Redefining Exactitude at LNE-Cnam: The Last and Most Accurate Boltzmann Constant Measurement

Today, over 50% of measurements worldwide involve thermometry, and there is a growing demand for traceability over extended periods (centuries) or in environments where recalibration is impossible, such as in space. The establishment of a direct link between the kelvin and a fundamental constant, according to the 2019 definition, is already enabling new possibilities, where no temperature (e.g. the triple point of water) is more important than another and where thermometry techniques based on different physical principles can be used with equal merit.
To meet these challenges, in May 2019, the SI unit of temperature, the kelvin, was redefined using a fixed value of the Boltzmann constant k = 1.380 649 ×10−23J⋅K−1 derived from a weighted average of precise measurements performed worldwide. The LNE-Cnam determined k using acoustic thermometry with helium-4 gas in a 3-litre quasi-spherical resonator (QSR), a tri-axial ellipsoid, achieving the lowest uncertainty ever recorded for this measurement - an uncertainty that will remain unmatched now the numerical value of k is fixed.
The LNE-Cnam method involved measuring the speed of sound in helium gas by analyzing acoustic and microwave resonances. For an ideal gas at zero pressure, the speed depends only on k, the thermodynamic temperature T, the molar mass M and the Avogadro constant NA. For maximal thermometric accuracy, the resonator was maintained at a stable temperature of 273.16 K corresponding to the triple point of water which defined the kelvin at the time. Acoustic resonances were measured at different pressures to allow extrapolation to zero pressure, while the three radii of the ellipsoid were determined in situ using microwave resonances. To guarantee the most accurate molar mass, the helium gas was continuously purified to remove contaminants, the tiny amount of the only unavoidable impurity, helium-3 gas being quantified using mass spectrometry on samples from the same source as the experiment.
The measurements yielded a value for the universal gas constant R = 8.314 461 4(50) J⋅mol−1⋅K−1, related to k via R = kNA. The Avogadro constant was known at the time with a relative uncertainty of 2 ×10−8 which thus contributed negligibly to the uncertainty in k. Thus k was calculated to be 1.380 648 78(83) ×10−23J⋅K−1, the relative standard uncertainty being 0.59×10−6 (68% confidence level).
The LNE-Cnam's value for k was adopted by the CODATA Task Group on Fundamental Physical Constants in the set of values to be averaged, representing some 55% of the total weight in the adjustment. The resulting proximity of the LNE value to the fixed definitive one shows just how reliable and accurate the LNE-Cnam determination was regarded.