High-precision measurement of the Boltzmann constant

Ludwig Boltzmann probably never dreamed that the constant named after him would attract so much attention one day. Within the scope of the redefinition of the base units of the International System of Units via the fixing of fundamental constants, however, research groups from all over the world have been engaged in determining the value of k with the smallest possible uncertainty in order to enable the redefinition of the unit "kelvin".

For the determination of the Boltzmann constant, numerous research groups are using acoustic gas thermometry, as this method has provided the most accurate values so far. PTB, in contrast, wants to rule out systematic error sources by means of an alternative and completely independent primary-thermometry method and thus to provide the new definition with a sound footing. This alternative method is dielectric-constant gas thermometry (DCGT). DGCT is based on determining the density of the measuring gas, helium, via the dielectric constant. In practice, the PTB researchers measure to what degree the gas changes the capacitance of a special, highly stable measuring capacitor. From experiments at the triple point of water at exactly 0.01 °C and at various gas pressures (measurement of isotherms), k can be determined by means of fundamental relations. In this way, it has been possible to reduce the relative uncertainty down to 4 ppm.

The measurements were extremely demanding with regard to capacitance, pressure, temperature and dimensional measurements. They could only be carried out successfully thanks to close cooperation between different PTB working groups and industry. Pressure, for example, had to be measured up to 7 MPa with a relative uncertainty of 1 ppm applying pressure balances; relative capacitance changes even had to be measured with 0.001 ppm uncertainty. Exhaustive comparisons between pressure balances of different effective cross-sectional areas, combined with dimensional data, have now led to pressure measurements with the worldwide lowest measurement uncertainty. The required temperature stability was provided by a large bath thermostat which was manufactured and optimized in cooperation with the Italian national metrology institute (INRIM).

Recently, a cooperation project between the Chinese (NIM) and the American metrology institute (NIST) allowed the relative uncertainty of the measurement of k to be reduced to a few parts per million thanks to yet another primarythermometry procedure, known as noise thermometry. Acoustic gas thermometry, dielectric-constant gas thermometry and noise thermometry – as complementary methods – thus constitute the basis for the determination of the Boltzmann constant with an aimed-for relative standard measurement uncertainty of 1 ppm.