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**Temperature and thermal quantities

General speaking, the national references are the materialization of the units or sometimes the measuring bench that allows to access the quantity consider. Regarding the thermal quantities, the references are shown under four sections :

Scheme of traceability between the different quantities


The unit of thermodynamic temperature (the kelvin) is defined on the basis of the value assigned to the triple point of water, 273,16 K (or 0,01 °C).

The temperature standards should be, in principle, the materialization of the kelvin or of certain values of the thermodynamic temperature or the apparatuses for absolute measurement of the thermodynamic temperature.

IThere are direct measuring instruments of the thermodynamic temperature and it is possible to consider the temperature standards as these instruments. This is also done for the temperatures close to absolute zero. However, these instruments are complex to implement and above all, the experimental results obtained with these instruments show great dispersion.

That’s why, since 1927, the metrologists have tried to overcome this problem by developing one temperature scale. All of the different scales proposed over time are based on a certain number of states of thermodynamic equilibrium which value is set using these absolute measuring instruments. These states of equilibrium (phase transitions of pure substances) are called fixed points and constitute the basis of one temperature scale. The scale is fully defined by associating to these fixed points one specific measuring instrument and one interpolation formula.

Two scales are currently used: the ITS-90 (International Temperature Scale of 1990) and the PLTS-2000 (Provisional Low Temperature Scale of 2000):

Second-sound thermometer and helium-3 melting-pressure thermometer assembled on the LNE-INM dilution refrigerator.
Second-sound thermometer and helium-3 melting-pressure thermometer assembled on the LNE-INM dilution refrigerator.

Fixed point temperature (in K) Substance Type of point
from 3 to 5 Helium Vapour pressure
13,803 3 Hydrogen Triple
about 17 Hydrogen (or Helium) Vapour pressure (or gas thermometer)
about 20,3 Hydrogen (or Helium) Vapour pressure (or gas thermometer)
24,556 1 Neon Triple
54,358 4 Oxygen Triple
83,805 8 Argon Triple
234,315 6 Mercury Triple
273,16 Water Triple
302,914 6 Gallium Melting
429,748 5 Indium Freezing
505,078 Tin Freezing
692,677 Zinc Freezing
933,473 Aluminium Freezing
1 234,93 Silver Freezing
1 337,33 Gold Freezing
1 357,77 Copper Freezing

More particularly, for the most common temperatures, the ITS-90 defines:

Standard platinum resistance thermometer
Standard platinum resistance thermometer

A book "Supplementary Information for the International Temperature Scale of 1990" published by the BIPM) describes the techniques and means required for implementing the ITS-90 in a laboratory. The French version is the monography n° 17 published by the BNM "Compléments d’information à l’Echelle internationale de température de 1990". It also includes the full text of the ITS-90.

The temperature standards (or references) are therefore the practical realizations of these fixed points associated with the instruments specified in the ITS-90. The specified means necessary for the generation of the phase transitions of the substances have been implemented.

A thermometer is placed in thermal equilibrium with the pure substance. By observing the evolution of the pure substance temperature over time, the phase change is located and the temperature corresponding to this point is assigned to the thermometer to be calibrated.

Owing to the range of the ITS-90 (from cryogenic temperatures to the highest temperatures), the materialization of the fixed points requires very different techniques. The wide-ranging research works that have been carried out over these last years have led to the development of original and high performance methods and instrumentations.

The French national laboratories (LNE-INM and LNE) hold all the materializations of the fixed points of the ITS-90 (most of which were devised by the LNE-INM), and the means for the development of these fixed points as well as the measuring and calibrating instruments matching these references.

Thermometric cells at the LNE-INM
Thermometric cells at the LNE-INM

Regarding the field of contact thermometry, for each fixed point, the references comprise a batch of thermometric cells that are regularly compared between themselves and maintained at the best metrology level. The standard platinum resistance thermometers are regularly calibrated against these references.

Concerning the area of measurement by radiation thermometry, the LNE-INM has devised and realized three blackbodies associated to the three fixed points of the ITS-90 (silver, gold and copper) together with a radiance comparator. The latter allows measuring the temperature of the blackbodies (lamps or cavities) in relation to these fixed-points blackbodies.

Fixed-points blackbodies
Fixed-points blackbodies


Humidity equals the quantity of water contained in a quantity of dry gas. According to the field of application, different quantities are used in hygrometry. Three of them are particularly used in metrology: the mixture ratio, the dew point and relative humidity.

  • The mixing ratio (r = mv/ma) is the ratio of the mass of water vapour (mv) per mass of dry air (ma) with which water vapour is associated ;
  • The dew-point temperature (Td), or the frost-point temperature (Tf), is the temperature of humid air, at a given pressure and with a constant mixing ratio to which humid air is saturated in relation to water, or in relation to ice ;
  • Relative humidity of humid air in relation to water (Uw), or in relation to ice (Ui), to pressure p and the temperature T, is the relation between partial vapour pressure and saturation vapour pressure that would be in the air if air was saturated to water, or to ice, at the same pressure p and the same temperature T.

    If we consider that the parameter that allows more direct access to the definition of humidity is the mixing ratio, the primary references of humidity should then be established through the measurement of masses.

    Dozens of years ago, a few laboratories around the world (two or three) realized a gravimetric bench meant for the measurements of humidity. The French laboratories did not embarked on this adventure, notably because of the cost, the complex implementation and the restrictions in the operating temperature ranges (-30 °C to 30 °C). It was then decided to calibrate a reference hygrometer of the condensation hygrometer type on the NIST’s gravimetric bench.

    In France, this condensation hygrometer was, until 1994, the national reference for the humidity measurements. This standard allowed calibrating a calibrating bench (at CETIAT) and hence connect the French humidity calibration chain.

View of the CETIAT humid air generator during calibration of the condensation hygrometer
View of the CETIAT humid air generator
during calibration of the condensation hygrometer

Since 1994, thanks to the new means (high performance saturators) developed in France for the calibration of hygrometers, humid air temperature in the saturators was taken as a reference. From the metrology point of view, humidity is therefore related to temperature, and thus to the ITS-90. The standard instrument is a platinum resistance thermometer associated to a humid air generator.

The range of dew point measurement, at the highest metrology level, extends chiefly from -60 °C to +80 °C. Additionally, it is possible to cover the calibration needs for the very low dew points ranging from -100 °C to -60 °C.

Thermophysical properties of the materials

The conduction thermal exchanges are primarily characterised by three thermophysical properties of materials related between themselves:

  • Thermal conductivity characterises the material capacity to transmit heat ;
  • Thermal diffusivity characterises the heat propagation speed inside the material ;
  • Specific heat capacity characterises the material capacity to store heat.

For these three quantities, the LNE holds measurement benches at different metrological levels though. For the time being, only two benches have been sufficiently characterized (calculation of uncertainties) to be considered as reference benches :

  • Thermal conductivity of insulating materials is measured using a reference bench of the “guarded hot-plate” type. The range of measure extends from 0,015 W.m-1.K-1 to 1,5 W.m-1.K-1 for temperatures comprised between -10 °C and 60 °C. Two batches of materials (expanded polystyrene and glass wool) have been formed from which test tubes are sampled to transfer the references to the industry.
  • Thermal diffusivity is measured using a measurement bench that involves the laser flash method. This bench is characterized for the homogeneous good conductors materials (metals type) and for temperatures ranging from 20 °C to 800 °C.

Thermoradiative properties of materials

Emissivity is a property characterising the capacity of a material to exchange heat through radiation. Concerning the emissivity of materials, the LNE holds three reference measurement benches. Although the measurements of thermoradiative properties call for radiometry techniques, they are classified under the “thermal quantities” field since they are used to calculate the radiance temperature of the blackbodies applying Planck’s radiance law.

  • Spectral directional emissivity is measured indirectly via measurement of the spectral directional hemispherical reflectance. The bench allows to measure emissivity of all the solid materials at low temperature (between 20 °C and 150 °C) to the wavelengths ranging from 0,8 µm to 14 µm.
  • Spectral normal emissivity is measured on opaque and good thermal conductors materials, under steady-state temperature (between 150 °C and 800 °C), by comparison of the spectral radiance of the sample to the one of the blackbody for the wavelengths ranging from 2,5 µm to 13 µm.
  • Total hemispheric emissivity is measured for average and good thermal conductors solid and opaque materials, through calorimetric means under steady-state temperature comprised between -20 °C and 200 °C.

Measurement bench for HT° emissivity for good thermal conductors
Measurement bench for HT° emissivity
for good thermal conductors