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An improved electronic measurement of the Boltzmann constant by Johnson noise thermometry



Jifeng Qu, Samuel Benz, Kevin Coakley, Horst Rogalla, Weston L. Tew, David R. White, Kunli Zhou, Zhenyu Zhou


Recent measurements using acoustic gas thermometry have determined the value of the Boltzmann constant, k, with a relative uncertainty less than 110-6. These results have been supported by a measurement with a relative uncertainty of 1.910-6 made with dielectric constant gas thermometry. Together, the measurements meet the requirements of the International Committee for Weights and Measures and enable them to proceed with the redefinition of the kelvin in 2018. In further support, we provide a new determination of k using a purely electronic approach, Johnson noise thermometry, in which the thermal noise power generated by a sensing resistor immersed in a triple-point-of-water cell is compared to the noise power of a quantum- accurate pseudo-random noise waveform of nominally equal noise power. The experimental setup differs from that of the 2015 determinations in several respects: a 100 Ω resistor was used as thermal noise source, identical thin coaxial cables made of solid beryllium-copper conductors and foam dielectric were used to connect the thermal and quantum-accurate noise sources to the correlator so as to minimise the temperature and frequency sensitivity of the impedances in the connecting leads, and further, no trimming capacitors or inductors were inserted into the connecting leads. The combination of the reduced uncertainty due to spectral mismatches in the connecting leads and reduced statistical uncertainty due to a longer integration period of 100 days results in an improved determination of k = 1.3806497(38)10^-23 J/K with a relative standard uncertainty of 2.810^-6 and relative offset 0.8910^-6 from the CODATA 2014 recommended value. The most significant terms in the uncertainty budget, the statistical uncertainty and the spectral-mismatch uncertainty, are uncorrelated with the corresponding uncertainties in the 2015 measurements.


fundamental constant, thermometry, quantum standards, SI Units, Boltzmann constant


Qu, J. , Benz, S. , Coakley, K. , Rogalla, H. , Tew, W. , White, D. , Zhou, K. and Zhou, Z. (2017), An improved electronic measurement of the Boltzmann constant by Johnson noise thermometry, Metrologia, [online],, (Accessed May 30, 2024)


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Created July 17, 2017, Updated October 12, 2021