Optimized Volume Determinations and Uncertainties for Accurate and Precise Manometry

Precise manometric pressure, volume, and temperature (P-V-T) measurements of carbon in samples, standards, and blanks are critical for radiocarbon studies. While P and T uncertainties depend on instrument choice and environmental stability, V uncertainties depend on their method of measurement and are often overlooked. We used numerical simulations and error propagation to find optimum procedures for measuring cold-finger volumes equipped with capacitance diaphragm gauges (CDGs) by two common application of Boyle's Law: cryogenic transfers and serial gas expansions with a reference flask of known volume. Minimum relative uncertainties of cold-finger volumes are comparable for these two methods (∼0.002), but the serial gas expansion method is preferred due to its convenience. Serial gas expansions can be performed to high precision by using dry air, an initial pressure ∼76% full-scale (e.g., 760 Torr), and a reference flask with an optimal volume based on preliminary estimates of cold-finger volumes and an empirical power function. The volumes of cold-fingers ≥ 12 cm³ can be determined with minimum achievable relative uncertainties of 0.0021 to 0.0023. This limit translates to minimum achievable relative uncertainties of 0.0026 to 0.0027 for P-V-T measurements of moles of gas simulated here.