Can a Pressure Standard be Based on Capacitance Measurements?

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 u_r(p) would exceed 20 × 10⁻⁶, the relative uncertainty of the value of the molar polarizability of helium A_ϵ calculated ab initio. If the relativistic corrections to A_ϵ were calculated as accurately as the classical value is now known, a capacitance-based pressure standard might attain u_r(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.