Eighth-order virial equation of state and speed-of-sound measurements for krypton

Abstract

An eighth-order virial equation of state (VEOS) for krypton, valid for temperatures up to 5000 K, was developed using the accurate potential functions proposed by Jäger et al. [J. Chem. Phys. 144, 114304 (2016)] for the pair interactions and nonadditive three-body interactions between krypton atoms. While the second and third virial coefficients were already calculated by Jäger et al., the fourth- to eighth-order coefficients were determined in the present work. A simple analytical function was fitted individually to the calculated values of each virial coefficient to obtain the VEOS in an easy-to-use analytical form. To enable a stringent test of the quality of the new VEOS, we measured the speed of sound in krypton in the temperature range from 200 K to 420 K and at pressures up to 100 MPa with a very low uncertainty (at the 0.95 confidence level) of 0.005%–0.018% employing the pulse-echo technique. In order to verify that the isotopic composition of the krypton sample conforms to that of natural krypton in air, high-precision measurements of krypton isotope ratios using a high-sensitivity noble gas mass spectrometer were performed. The extensive comparison with the new speed-of-sound data as well as with experimental p-ρ-T and speed-of-sound data from the literature indicates that pressures and speeds of sound calculated using our new VEOS have uncertainties (at the 0.95 confidence level) of less than 0.1% at state points at which the VEOS is sufficiently converged.

The accurate estimation of the third virial coefficients for helium using three‐body neural network potentials

“…High-order virial coefficients are essential physical quantities when one aims to estimate the highly accurate pressure of gas. [27][28][29][30] For example, Egan et al 28 developed a pressure sensor for accurate measure of pressure using a laser refractometer. The pressure of gas was estimated from the relationship between gas refractivity and pressure, which includes the second and third virial coefficients.…”

“…High‐order virial coefficients are essential physical quantities when one aims to estimate the highly accurate pressure of gas 27–30 . For example, Egan et al 28 developed a pressure sensor for accurate measure of pressure using a laser refractometer.…”

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

“…Early theoretical attention to the VEOS was focused on simple molecular models, such as hard spheres, square well, and Lennard-Jones. , Study of such models continues to be of interest, both for the fundamental insight they offer and their relevance to some systems, such as colloids and nanoparticles. , More recently, additional attention has been paid to realistic molecular models, including those based on ab initio calculations − (also see Table ) and other models that have been fitted to experiment. ,− These applications are interesting because they promise a robust route to thermophysical properties that is reliable outside the range where experiments have been applied, or that is even entirely first-principles in nature.…”

Entropy Scaling of Viscosity—I: A Case Study of Propane

“…If instead of an expansion in number density, an expansion in s + is constructed, a similar form is obtained: After some mathematics (see the SI, section 3.3), it can be shown that the viscosity virial coefficient in a s + expansion is related to that of the density expansion by in which and B 3 is the third virial coefficient. The values of B 3 are rarely known very accurately, aside for a few special cases (e.g., the Lennard-Jones fluid, helium-4, nitrogen, argon, krypton, CO 2 , two-center Lennard-Jones dimer with embedded quadrupole); many of the multiparameter equations of state yield erroneous virial coefficients above B 2 . But even the second virial coefficient B 2 causes trouble: for many fluids the paucity of data in the gas phase means that the EOS values for B 2 are guided by intuition rather than data.…”

“…and B 3 is the third virial coefficient. The values of B 3 are rarely known very accurately, aside for a few special cases (e.g., the Lennard-Jones fluid, 81 helium-4, 82 nitrogen, 65 argon, 83 krypton, 84 CO 2 , 85 two-center Lennard-Jones dimer with embedded quadrupole 86 ); many of the multiparameter equations of state yield erroneous virial coefficients above B 2 . But even the second virial coefficient B 2 causes trouble: for many fluids the paucity of data in the gas phase means that the EOS values for B 2 are guided by intuition rather than data.…”