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‘Weighing’ a gas with microwave and acoustic resonances

2015; IOP Publishing; Volume: 52; Issue: 2 Linguagem: Inglês

10.1088/0026-1394/52/2/337

1681-7575

Keith A. Gillis, James B. Mehl, James W. Schmidt, Michael R. Moldover,

Atomic and Subatomic Physics Research

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 m3 commercially manufactured pressure vessel ('tank') with a relative standard uncertainty of ur(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 Vmicro with ur(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 kcalc of the four lowest-frequency acoustic modes of the gas. When we compared kcalc to the measured wavenumbers kmeas, 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 kmeas/kcalc 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 Δfmeas / f meas = (0.2 ± 1.3) × 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 ΔT 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 ΔT 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.