Acoustic thermometry: new results from 273 K to 77 K and progress towards 4 K

Abstract

We used a quasi-spherical cavity as an acoustic and microwave resonator to measure the thermodynamic temperatures, T , of the triple points of equilibrium hydrogen, neon, argon and mercury and to measure the difference T − T 90 , in the range 7 K to 273 K. (T 90 is the temperature on the International Temperature Scale of 1990 (ITS-90).) In the range 7 K to 24.5 K, our preliminary values of T − T 90 agree with recent results from dielectric-constant gas thermometry and achieve uncertainties that are comparable to or smaller than those achievable using the interpolating constant volume gas thermometer as currently defined on the ITS-90. In the range 90 K to 273 K, the present results for T − T 90 obtained using a helium-filled, copper-walled, quasi-spherical cavity agree with earlier results obtained using argon-filled, steel-walled or aluminium-walled, spherical cavities. The agreement confirms our understanding of both acoustic and microwave cavity resonators and demonstrates that resonators function as primary thermometers spanning wide temperature ranges. The mutually consistent acoustic thermometry data from several laboratories imply that the values of (T − T 90)/T 90 are 5 times larger than the uncertainty of T /T 90 near 150 K and near 400 K. They also imply that the derivative dT /dT 90 is too large by approximately 10 −4 near 273.16 K and that dT /dT 90 has a discontinuity of 4 × 10 −5 at 273.16 K.

Optimizing acoustic measurements of the Boltzmann constant

“…They also modeled shells with spherical inner surfaces and outer surfaces that had large bosses and/or flanges similar to those on the resonators used for acoustic thermometry. [5,6,7,8,9] Consistent with the observations of Pitre et al and Gavioso et al, the models predict that radial acoustic modes do couple to non-radial shell modes when the spherical symmetry is broken, either by the shape of the outer surface or by a stiff support. Optimizing an acoustic resonator to measure k B will minimize its departures from spherical symmetry.…”

“…[4] This article reviews the advances in both understanding and technique that have occurred since the work of Quinn et al and Moldover et al Nearly all of these advances were introduced to reduce the uncertainty and complexity of primary acoustic thermometry at temperatures that extend well above and well below T TPW . [5,6,7,8,9] Because primary acoustic thermometry requires the accurate measurement of the zero-pressure limit of speed-of-sound ratios for pure monatomic gases, many thermometry-motivated improvements are applicable to acoustic determinations of k B . Such improvements include:…”

“…(1) flowing pure gas through the acoustic cavity to reduce the effects of out-gassing [10], (2) tuning ducts that allow gas flow through the cavity to reduce the ducts' perturbations to the cavity's acoustic resonance frequencies [11], (3) minimizing gas contamination by using a bakeable gas-handling system and transducers, (4) analyzing the gas exiting the resonator via gas chromatography [9], (5) measuring microwave resonance frequencies of the cavity to determine its thermal expansion and possibly its volume [12], (6) using a quasi-spherical cavity to retain the advantages of radially-symmetric acoustic modes while splitting the degenerate microwave modes [13], (7) using removable thermometers and multiple thermometer wells in the cavity's walls to compare the resonator's temperature to T TPW at the time of use and to detect temperature gradients [9], (8) using theory to reduce the uncertainties of the thermal conductivity of helium and argon gas and the acoustic virials of helium [8], (9) using finite element models of the elastic response of the cavity's walls to the acoustic resonances, [14] and (10) accurately modeling acoustic transducers [15].…”

Determination of the Boltzmann constant using a quasi-spherical acoustic resonator

“…This experimental technique allows the measurement of the thermal expansion of spherical cavities in acoustic thermometry, and has successfully been applied in several experiments [14][15][16][17][18][19]. The radius a(p, T TPW ) of the cavity can be obtained using…”

“…For the acoustic measurements, the experimental techniques and data analysis methods are built on foundations established over two decades [1,11], and subsequently applied to temperature measurements from 7 to 552 K [17,24,25]. In our experiment, we measured the velocity of sound in argon inside our cavity from the measurement of the acoustic resonance frequencies, f A 0,n .…”