Can a pressure standard be based on capacitance measurements?

Abstract

We consider the feasibility of basing a pressure standard on measurements of the dielectric constant ϵ and the thermodynamic temperature T of helium near 0 °C. The pressure p of the helium would be calculated from fundamental constants, quantum mechanics, and statistical mechanics. At present, the relative standard uncertainty of the pressure ur(p) would exceed 20 × 10−6, the relative uncertainty of the value of the molar polarizability of helium Aϵ calculated ab initio. If the relativistic corrections to Aϵ were calculated as accurately as the classical value is now known, a capacitance-based pressure standard might attain ur(p) < 6 × 10−6 for pressures near 1 MPa, a result of considerable interest for pressure metrology. One obtains p by eliminating the density from the virial expansions for p and ϵ − 1. If ϵ − 1 were measured with a very stable, 0.5 pF toroidal cross capacitor, the small capacitance and the small values of ϵ − 1 would require state-of-the-art capacitance measurements to achieve a useful pressure standard.

Apparatus for wide-ranging, high-accuracy fluid (p,ρ,T) measurements based on a compact two-sinker densimeter

“…The present results show excellent agreement with the theoretical values and also the experimental values of Gammon [31], and Blancett et al [32]. These references were identified by Hurly and Moldover [30] and Moldover [33] as the most reliable literature sources. The differences are well within the mutual uncertainties, except that the second virials of Gammon are just outside the uncertainties of the ab initio calculations.…”

Using ab initio “data” to accurately determine the fourth density virial coefficient of helium

“…At the higher density, q = 10 mol Á L À1 , the contributions from C and D are comparable, while those from R and B are much smaller; the combined uncertainty at this density is 21 ppm. Moldover speculated in 1998 [21] that this approach might yield a minimum uncertainty on the order of 5 ppm at pressures near 1 MPa; this would make it comparable to that achieved with artifact standards, such as piston gages. Recent improvements in the ab initio calculations of helium have pushed the feasible pressure up to perhaps 10 MPa.…”

“…As one example, Moldover et al [3,21] proposed a pressure standard based on the dielectric constant of helium. In essence, the idea is to calculate ab initio the relative dielectric permittivity (or refractive index) of helium as a function of temperature and density (T, q) so that capacitance measurements (or microwave resonance frequency measurements) could be used to determine the density; this would then be combined with the pressure of helium computed as a function of (T, q) from the virial expansion.…”

Radiative Corrections to the Polarizability of Helium

“…The well-known statistical mechanics relation between the pressure of a gas, its temperature, dielectric constant, and molar polarizability [1][2][3] opens up a possibility of establishing pressure and/or temperature standards based on capacitance measurements of the dielectric constant. The uncertainty of the determined pressure would then depend on the uncertainty of the molar polarizability of the gas and of its virial coefficients.…”