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.

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.

We have determined the acoustic and microwave frequencies of a misaligned spherical resonator maintained near the temperature of the triple point of water and filled with helium with carefully characterized molar mass M = (4.002 6032 ± 0.000 0015) g mol

Since the beginning of measurement of pressure in the 17th century, the unit of pressure has been defined by the relationship of force per unit area. The present state of optical technology now offers the possibility of using a thermodynamic definition-specifically the ideal gas law-for the realization of the pressure unit, in the vacuum regime and slightly above, with an accuracy comparable to or better than the traditional methods of force per area. The changes planned for the SI in 2018 support the application of this thermodynamic definition that is based on the ideal gas law with the necessary corrections for real-gas effects. The paper reviews the theoretical and experimental foundations of those optical methods that are considered to be most promising to realize the unit of pressure at the highest level of metrology.

Within an international project directed to the new definition of the base unit kelvin, the Boltzmann constant k has been determined by dielectric-constant gas thermometry at PTB. In the pressure range from about 1 MPa to 7 MPa, 11 helium isotherms have been measured at the triple point of water (TPW) by applying a new special experimental setup consisting of a large-volume thermostat, a vacuum-isolated measuring system, stainless-steel 10 pF cylindrical capacitors, an autotransformer ratio capacitance bridge, a high-purity gas-handling system including a mass spectrometer, and traceably calibrated special pressure balances with piston–cylinder assemblies having effective areas of 2 cm2. The value of k has been deduced from the linear, ideal-gas term of an appropriate virial expansion fitted to the combined isotherms. A detailed uncertainty budget has been established by performing Monte Carlo simulations. The main uncertainty components result from the measurement of pressure and capacitance as well as the influence of the effective compressibility of the measuring capacitor and impurities contained in the helium gas. The combination of the results obtained at the TPW (kTPW = 1.380 654 × 10−23 J K−1, relative standard uncertainty 9.2 parts per million) with data measured earlier at low temperatures (21 K to 27 K, kLT = 1.380 657 × 10−23 J K−1, 15.9 parts per million) has yielded a value of k = 1.380 655 × 10−23 J K−1 with uncertainty of 7.9 parts per million.