T from 2.6 to 1000 K and for n from 2 to 7; those for n = 2-5 include nuclear quantum effects but not exchange, and those for n = 6 and 7 are semiclassical. Analysis of experimental data for the speed of sound from the literature is performed to estimate thermodynamic temperatures, to regress coefficient values to compare to ab initio results, and to evaluate the performance of the AVEOS for pressures up to 1000 MPa. A study of the convergence of the series shows that the pressure-expanded AVEOS diverges at about 100 MPa, while the density-expanded series appears to remain convergent over the entire pressure range; at the highest pressures, the seventh-order series still yields results that are within 1% of the correct value of the speed of sound, at least when applied at temperatures above 200 K.