Microwave determination of the volume of a pressure vessel

Using microwave techniques that are scalable to very large volumes, we measured the interior volume of a 0.3 m³, commercially manufactured pressure vessel with a relative uncertainty of 0.06%, as confirmed by independent, more-accurate gas-expansion measurements. This pressure vessel (or a much larger one of a similar design) could be used as either a calibrated volume standard or as a gas source and/or a gas collector for the calibration of gas-flow meters. In addition, we determined the expansion of the vessel with temperature (∂V/∂T)_p/V = (35.3  ±  1.9) × 10⁻⁶ K⁻¹, and we estimated the pressure expansion (∂V/∂p)_T/V = 0.9  ×  10⁻³ MPa⁻¹. The volume measurement did not require careful thermostatting; its uncertainty was dominated by imperfect modeling of the volume's shape. (The estimated uncertainties are one standard uncertainty with coverage factor k = 1 corresponding to 68% confidence level.) (paper)