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 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.

Fellmuth et al (2011 Metrologia 48 382-90) published the first value of the Boltzmann constant k determined by dielectric-constant gas thermometry at the triple point of water (k = 1.380 654 × 10 −23 J K −1 , standard uncertainty 9.2 parts per million (9.2 ppm)). Since that time, essential progress of this primary thermometry method has been achieved concerning the design and the assembly of the measuring capacitor, the determination of its effective compressibility, the sensitivity of the capacitance bridge, the influence of stray capacitances, the purity of the measuring gas, the pressure measurement, and the scattering and the evaluation of the data. The resulting new k value amounts to k = 1.380 650 9 × 10 −23 J K −1 with a standard uncertainty of 4.3 ppm. This value is about 1.5 ppm larger than the CODATA 2010 one, which has a relative uncertainty of 0.9 ppm.

Gaiser et al published in 2013 (Metrologia 50 L7-11) a second, improved value of the Boltzmann constant k determined by dielectric-constant gas thermometry at the triple point of water (k = 1.380 6509 × 10 −23 J K −1 , relative standard uncertainty 4.3 parts per million (4.3 ppm)). Subsequently, the uncertainty was able to be reduced to 4.0 ppm by reanalysing the pressure measurement. Since 2013, further progress regarding this primarythermometry method has been achieved in terms of the design and the assembly of the measuring capacitors, the determination of their effective compressibility, the sensitivity of the capacitance bridge, and the scattering and the evaluation of the data. Based on a huge amount of data, two new k values have been obtained by applying two different capacitors. The combination of these two values with the 2013 result, fully taking into account the correlations, has yielded a final result of k = 1.380 6482 × 10 −23 J K −1 with a relative standard uncertainty of 1.9 ppm. This value is about 0.2 ppm smaller than the CODATA 2014 one, which has a relative standard uncertainty of 0.57 ppm.

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