Can a pressure standard be based on capacitance measurements?

We consider the feasibility of basing a pressure standard on measurements of the dielectric constant 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 A calculated ab initio . If the relativistic corrections to A 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 1. If 1 were measured with a very stable, 0.5 pF toroidal cross capacitor, the small capacitance and the small values of 1 would require state-of-the-art capacitance measurements to achieve a useful pressure standard.