The Boltzmann project

Abstract

The International Committee for Weights and Measures (CIPM), at its meeting in October 2017, followed the recommendation of the Consultative Committee for Units (CCU) on the redefinition of the kilogram, ampere, kelvin and mole. For the redefinition of the kelvin, the Boltzmann constant will be fixed with the numerical value 1.380 649 × 10^-23 J K^-1. The relative standard uncertainty to be transferred to the thermodynamic temperature value of the triple point of water will be 3.7 × 10^-7, corresponding to an uncertainty in temperature of 0.10 mK, sufficiently low for all practical purposes. With the redefinition of the kelvin, the broad research activities of the temperature community on the determination of the Boltzmann constant have been very successfully completed. In the following, a review of the determinations of the Boltzmann constant k, important for the new definition of the kelvin and performed in the last decade, is given.

Keywords: Boltzmann constant; International System of Units (SI); fundamental constant; primary thermometry; revised SI.

Figure 1

History of the adjusted values of the Boltzmann constant taken from the periodic reviews of the CODATA TGFC with relative uncertainties indicated. Contributing measurements and method indicated. Note that on the time axis are the dates of the CODATA adjustments, not the dates of the contributing measurements. The error bars indicate standard uncertainties.

Figure 2

The LNE-CNAM resonator BCU4 used for the lowest uncertainty estimate of the Boltzmann constant. The copper resonator is assembled from two diamond-turned hemispheres to create a triaxial ellipsoid with an internal volume of approximately 3 l.

Figure 3

NIM have developed several cylindrical resonators. Left: schematic illustration of the use of two cylinders differing in length by a factor two, in which the end effects can be cancelled out. Right: a diamond-turned copper cylinder using the final NIM experiments.

Figure 4

Schematic sketch of the DCGT setup used at PTB (reference capacitor on the left, measuring capacitor on the right). Three quantities must be measured: pressure p, capacitance C( p ) and temperature T via the resistance R of a thermometer, which was calibrated at the TPW. χ = ε_r − 1 is the dielectric susceptibility of the gas.

Figure 5

The black dots show the development of the determinations of k with DCGT since 2011. The data is taken from the papers published in 2011 [54, 59], 2013 [60], 2015 [48] and 2017 [52]. The red line shows the CODATA 2017 [13] estimate for k (for more details see text).

Figure 6

Simplified schematic diagram of a QVNS calibrated JNT. The switch alternately connects the thermal noise source or QVNS to the two amplifier channels that consist of preamplifiers (Preamp), low pass filters (LPF), buffer amplifiers (Buffer), and analogue-to-digital convertors (ADC).

Figure 7

(a) The noise power ratio spectrum from the NIM 2017 measurements, where S_R and S_Q are the measured power spectral densities of thermal noise and quantum voltage noise, respectively, and (b) the estimate of relative offset of k from CODATA recommended value versus bandwidth and order of the even-order polynomial fit.

Figure 8

Experimental setup used at Laboratoire de Physique des Lasers (AM: amplitude modulation, EOM: electro-optic modulator, FPC: Fabry Perot cavity, lock-in: lock-in amplifier).

Figure 9

Schematic diagram of the third-generation spectrometer developed at Università degli Studi della Campania. ECDL stands for extended-cavity diode laser, M for mirror, SM for spherical mirror, L for lens, BS for beam splitter, Ph for photodiode, FPh for fast photodiode, G for grating, AOM for acousto-optic modulator. The reference optical oscillator is directly linked to an optical frequency comb synthesizer. The probe ECDL is phase locked to the reference oscillator, with a tunable offset frequency. The intensity of the probe beam is actively stabilized.

Figure 10

Determinations of the Boltzmann constant in chronological order. Black dots: all contributions to the adjusted CODATA value of 2014. Red dots: new measurements contributing to the CODATA 2017 adjustment. The uncertainties of the recent determinations UVa/CEM-17 with AGT and NIST-17 with JNT did not meet the CODATA TGFC criterion for inclusion in the adjustment (yellow dots). In addition, the CODATA adjusted values of 2010 and 2014 are shown as open circles. All bars denote standard uncertainties.

Figure 11

All determinations of the Boltzmann constant contributing to the adjusted CODATA value of 2017. For clarity, all four results of LNE have been combined to a mean value [26]. In addition, the CODATA adjusted values of 2014 [12] and 2017 [13] are shown as open circles. All bars denote standard uncertainties and the blue band that of the 2017 CODATA value.