The Boltzmann project

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.

[1]  Samuel P. Benz,et al.  Flat Frequency Response in the Electronic Measurement of Boltzmann's Constant , 2013, IEEE Transactions on Instrumentation and Measurement.

[2]  John M. Martinis,et al.  An AC Josephson source for Johnson noise thermometry , 2002, Conference Digest Conference on Precision Electromagnetic Measurements.

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[5]  Peter J. Mohr,et al.  The CODATA 2017 values of h, e, k, and NA for the revision of the SI , 2018 .

[6]  Weston L. Tew,et al.  Electronic measurement of the Boltzmann constant with a quantum-voltage-calibrated Johnson noise thermometer , 2009 .

[7]  K. Anhalt,et al.  Thermodynamic temperature by primary radiometry , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  L. Gianfrani.  Linking the thermodynamic temperature to an optical frequency: recent advances in Doppler broadening thermometry , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[9]  K. Gillis.  Second-order boundary corrections to the radial acoustic eigenvalues for a spherical cavity , 2012 .

[10]  A Amy-Klein,et al.  Direct determination of the Boltzmann constant by an optical method. , 2007, Physical review letters.

[11]  B. Taylor,et al.  CODATA Recommended Values of the Fundamental Physical Constants: 2010 | NIST , 2007, 0801.0028.

[12]  Samuel P. Benz,et al.  Johnson noise thermometry measurement of the Boltzmann constant with a 200 Ω sense resistor , 2012, 2012 Conference on Precision electromagnetic Measurements.

[13]  Y. Duan,et al.  Progress Toward Redetermining the Boltzmann Constant with a Fixed-Path-Length Cylindrical Resonator , 2011 .

[14]  M. Moldover,et al.  Test of a virtual cylindrical acoustic resonator for determining the Boltzmann constant , 2015 .

[15]  Michael R. Moldover,et al.  Designing quasi-spherical resonators for acoustic thermometry , 2004 .

[16]  Second-order electromagnetic eigenfrequencies of a triaxial ellipsoid , 2015 .

[17]  L. Moretti,et al.  Investigating the ultimate accuracy of Doppler-broadening thermometry by means of a global fitting procedure , 2015 .

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[20]  S. Briaudeau,et al.  Measuring the Boltzmann constant by mid-infrared laser spectroscopy of ammonia , 2015, 1506.01828.

[21]  M. Moldover,et al.  Determination of the Boltzmann constant with cylindrical acoustic gas thermometry: new and previous results combined , 2017, Metrologia.

[22]  M. Himbert,et al.  Measurement of the Boltzmann Constant kB Using a Quasi-Spherical Acoustic Resonator , 2011 .

[23]  John M. Martinis,et al.  A New Approach to Johnson Noise Thermometry using a Josephson Quantized Voltage Source , 2002 .

[24]  D. Mark,et al.  Correction of NPL-2013 estimate of the Boltzmann constant for argon isotopic composition and thermal conductivity , 2015 .

[25]  D. Newell,et al.  Correlations among acoustic measurements of the Boltzmann constant , 2015 .

[26]  Progress towards an acoustic determination of the Boltzmann constant at CEM-UVa , 2015 .

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[28]  G. Edwards,et al.  The electromagnetic fields of a triaxial ellipsoid calculated by modal superposition , 2011 .

[29]  E. May,et al.  Characterization of the volume and shape of quasi-spherical resonators using coordinate measurement machines , 2010 .

[30]  Bernd Fellmuth,et al.  High-Precision Capacitance Bridge for Dielectric-Constant Gas Thermometry , 2011, IEEE Transactions on Instrumentation and Measurement.

[31]  F. Stuart,et al.  A low-uncertainty measurement of the Boltzmann constant , 2013 .

[32]  G. Sutton,et al.  Acoustic Resonator Experiments at the Triple Point of Water: First Results for the Boltzmann Constant and Remaining Challenges , 2010 .

[33]  A low-uncertainty measurement of the Boltzmann constant , 2013 .

[34]  T. Quinn,et al.  An acoustic redetermination of the gas constant , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[35]  John M. Martinis,et al.  Johnson noise thermometry measurements using a quantized voltage noise source for calibration , 2003, IEEE Trans. Instrum. Meas..

[36]  R. Hellmann,et al.  Ab initio pair potential energy curve for the argon atom pair and thermophysical properties for the dilute argon gas. II. Thermophysical properties for low-density argon , 2008 .

[37]  T. Odintsova,et al.  Hyperfine structure effects in Doppler-broadening thermometry on water vapor at 1.4 μm , 2016 .

[38]  Samuel P. Benz,et al.  Reduced non-linearities and improved temperature measurements for the NIST Johnson noise thermometer , 2009 .

[39]  John L. Sarrao,et al.  Resonant ultrasound spectroscopic techniques for measurement of the elastic moduli of solids , 1993 .

[40]  M. Himbert,et al.  Determination of the Boltzmann constant k from the speed of sound in helium gas at the triple point of water , 2015 .

[41]  M. Triki,et al.  Progress towards an accurate determination of the Boltzmann constant by Doppler spectroscopy , 2010, 1012.4181.

[42]  B. Taylor,et al.  CODATA recommended values of the fundamental physical constants: 2006 | NIST , 2007, 0801.0028.

[43]  Peter J. Mohr,et al.  Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005) , 2006 .

[44]  James B. Mehl,et al.  Acoustic resonance frequencies of deformed spherical resonators. II , 1982 .

[45]  Samuel P. Benz,et al.  A pulse‐driven programmable Josephson voltage standard , 1996 .

[46]  M. Moldover,et al.  Improved determination of the Boltzmann constant using a single, fixed-length cylindrical cavity , 2013 .

[47]  James B. Mehl,et al.  Spherical acoustic resonator: Effects of shell motion , 1985 .

[48]  C. Chardonnet,et al.  Absorption-line-shape recovery beyond the detection-bandwidth limit: Application to the precision spectroscopic measurement of the Boltzmann constant , 2014, 1406.2975.

[49]  Barry N. Taylor,et al.  The 1973 Least‐Squares Adjustment of the Fundamental Constants , 1973 .

[50]  C. Daussy,et al.  CO/sub 2/ laser stabilization to 0.1-Hz level using external electrooptic modulation , 1997 .

[51]  A. Merlone,et al.  A determination of the Boltzmann constant from speed of sound measurements in helium at a single thermodynamic state , 2010 .

[52]  Davis,et al.  Measurement of the universal gas constant R using a spherical acoustic resonator. , 1987, Physical review letters.

[53]  E. Grüneisen.  Zusammenhang zwischen Kompressibilität, thermischer Ausdehnung, Atomvolumen und Atomwärme der Metalle , 1908 .

[54]  J. Segovia,et al.  Updated determination of the molar gas constant R by acoustic measurements in argon at UVa-CEM , 2017 .

[55]  Barry N. Taylor,et al.  THE 1986 ADJUSTMENT OF THE FUNDAMENTAL PHYSICAL CONSTANTS: A REPORT OF THE CODATA TASK GROUP ON FUNDAMENTAL CONSTANTS , 1987 .

[56]  Speed-dependent effects in NH 3 self-broadened spectra: Towards the determination of the Boltzmann constant , 2012, 1201.4087.

[57]  H. Callen,et al.  Irreversibility and Generalized Noise , 1951 .

[58]  Rod White,et al.  An improved electronic determination of the Boltzmann constant by Johnson noise thermometry , 2017, Metrologia.

[59]  P. Laporta,et al.  Primary gas thermometry by means of laser-absorption spectroscopy: determination of the Boltzmann constant. , 2008, Physical review letters.

[60]  Rod White,et al.  Improved electronic measurement of the Boltzmann constant by Johnson noise Thermometry , 2014 .

[61]  M. Moldover,et al.  Improving acoustic determinations of the Boltzmann constant with mass spectrometer measurements of the molar mass of argon , 2015 .

[62]  P. Laporta,et al.  Determination of the Boltzmann constant by means of precision measurements of H2(18)O line shapes at 1.39  μm. , 2013, Physical review letters.

[63]  K. Szalewicz,et al.  Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium. , 2012, The Journal of chemical physics.

[64]  C. Bord,et al.  Atomic clocks and inertial sensors , 2002 .

[65]  P. Morantz,et al.  Pyknometric volume measurement of a quasispherical resonator , 2012 .

[66]  N. Kaneko,et al.  Measurement of the Boltzmann constant by Johnson noise thermometry using a superconducting integrated circuit , 2017 .

[67]  Joachim Fischer,et al.  Determination of the Boltzmann constant—status and prospects , 2006 .

[68]  M de Podesta,et al.  Acoustic gas thermometry , 2014 .

[69]  M. Moldover,et al.  New measurement of the Boltzmann constant k by acoustic thermometry of helium-4 gas , 2017 .

[70]  Krzysztof Szalewicz,et al.  Frequency-dependent polarizability of helium including relativistic effects with nuclear recoil terms. , 2015, Physical review letters.

[71]  Mehl,et al.  Measurement of the ratio of the speed of sound to the speed of light. , 1986, Physical review. A, General physics.

[72]  Paul Morantz,et al.  Dimensional characterization of a quasispherical resonator by microwave and coordinate measurement techniques , 2011 .

[73]  S. Picard,et al.  The kelvin redefinition and its mise en pratique , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[74]  S. P. Benz,et al.  Constraints on a synthetic-noise source for Johnson noise thermometry , 2008 .

[75]  A. Merlone,et al.  Capabilities for Dielectric-Constant Gas Thermometry in a Special Large-Volume Liquid-Bath Thermostat , 2011 .

[76]  Weston L. Tew,et al.  Measurement time and statistics for a noise thermometer with a synthetic-noise reference , 2008 .

[77]  L. Moretti,et al.  The Boltzmann constant from the shape of a molecular spectral line , 2014 .

[78]  J. Mehl.  Acoustic Eigenvalues of a Quasispherical Resonator: Second Order Shape Perturbation Theory for Arbitrary Modes , 2007, Journal of research of the National Institute of Standards and Technology.

[79]  Weston L. Tew,et al.  An electronic measurement of the Boltzmann constant , 2011 .

[80]  M. Triki,et al.  A revised uncertainty budget for measuring the Boltzmann constant using the Doppler broadening technique on ammonia , 2013, 1309.4549.

[81]  Bernd Fellmuth,et al.  Dielectric-constant gas thermometry , 2015 .

[82]  B. Fellmuth,et al.  Low-temperature determination of the Boltzmann constant by dielectric-constant gas thermometry , 2012 .

[83]  H. Nyquist.  Thermal Agitation of Electric Charge in Conductors , 1928 .

[84]  K. Gillis,et al.  Characterization of Piezoelectric Ceramic Transducer for Accurate Speed-of-Sound Measurement , 2010 .

[85]  D. White,et al.  Frequency-response mismatch effects in Johnson noise thermometry , 2018 .

[86]  A. Einstein.  Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [AdP 17, 549 (1905)] , 2005, Annalen der Physik.

[87]  A. Merlone,et al.  The Boltzmann constant from the H2 18O vibration–rotation spectrum: complementary tests and revised uncertainty budget , 2015 .

[88]  J.X. Przybysz,et al.  Pulse-driven Josephson digital/analog converter [voltage standard] , 1998, IEEE Transactions on Applied Superconductivity.

[89]  Wladimir Sabuga,et al.  Determination of the Boltzmann constant by dielectric-constant gas thermometry , 2013 .

[90]  Christian Chardonnet,et al.  A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy , 2014, 1404.1162.

[91]  Samuel P. Benz,et al.  Reduced Nonlinearity Effect on the Electronic Measurement of the Boltzmann Constant , 2011, IEEE Transactions on Instrumentation and Measurement.

[92]  D. Mark,et al.  Re-estimation of argon isotope ratios leading to a revised estimate of the Boltzmann constant , 2017 .

[93]  K. Coakley,et al.  Spectral model selection in the electronic measurement of the Boltzmann constant by Johnson noise thermometry , 2016, Metrologia.

[94]  M. Himbert,et al.  An improved acoustic method for the determination of the Boltzmann constant at LNE-INM/CNAM , 2009 .

[95]  W L Tew,et al.  A Boltzmann constant determination based on Johnson noise thermometry , 2017, Metrologia.

[96]  Aziz,et al.  Ab initio calculations for helium: A standard for transport property measurements. , 1995, Physical review letters.

[97]  Determination of the Boltzmann Constant by Laser Spectroscopy as a Basis for Future Measurements of the Thermodynamic Temperature , 2009, 0911.2507.

[98]  F. Bertiglia,et al.  Dual-laser absorption spectroscopy of C2H2 at 1.4 μm , 2016 .

[99]  B. Fellmuth,et al.  Measurement of pressures up to 7 MPa applying pressure balances for dielectric-constant gas thermometry , 2015 .

[100]  A Actis,et al.  The status of Johnson noise thermometry , 1996 .

[101]  B. Fellmuth,et al.  Dielectric-Constant Gas-Thermometry Measuring System for the Determination of the Boltzmann Constant at PTB , 2010 .