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"Weighing" a Gas With Microwave and Acoustic Resonances



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


With calibrations of large flow meters in mind, we established the feasibility of determining the mass Mof argon gas contained within a 0.3 m3 commercially manufactured pressure vessel ("tank") with a relative uncertainty of ur(M) = 0.0015 at 0.6 MPa by combining measurements of the argon pressure and the measured frequencies of the microwave and acoustic resonances within the pressure vessel with an accurate equation of state for argon. (All stated uncertainties have coverage factor k = 1 corresponding to 68 % confidence level.) Previously published microwave measurements determined the tank's internal volume Vmicro with a standard uncertainty of 0.06 % and determined the thermal expansion of the volume. [M. R. Moldover et al., Meas. Sci. Tech. 26 (2015) 015304] Here, we show that the microwave results accurately predict the wavenumbers kcalc of the four lowest-frequency acoustic modes of the gas. After we corrected kmeas for the tank's calculated pressure-dependent center-of-mass motion (but not correcting for the tank's vibrational modes) the largest component of ur(M) was 2×ur(kmeas/kcalc). Because the resonance frequencies fcalc 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 fcalc for a rigid cylindrical cavity is independent of temperature gradients. Consistent with this prediction, the average of fmeas for the 3 lowest-frequency, non-degenerate longitudinal modes changed only Δ}fmeas /fmeas = (0.2 plus or minus} 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 Δ}T for the average of fmeas for the nearly-degenerate doublet.


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


Gillis, K. , Mehl, J. , Schmidt, J. and Moldover, M. (2015), "Weighing" a Gas With Microwave and Acoustic Resonances, Metrologia, [online], (Accessed May 29, 2024)


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Created March 23, 2015, Updated October 12, 2021