The unit of temperature T, the kelvin, is presently defined by the temperature of the triple point of water (TPW), i.e., the kelvin is linked to a material property. Instead, it would be advantageous from a scientific point of view and also for practical temperature measurements to proceed in the same way as with other units: to relate the unit to a fundamental constant and fix its value. 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 fixing the value, k must first be determined with appropriate uncertainty to confirm present value.
The most promising methods to determine k with the required uncertainty for the redefinition of the kelvin are Acoustic Gas Thermometry (AGT) measuring the speed of sound, Dielectric Constant Gas Thermometry (DCGT) using audio-frequency capacitance bridges and Doppler Broadening Technique (DBT). Thus, an improved value of the Boltzmann constant proposed for defining the kelvin would ideally have been determined by the three fundamentally different methods AGT, DBT, and DCGT. The Contact Thermometry Group of the Thermodynamic Division, works for the temperature controls and metrological traceability of three different experiments, making INRIM the only NMI in Europe to be involved in all three methods, under the iMERA Joint Research Project T1.J1.4.
The principle of Acoustic Gas Thermometry is based on the theoretically well founded connection between the zero-pressure limit of the speed of sound u0 and the thermodynamic temperature T [1] according to the relation u20(T)=γ0 RT/M=A0(T), where γ0 is the ratio of the ideal gas heat capacities, R is the molar gas constant and M the molar mass. R is linked to the Boltzmann constant by the relation k =R/NA.
Three acoustic resonators operate in the physical acoustic laboratory of INRIM for the AGT experiment. Two thermostatic baths have been assembled and optimized in order to obtain temperature uniformity and stability better than 1mK during acoustic and microwave measurements. The traceability to the national temperature standards, namely to a batch of four triple point of water cells, is guaranteed by a series of special custom standard platinum resistance thermometers (SPRTs) and dedicated probes manufactured on purpose at INRIM (fig. 1).
Fig. 1 Insertion of a custom SPRT in the North pole of the spherical resonator of the AGT INRIM experiment.
Helium is the measuring gas chosen for the INRIM AGT experiment, due to recent significant progress in performing ab-initio calculations of its properties. A dedicated purification system, based on a special pipe line, a cold trap and a getter, has also been studied and assembled, also allowing the in-situ application of mass spectrometry.
The Doppler Broadening Technique for measuring the Boltzmann constant is a quite recent method consisting in recording by laser spectroscopy the Doppler profile of a well-isolated atomic or molecular absorption line of a gas in a cell at a well-controlled temperature. This profile will reflect the Maxwell-Boltzmann distribution of the longitudinal velocity distribution along the laser beam axis. A straightforward line analysis which can take into account residual pressure broadening, hyperfine structure, etc. leads to the determination of Doppler broadening, which is proportional to k [2]. The method can be applied easily to any gas. Within the framework a scientific cooperation between INRIM, the Seconda Università di Napoli (Caserta) and the Politecnico di Milano, a novel technique of primary gas thermometry, based on high-resolution laser spectrometry, is being improved. The thermodynamic temperature will be measured through the highly accurate measurement of the Doppler linewidth of a strong vibro-rotational transition of water vapour around 1.39 µm using an isothermal water vapour cell referred to the temperature of the triple point of water.
The cell containing the vapour has to be controlled in temperatures at the level of the millikelvin. For this purpose, the contact thermometry group of INRIM studied, assembled and characterised a dedicated temperature controlling system for the cell (fig. 2).
Fig. 2 The cooling chamber, part of the whole temperature controlling system, containing the cell for the DBT experiment.
By mixing techniques of low and intermediate temperature control, this system is based on a series of vacuum chambers, heating and cooling systems, reflectors, feeds through for the measuring gas, a couple of capsule SPRTs, and several structures to keep the whole system, the cell and the different optical windows aligned. Those structures are made in special materials, to avoid heat exchanges to the outside world, but being strong enough to keep the cell in position inside the first vacuum container and the container itself in a second chamber, made to avoid water condensation on the optical windows. The achieved temperature stability is within ± 0.05 mK and uniformity is at the level of 0.1 mK (fig. 3).
Fig. 3 The DBT cell temperature stability measured by means of a capsule SPRT, during a control run.
The method is based on high-precision measurement of the capacitance change of a capacitor by a measuring gas and of the gas pressure traceable to national primary standards. It is called dielectric-constant gas thermometry and has the main advantage that the gas density is measured in-situ, which avoids the troublesome density determination of conventional gas thermometry. This includes the investigation of the thermal behaviour of the measuring system, which contains materials having small thermal conductivities.
New challenges concerning the measurement and control of temperature are caused by the large dimension and heat capacity of the measuring system. A new large-volume high-precision thermostat with uncertainties of the order of 0.1 mK has been studied, developed and tested at INRIM for the DCGT experiment that is going to be started at PTB in Berlin [3].
For all the above three different methods, the Contact Thermometry Group studied, designed, manufactured, assembled and developed all the structures, components and devices involved (fig. 4).
Fig. 4 Two main components of the large volume thermostat made at INRIM for the PTB DCGT experiment during the assembling at INRIM. .
Specific electronics were made, together with dedicated software for the complete automatic control of the different apparatus. All the systems have been characterised and their control capabilities carefully optimized. The calibration of all the special SPRTs involved is also constantly carried on by the group that maintains the national temperature standards.
[1] G. Benedetto, R.M. Gavioso, R. Spagnolo, P. Marcarino, A. Merlone: "Acoustic measurements of the thermodynamic temperature between the triple point of mercury and 380 K", Metrologia, Vol. 41, no. 1, pp. 74-98, 2004.
[2] G. Casa, A. Castrillo, G. Galzerano, R. Wehr, A. Merlone, D. Di Serafino, P. Laporta, L. Gianfrani: "Primary Gas Thermometry by Means of Laser-Absorption Spectroscopy: Determination of the Boltzmann Constant", Physical Review Letters, Vol. 100, art. 200801, 2008.
[3] A. Merlone, F. Moro, T. Zandt, C. Gaiser, B. Fellmuth: "Construction and start up of a large-volume thermostat for dielectric-constant gas thermometry", International Journal of Thermophysics, in press.