Updated determination of the molar gas constant $R$ by acoustic measurements in argon at UVa-CEM

TL;DR

This paper presents a highly precise new measurement of the molar gas constant R using acoustic measurements in argon, employing a novel resonant cavity and improved techniques to reduce uncertainties.

Contribution

It introduces a new resonant cavity design and measurement methodology that significantly reduces the uncertainty in determining the molar gas constant R.

Findings

Measured R as 8.314449 J/(K mol) with a 6.7 ppm uncertainty.

Achieved half the previous uncertainty contributions in radius and acoustic measurements.

Value is slightly below the CODATA 2014 recommended value, within uncertainty range.

Abstract

A new determination of the molar gas constant was performed from measurements of the speed of sound in argon at the triple point of water and extrapolation to zero pressure. A new resonant cavity was used. This is a triaxial ellipsoid whose walls are gold-coated steel and which is divided into two identical halves that are bolted and sealed with an O-ring. Microwave and electroacoustic traducers are located in the northern and southern parts of the cavity, respectively, so that measurements of microwave and acoustic frequencies are carried out in the same experiment. Measurements were taken at pressures from 600 kPa to 60 kPa and at 273.16 K. The internal equivalent radius of the cavity was accurately determined by microwave measurements and the first four radial symmetric acoustic modes were simultaneously measured and used to calculate the speed of sound. The improvements made using the new cavity have reduced by half the main contributions to the uncertainty due to the radius determination using microwave measurements which amounts to 4.7 parts in $10^{6}$ and the acoustic measurements, 4.4 parts in $10^{6}$, where the main contribution (3.7 parts in $10^{6}$) is the relative excess half-widths associated with the limit of our acoustic model, compared with our previous measurements. As a result of all the improvements with the new cavity and the measurements performed, we determined the molar gas constant $R$ = (8.314 449 $\pm$ 0.000 056) J/(K mol) which corresponds to a relative standard uncertainty of 6.7 parts in $10^{6}$. The value reported in this paper lies -1.3 parts in $10^{6}$ below the recommended value of CODATA 2014, although still within the range consistent with it.