Measurement of the Boltzmann Constant k B Using a Quasi-Spherical Acoustic Resonator

Abstract

There is currently great interest in the international metrological community for new accurate determinations of the Boltzmann constant k B , with the prospect of a new definition of the unit of thermodynamic temperature, the kelvin. In fact, k B relates the unit of energy (the joule) to the unit of the thermodynamic temperature (the kelvin). One of the most accurate ways to access the value of the Boltzmann constant is from measurements of the velocity of the sound in a noble gas. In the method described here, the experimental determination has been performed in a closed quasi-spherical cavity. To improve the accuracy, all the parameters in the experiment (purity of the gas, static pressure, temperature, exact shape of the cavity monitored by EM microwaves, etc.) have to be carefully controlled. Correction terms have been computed using carefully validated theoretical models, and applied to the acoustic and microwave signals. We report on two sets of isothermal acoustic measurements yielding the value k B = 1.380 647 74(171) × 10 −23 J · K −1 with a relative standard uncertainty of 1.24 parts in 10 6 . This value lies 1.9 parts in 10 6 below the 2006 CODATA value (Mohr et al., Rev. Mod. Phys. 80, 633 (2008)), but, according to the uncertainties, remains consistent with it.

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

“…To date, they have shown x Ne ≤ 0.3 × 10 −6 [28]. -Our experiments performed with the getter and the cold trap show that the impurity bounds provided by the IRMM are overestimated by almost a factor 10 [23]. -The argon is produced by an air-liquefaction process, where helium and neon are present only in sub-part-per-million levels.…”

“…Nonlinear effects were negligible at the low sound pressure levels used in the experiment. A detailed description of the experiment will be published elsewhere [23]. Figure 6 shows the results obtained in two runs of the same experiment: one performed in May 2009 and one in July 2009.…”

“…The main uncertainty component in table 3 is the dispersion of the acoustic modes related to the term 1/p in the acoustic virial expansion of the squared speed of sound c 2 a (p, T TPW ) [23]. Physically, this effect is generally associated with the heat flux across the interface between the gas and the walls of the resonator [1], but it can also be related to other effects, such as impurities in the gas.…”

Thermal correction to the molar polarizability of a Boltzmann gas

“…The corresponding shift is given in Eq. (15) and amounts to δ = 3.47 × 10 −12 for helium at room temperature.…”

Doppler Broadening Thermometry Based on Cavity Ring-Down Spectroscopy

“…The present CODATA [2] recommended value of k B is 1.3806488(13) × 10 −23 J/K, inferred from a group of results obtained from the acoustic gas thermometry (AGT) [3,4,5,6,7,8], the refractive index gas thermometry (RIGT) [9], and the Johnson noise thermometry (JNT) [10]. The combined relative uncertainty of k B is 0.91 ppm.…”