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 Ω_n and ω_n, respectively, are determined from previously reported values of the pressure virials B_n 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.

中文翻译：

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从 Ab Initio Acoustic Virial Coefficients 得到的 Helium-4 中的声速

我们提供了⁴ He 的温度相关声学维里系数值，这些值出现在气体中声速 (AVEOS) 的系列展开式中。系数是根据文献中的第一性原理分子模型计算的，并针对密度和压力的扩展而呈现。这些系数在这里分别标记为Ω _n和ω _n，它们是根据先前报告的作为温度T函数的压力维里B _n值确定的。提供了2.6 到 1000 K 的T和2 到 7 的n 的数据；n = 2-5 的那些包括核量子效应但不包括交换，那些n = 6 和 7 是半经典的。对文献中的声速实验数据进行分析，以估计热力学温度、回归系数值以与从头计算的结果进行比较，并评估 AVEEOS 在高达 1000 MPa 的压力下的性能。对系列收敛性的研究表明，压力膨胀的 AVEOS 在大约 100 MPa 处发散，而密度膨胀的系列似乎在整个压力范围内保持收敛；在最高压力下，七阶级数仍然产生在声速正确值 1% 以内的结果，至少在高于 200 K 的温度下应用时如此。