The present definition of the kelvin links the unit of temperature with a material property, namely the triple point temperature of water. It would be more consistent with the current approaches to other base units of the International System of Units to fix the value of the Boltzmann constant k, instead. This would rationalize the definition and make it separate from any technique of realization. Furthermore, it is needed to improve temperature measurement, particularly at temperatures far away from the triple point of water. For this purpose, k must first be determined with appropriately small uncertainty applying different measurement methods. In this paper, the primary-thermometry methods for determining the Boltzmann constant (acoustic gas thermometry, thermal-equation-of-state methods, radiation thermometry and methods based directly on statistics and quantization) and their state-of-the-art level of uncertainty are discussed. Special emphasis is given to the basic physics underlying these methods, the fundamental error sources and the uncertainty, which seems to be attainable on a five-year timescale in view of some new developments and the foreseeable progress. Finally, a possible simple new definition of the kelvin is proposed.

Primary dielectric constant gas thermometry (DCGT) has been used to establish a quasi-continuous temperature scale in the range 4,2 K to 27,0 K with a measurement uncertainty which increases with rising temperature from 0,6 mK to 1,2 mK (confidence level 95 %). (It should be noted that previous papers refer to the 68 % level which yields about one half of the uncertainty values.) The large number of experimental data for 4 He (about thirty isotherms, more than 200 triplets of pressure, temperature, and dielectric constant) allowed, furthermore, the determination of the temperature dependencies of the second and third virial coefficients, without any constraints. The virial coefficients thus obtained exhibit good agreement with data based primarily on conventional gas thermometry and potential calculations. The established temperature scale is compared with the isotherm and constant volume gas thermometry scale NPL-75. A flat sinusoidal form for the differences between the two scales may be seen, which is in accordance with other published data. However, the differences are well within the thermodynamic uncertainties estimated for the NPL-75 and the DCGT scale. This result supports the theoretical polarizability value with a relative combined uncertainty of 6 10 -5 , i.e. the bounds for the polarizability value of 4 He have been decreased by one order of magnitude compared with the available rigorous theoretical bounds.

The principles, techniques and results from dielectric-constant gas thermometry (DCGT) are reviewed. Primary DCGT with helium has been used for measuring T-T 90 below the triple point of water (TPW), where T is the thermodynamic temperature and T 90 is the temperature on the international temperature scale of 1990 (ITS-90), and, in an inverse regime with T as input quantity, for determining the Boltzmann constant at the TPW. Furthermore, DCGT allows the determination of several important material properties including the polarizability of neon and argon as well as the virial coefficients of helium, neon, and argon. With interpolating DCGT (IDCGT), the ITS-90 has been approximated in the temperature range from 4 K to 25 K. An overview and uncertainty budget for each of these applications of DCGT is provided, accompanied by corroborating evidence from the literature or, for IDCGT, a CIPM key comparison.

Within an international collaboration of the eight metrological institutes represented by the authors, the dependence of the triple-point temperature of equilibrium hydrogen on the deuterium content at low concentrations has been precisely determined so that the uncertainty in realizing the triple point as a temperature fixed point might be reduced by nearly one order of magnitude. To investigate the thermodynamic properties of the hydrogen-deuterium mixtures and to elucidate the factors that influence the melting temperature, 28 sealed fixed-point cells have been filled and measured, and some of these have been compared with an open-cell system. Hydrogen gas with a deuterium content ranging from 27.2 µmol D/mol H to 154.9 µmol D/mol H was studied using cells containing five different types of spin-conversion catalyst, with different catalyst-to-liquid volume ratios (a few per cent to more than 100%) and of different designs. The latter consideration is especially influential in determining the thermal behaviour of the cells and, thus, the temperature-measurement errors. The cells were measured at the eight participating institutes in accordance with a detailed protocol that facilitates a direct comparison of the results. Through analysis of the measurements, significant inter-institute deviations due to different measurement facilities and methods have been ruled out with respect to the determination of both the melting temperatures and the thermal parameters of the cells. The uncertainty estimates for the determination of the deuterium content have been verified by including isotopic analysis results from four different sources. The slope of the dependence of the triple-point temperature of equilibrium hydrogen isotopic mixtures on the deuterium content has been deduced from the melting temperatures of those sample portions not in direct contact with the catalysts. Evaluation of the data using different mathematical methods has yielded an average value of 5.4 2 µK per µmol D/mol H, with an upper bound of the standard uncertainty of 0.3 1 µK per µmol D/mol H. This is close to the literature value of 5.6 µK per µmol D/mol H that was obtained at higher deuterium concentrations.

The sum of individual estimates (SIE) and the overall maximum estimate (OME) are two methods recommended to estimate the influence of impurities on the temperatures of the liquid-solid phase transformations of high-purity substances. The methods are discussed starting with the basic crystallographic facts, and their application is demonstrated in detail by applying them to the freezing point of tin as a first example. The SIE method leads to a temperature correction with a corresponding uncertainty while the OME method yields only an uncertainty that is, perhaps not unexpectedly, larger than that of the SIE approach. The necessary sensitivity coefficients (derivatives of the liquidus lines) are tabulated, together with the equilibrium distribution coefficients. Other than the necessity of obtaining a complete elemental analysis of the fixed-point material using glow discharge mass spectrometry (or other suitable techniques), there remain no technical barriers to adopting the preferred SIE method. While the use of the method, and particularly the application of a temperature correction to account for the impurity influence, requires a paradigm shift within the thermometry community, improved interoperability and harmonization of approach are highly desirable goals. The SIE approach maximizes the application of scientific knowledge and represents the best chance of achieving these common goals.

Following the finalization of the work performed to establish the triplepoint temperature versus isotopic composition relationship for protium (Metrologia 42, 171 (2005)) adopted into the ITS-90 definition by the International Committee for Weights and Measures (CIPM) in 2005, and a preliminary exploration of the variability in the triple-point temperature of neon gas samples arising from differences in isotopic

In this paper, we specify the purpose of an international temperature scale and present some definitions that are basic to the International Temperature Scale of 1990. These definitions include those for non-uniqueness and for the temperature fixed points underlying the scale. Three types of non-uniqueness are identified.

In 2018, it is expected that there will be a major revision of the International System of Units (SI) which will result in all of the seven base units being defined by fixing the values of certain atomic or fundamental constants. As part of this revision, the kelvin, unit of thermodynamic temperature, will be redefined by assigning a value to the Boltzmann constant k. This explicit-constant definition will define the kelvin in terms of the SI derived unit of energy, the joule. It is sufficiently wide to encompass any form of thermometry. The planned redefinition has motivated the creation of an extended mise en pratique ('practical realization') of the definition of the kelvin (MeP-K), which describes how the new definition can be put into practice. The MeP-K incorporates both of the defined International Temperature Scales (ITS-90 and PLTS-2000) in current use and approved primary-thermometry methods for determining thermodynamic temperature values. The MeP-K is a guide that provides or makes reference to the information needed to perform measurements of temperature in accord with the SI at the highest level. In this article, the background and the content of the extended second version of the MeP-K are presented.