portrait of Boltzmann

Boltzmann constant

A natural constant relating energy to temperature. Symbol, k. As part of the redefinition of the kelvin, in 2018 the CGPM assigned it an exact numerical value within SI, of 1.380 649 × 10⁻²³ joules per kelvin.

The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 × 10⁻²³ when expressed in the unit J K⁻¹, which is equal to kg m² s⁻² K⁻¹, where the kilogram, metre and second are defined in terms of h, c and Δνcs.

Resolutions Adopted.
Resolution 1, appendix 3.
26 CGPM, Versailles 13-16 November 2018.

Here h is the Planck constant, c is the speed of light, and Δνcs refers to the frequency of light emitted by a cesium atom under specified conditions.

It is named for the German physicist Ludwig Boltzmann.

Boltzmann himself (and his mentor Stefan) did not regard this number as a constant, but as a conversion factor. Apparently Max Planck was the first person to refer to it as a constant. By the 1920's the usage “Boltzmann constant” was thoroughly established.

Recent history

At its 24th meeting (Paris, October 2011), the CGPM declared its intention to make the value of the Boltzmann constant a matter of definition, rather than something to be determined experimentally. The new value was to be exactly 1.380 6X × 10⁻²³ joule per kelvin, where X stood for one or more yet to be determined digits. The new definition was not be adopted before 2014. For comparison, the 2006 CODATA recommended values give k = 1.380 6504 × 10⁻²³ joule per kelvin, with a standard uncertainty of 0.000 0024 × 10⁻²³ joule per kelvin.

Work on refining the value of the Boltzmann constant has continued at such centers as the Physikalisch-Technische Bundesanstalt.

group portrait of workshop attendees

Photograph courtesy Physikalisch-Technische Bundesanstalt

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