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New Determinations of the Boltzmann Constant

Project Description

A - Motivation:

The unit of temperature T, the kelvin is presently defined by the temperature of the triple point of water (TPW). Thus, the kelvin is linked to a material property. Instead, it would be advantageous to proceed in the same way as with other units: to relate the unit to a fundamental constant and fix its value. By this no temperature value and no measurement method would be favoured. For the kelvin, the corresponding constant is the Boltzmann constant k, because temperature always appears as thermal energy kT in fundamental laws of physics. For fixing the value, k must first be determined with lower uncertainty or at least the present value needs to be confirmed. This project coordinates the most promising experimental methods having potential to contribute to new determinations of k.

B - Description of the work:

An improved value of the Boltzmann constant proposed for defining the kelvin would ideally have been determined by several fundamentally different methods. Nearly all partners involved use different methods, like acoustic or dielectric constant gas thermometry, or spectroscopic and optical methods. All partners will determine the Boltzmann constant independently using their own equipment aiming at a relative standard uncertainty close to 1 ppm. These new values will be compared with the present CODATA value of k determined by acoustic gas thermometry of NIST. At several meetings during the project the individual progress of the different methods will be discussed and reviewed.

Progress Report 08.02.2016

LNE-CNAM is making last changes on the 3 liter sphere (BCU4) in order to remove the inconsistency of the acoustic modes. They achieved good agreement with microwaves (dispersion over the modes is within 0.1 ppm) but acoustic modes gave at the same time 2.5 ppm dispersion.

NPL is preparing gravimetrically-determined mixtures of 40Ar and 36Ar which they hope to use to calibrate the mass discrimination and fraction effects in the SUERC ARGOS mass spectrometer.

INRiM current activities in acoustic gas thermometry are limited to T-T90 measurements and are thus not currently pursuing an improved Boltzmann constant determination.

KRISS is working on preparing a new batch of 36Ar-40Ar mixtures by the gravimetric method to reduce the uncertainty of molar mass measurements related to the Boltzmann constant determinations.

For the DCGT experiment of PTB new highly stable tungsten carbide capacitors were developed which are currently under test.

At the DBT experiment of Second University of Naples, in close cooperation with INRiM, new spectroscopic measurements were made with acetylene gas at a wavelength of 1.39 µm. They plan to observe water and acetylene spectra simultaneously in the same gas cell and to use a self-referenced frequency comb.

For the DBT experiment of University Paris North, a new setup for IR quantum cascade lasers frequency control was developed and in improvement of the laser stability and accuracy by almost one order of magnitude was demonstrated.

Progress Report 20.02.2015

LNE-CNAM published in 2015 the series of measurements of May 2012 and January 2013 using helium gas with the 0.5 liter copper quasi-sphere BCU3 (50 mm radius). The value is in good agreement with the earlier measurements in argon. The weighted mean of the measurements has a relative uncertainty of 1.02 × 10-6. The values of the uncertainty contributions are nearly equally spread over the measurements of acoustic frequency, resonator volume, molar mass, and temperature, the latter being the lowest. For 2016 new results are expected with the 3.1 liter quasi-sphere BCU4 having 90 mm radius to be operated with helium and argon.

INRiM has pursued an accurate determination of the speed of sound in helium at 273.16 K with a 3-liter volume copper sphere assembled in 2013. Acoustic and microwave results indicate that the performance of the experiment has significantly improved with respect to previous INRiM achievements. Also, with three newly calibrated capsule-type standard platinum resistance thermometers, temperature measurement and thermal gradients across the resonator are satisfactory. An accurate and reliable assessment of the molar mass was achieved by a cross-check of the current estimate of helium impurities by using the mass spectrometry facilities made available by PTB. The value of the Boltzmann constant has a relative uncertainty of 1.17 × 10-6.

KRISS performed extensive molar mass measurements between October and December 2014. The determinations of the molar mass of Argon between KRISS and IRMM disagreed by up to 3.5 ppm. The Argon results of LNE-CNAM are based on the molar mass determinations of IRMM. The absolute molar mass was determined for a gas bottle used in the NPL experiment of 2013. The value is 2.73 x 10-6 lower than the SUERC value on that bottle. The NPL molar mass determination is based on the SUERC. Through the recent more indirect acoustic comparison of LNE-CNAM, the KRISS-SUERC discrepancy was determined to be 3.61 x 10-6. The discrepancy to the direct determination as stated above is too small to make any suggestion on the Boltzmann determination of LNE-CNAM in 2011 with Argon. No meaningful change in numbers would result. It was agreed between all institutes involved that one would correct only the value of the Boltzmann constant of the NPL 2013 experiment by the relative amount of - 2.73 x 10-6. This correction completely resolves the discrepancy in the Boltzmann constant results with Argon gas of NPL 2013 and LNE 2011.

At the DCGT experiment of PTB activities to reduce the uncertainties of the pressure measurement to a level of 1 × 10-6 were successfully completed in 2014. This included extensive cross-float comparisons between six independent primary piston–cylinder assemblies to improve the consistency of their effective areas and pressure-distortion coefficients. Moreover, an uncertainty reduction came from a careful comparison of the pressure distortion coefficients up to 7 MPa. The resulting new relative uncertainty for the Boltzmann constant amounts to 4.0 × 10-6. The largest uncertainty contributions are now the type A estimate and the determination of the effective compressibility.

For the DBT experiment of Second University of Naples further reduction of uncertainties is expected by the use of a low-pressure long path absorption cell, by increasing the number of spectra, by improving the signal-to-noise ratio and by removing the dither on the reference laser. As for this latter upgrade, they have presently implemented a technique known as noise-immune cavity-enhanced optical heterodyne molecular spectroscopy for the highly sensitive detection of the sub-Doppler line.

For the DBT experiment of University Paris North, some improvements have been made to the mid-infrared spectrometer including the use of a phase-stabilized quantum cascade laser. A line shape analysis based on a refined physical model and a first evaluation of the saturation parameter and its impact on the measurement of kB have been performed leading to a revision of the type B uncertainty budget.

Further Information

[15-02-2006] It is anticipated that NIST (USA) will join the project at an appropriate stage.


The project is an agreed iMERA joint research project.

Thermometry (T)
Joachim Fischer, PTB (Germany)
Coordinating Institute
PTB (Germany)
Further Partners
Second University of Naples (IT)
Polytechnic of Milan (IT)
University of Valladolid (ES)
University Paris North (FR)


Reg. No.
Collaboration Type
Final Report