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 of helium near 0 °C. The pressure of the helium would be calculated from fundamental constants, quantum mechanics, and statistical mechanics. At present, the relative standard uncertainty of the pressure () would exceed 20 × 10, the relative uncertainty of the value of the molar polarizability of helium calculated . If the relativistic corrections to were calculated as accurately as the classical value is now known, a capacitance-based pressure standard might attain () < 6 × 10 for pressures near 1 MPa, a result of considerable interest for pressure metrology. One obtains by eliminating the density from the virial expansions for 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.