The kelvin redefinition and the MeP-K
Dr Bernd Fellmuth, Physikalisch-Technische Bundesanstalt, Germany
Historically, the best guide for the realisation of the kelvin has been the text of the International Temperature Scales and accompanying documents. Recent developments and its redefinition have motivated the creation of a more flexible document: the Mise-en-Pratique of the definition of the kelvin (MeP-K). The MeP-K provides the information needed to perform a practical measurement of temperature.
In this contribution, the background and the content of the second version of the MeP-K is presented. This version is based on the planned redefinition of SI base unit kelvin via an explicit-constant definition. The kelvin will be defined in terms of the SI derived unit of energy, the joule, by fixing the value of the Boltzmann constant. The explicit-constant definition is sufficiently wide to encompass any form of thermometry and leaves the MeP-K to spell out the practical details.
The second version of the MeP-K consists of four parts:
Introduction, stating the redefinition of the kelvin, the rationale for the change, and the effect on its realisation.
- Nomenclature, defining fundamental terms of thermometry to support an unambiguous taxonomy of methods.
- Primary thermometry, describing the realisation based on fundamental laws of statistical thermodynamics. Two primary methods, namely acoustic gas thermometry and radiometric thermometry, are shortly described. Details are given in appendices.
Defined temperature scales, providing information for the ITS 90 and PLTS 2000. Further important information is given in appendices and guides.
Low uncertainty Boltzmann constant determinations and the kelvin redefinition
Dr Joachim Fischer, Physikalisch-Technische Bundesanstalt, Germany
The General Conference on Weights and Measures agreed at its 24th meeting in October 2011 on new definitions for four of the seven base units of the International System of Units (SI). Kilogram, ampere, kelvin, and mole will be defined in terms of fixed numerical values of the Planck constant, elementary charge, Boltzmann constant and Avogadro constant, respectively.
The effect of the new definition of the kelvin referenced to the value of the Boltzmann constant is that the kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy kT by 1.380 650 x 10−23 J. The new definition would be in line with modern science where nature is characterised by statistical thermodynamics, which implies the equivalence of energy E and temperature T as expressed by the Maxwell-Boltzmann equation E = kT.
A refined value of the Boltzmann constant suitable for defining the kelvin is presently determined by fundamentally different primary methods like acoustic gas thermometry, dielectric constant gas thermometry, noise thermometry, and the Doppler broadening technique. Details of the measurements, progress to date, and further perspectives will be reported.
Necessary conditions to be met before proceeding with changing the definition are given. The consequences of the new definition of the kelvin on temperature measurement will be outlined.
On the meaning of temperature
Professor Peter Hänggi, University of Augsburg, Germany
Most importantly, temperature is a derived quantity. It is given as the thermodynamic force of the thermodynamic state function, known as the entropy S. The absolute temperature T then obeys: 1/T = ∂S/∂E, wherein E denotes the internal thermodynamic energy state function. The inverse absolute temperature provides the integrating factor for the Second Law of thermodynamics, dS = δQrev/T, where δQrev refers to the reversible, quasi-static heat exchange.
JW Gibbs introduced two thermodynamic entropy expressions. A first one (i) known as volume entropy, termed here the `Gibbs entropy’ SG, reading: SG(E, λ) = kB ln Ω(E, λ), with λ denoting the set of external control parameters, such as the available volume, magnetic field, etc. Ω(E, λ) is the integrated, non-negative valued density of states. Gibbs also discussed a second entropy expression (ii) that is referred to as surface entropy SB (nowadays, commonly known also as the Boltzmann entropy), reading SB(E, λ) = kB ln [ε ω(E, λ)], with ε being some small energy constant so that the argument of the logarithm becomes dimensionless.
As recently shown with Ref. , for the consistency of an entropy function S with thermodynamics, that is to say with S obeying the celebrated 0th, 1st and 2nd thermodynamic laws singles out the Gibbs-entropy . I point out shortcomings for the thermodynamics of systems of finite size and/or with an upper bound in energy if using (Boltzmann) entropy. The two corresponding thermodynamic temperatures TG and TB are then not equivalent and can considerably differ.
 S. Hilbert, P. Hänggi, and J. Dunkel, Thermodynamic Laws in Isolated Systems, Phys. Rev. E 90, 062116 (2014).
The new SI: progress and prospects
Professor Marc E. Himbert, LNE-Cnam, France
Most national metrology laboratories and some major physics laboratories have been working for decades to improve the determination of several fundamental physical constants. As the uncertainty in the measurements tends to the accuracy of the materialisations of the relevant SI units, time has come for a major change in the SI definitions, where the so-called based units will be scaled relative to fixed values of a set of fundamental constants or constants of nature.
The frame of this new SI was proposed 10 years ago. Major resolutions were adopted by the CIPM and the CGPM to fix which conditions should be fulfilled before a final decision for the change. Such a decision is expected to be taken in 2018. The new SI will highly improve the accuracy and the sustainability of the set of references. It will also open the way to an easier traceability at the nano- and quantum scales.
The new kelvin will be linked to a fixed value of the Boltzmann constant k. Consequently the triple point of water will remain as a practical reference, to be calibrated. A draft of the future SI brochure, with the new definition of the kelvin, is on the way. New techniques, new concepts and new technologies are investigated to link new ways of measurements to the International temperature scale. The aim is to make profit of this new definition for absolute and relative determinations of temperatures.
Professor Martin Trusler, Imperial College London, UK