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.

This paper presents results of the dimensional calibration of piston-cylinder assemblies to be used for the joint NMI project “Re-determination of the Boltzmann constant”. Several measurements optimization strategies are described. For the first time 3D uncertainties in the range of 8 nm (piston) and 16 nm (cylinder) could be achieved.

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To support new determinations of the Boltzmann constant, which have been requested by the International Committee for Weights and Measures (CIPM) and which are necessary for preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole, an iMERAPlus joint research project is coordinating the European activities in this field in Spain (CEM), Denmark (DFM), France (LNE-