'Weighing' a gas with microwave and acoustic resonances

作者：Gillis K A^*; Mehl J B; Schmidt J W; Moldover M R

来源：Metrologia, 2014, 52(2): 337-352.

DOI：10.1088/0026-1394/52/2/337

• volume
• pressure vessel
• flow metrology
• flow calibrations
• acoustic resonances
• microwave resonances
• temperature

With calibrations of large flow meters in mind, we established the feasibility of determining the mass M of argon gas contained within a 0.3 m(3) commercially manufactured pressure vessel ('tank') with a relative standard uncertainty of u(r)(M) = 0.0016 at 0.6 MPa by combining the measured argon pressure and the measured microwave and acoustic resonance frequencies within the pressure vessel with an accurate equation of state for argon. (All stated uncertainties correspond to the 68% confidence level.) Previously, we used microwaves to determine the tank's internal volume V-micro with u(r)(V) = 0.0006 and to determine the thermal expansion of the volume (Moldover et al 2015 Meas. Sci. Tech. 26 015304). Here, we show that the microwave results accurately predict the wavenumbers k(calc) of the four lowest-frequency acoustic modes of the gas. When we compared k(calc) to the measured wavenumbers k(meas), which included corrections for known perturbations, such as the tank's calculated pressure-dependent center-of-mass motion (but not the tank's vibrational modes), the inconsistency of the ratio k(meas)/k(calc) among the modes was the largest component of ur(M). Because the resonance frequencies f(calc) of the acoustic modes depend on the average speed of sound (and therefore the average temperature) of the gas in the tank, first-order perturbation theory predicts that f(calc) for a rigid cylindrical cavity is independent of linear temperature gradients. Consistent with this prediction, the average of f(meas) for the 3 lowest-frequency, non-degenerate longitudinal modes changed only Delta f(meas)/f(meas) = (0.2 +/- 1.3) x 10(-4) when, near ambient temperature, we heated the tank's top 13 K warmer than its bottom. However, we observed a linear dependence on Delta T for the average of f(meas) for the nearly-degenerate doublet modes, which the rigid cylinder theory does not predict. We argue that the linear dependence on Delta T was caused by anisotropic changes in the tank's shape in response to the applied temperature gradient. We conclude that resonance frequencies can be used to 'weigh' the compressed gas in much larger tanks, which are possibly made from ferromagnetic steel and possibly at high pressures in un-thermostatted environments; therefore, resonance measurements will have many applications in gas metrology.

• 出版日期2014-4