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 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.