The weak sensitivity of acoustic resonance frequencies to temperature gradients

Abstract

We determined the mass of argon gas contained within an un-thermostatted, commercially-manufactured 300 L pressure vessel (tank) with an uncertainty of 0.16 % at 0.6 MPa by combining measurements of the argon pressure, the frequencies of microwave and acoustic resonances within the tank, and an equation of state for argon. After correction for the thermoacoustic boundary layer and for the tank’s center-of-mass motion, the measured acoustic resonance frequencies f ac determined the average speed of sound, and therefore the average temperature, of the argon in the tank. We show that, consistent with first-order perturbation theory, f ac for the 3 lowest-frequency longitudinal gas modes gave the correct average temperature even when we imposed a 13 K temperature difference ΔT across the tank’s diameter. However for the nearly degenerate doublet modes, we observed a linear dependence on ΔT for f ac, which the theory does not predict. Using the thermal expansion deduced from the microwave measurements, we show that the linear dependence on ΔT was consistent with anisotropic changes in the tank’s shape in response to the applied temperature gradient. We will discuss the predictions from perturbation theory of the changes in f ac due to temperature gradients in cylindrical and spherical cavities. From these results, we argue that resonance frequencies can be used to “weigh” a compressed gas in much larger tanks in un-thermostatted environments and at high pressures.