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Redefinition of the temperature unit?

The present definition of the kelvin links the unit of temperature with a material property. It would be more consistent to determine the value of the Boltzmann constant, k, instead. For this purpose, k must first be determined with distinctly lower uncertainty than presently possible. PTB seeks to achieve this objective through improved dielectric constant gas thermometry.

Ludwig Boltzmann, 1844-1906

The temperature of the triple point of water is presently determined to be 273,16 K by definition. Thus, the unit kelvin is linked to a material property which is rather arbitrary. Instead, it would be advantageous to proceed in the same way as with other units: to relate the unit to a fundamental constant and fix the value of this constant. By this no temperature value (and no measurement method) would be favoured. For the kelvin, the corresponding constant is the Boltzmann constant, k, because temperature always appears as “thermal energy” kT in fundamental laws of physics. For example, according to present knowledge one might think of redefining the kelvin as the change of temperature that results in a change of the internal energy of 20 709 755 J for an ideal gas of 1030 point particles without internal degrees of freedom.

To ensure that such a redefinition would maintain the relative uncertainty of about 3 · 10-7 currently achieved for the realization of the temperature unit, the Boltzmann constant must be known with similar accuracy. At present, however, its relative uncertainty is still about 2 · 10-6. First of all, therefore, this uncertainty must be reduced considerably.

In principle the Boltzmann constant can be determined with any primary thermometer by measuring kT at a known temperature (ideally at the triple point of water). The present value of k has been determined at NIST by acoustic gas thermometry measuring the velocity of sound in a gas. A study recently completed by PTB shows that another variant of gas thermometry, dielectric constant gas thermometry with helium, offers good chances of further reducing the uncertainty as required – in particular, because the polarizability of the helium atom can now be calculated very precisely by quantum-mechanics. This measurement method determines the temperature- and pressure-dependent dielectric constant of helium from the change in capacitance occurring when the gas is pumped out of a helium-filled capacitor. For many years now PTB has successfully applied dielectric constant gas thermometry in the low-temperature range. PTB has therefore set itself the goal of further improving dielectric constant gas thermometry. The relative standard uncertainty which can be achieved today in determining the Boltzmann constant will be reduced from 15 · 10-6 to 2 · 10-6 in a first step and by another order of magnitude in a second step.

This project, which will certainly take a decade, has now been tackled, with first investigations carried out on a gas thermometer system recently installed. Spectral radiation measurements on the basis of Planck’s radiation formula will support the project and help confirm the results.

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