*The International Temperature Scale of 1990 (ITS-90) is a word wide recognized temperature scale introduced by the International Committee for Weights and Measures (CIPM). It serves as a global standard for precise temperature measurements and is based on the concept of thermodynamic temperature. The ITS-90 is a revised version of the previous International Practical Temperature Scale of 1968 (IPTS-68).*

*The ITS-90 uses various precisely defined fixed points and interpolation methods for temperature determination. Fixed points are the temperatures of phase transitions of certain substances, such as freezing or triple points.*

*The ITS-90 uses the Kelvin scale (K) as the unit, replacing the Celsius scale used in the IPTS-68. However, both units are still used, with 1 Kelvin degree and 1 Celsius degree being the same size, and the Celsius zero point being at 273.15 K.*

*To convert from the Kelvin scale (K) to the Celsius scale (°C), simply subtract 273.15 from the temperature in Kelvin: T(°C) = T(K) – 273.15.*

## Fixed Points of the ITS-90 Temperature Scale

The International Temperature Scale of 1990 (ITS-90) uses various “fixed points” as defined temperatures. A temperature fixed point is a temperature characterized by a specific, reproducible physical event, such as a phase change of a particular substance.

The International Temperature Scale of 1990 (ITS-90) uses triple points, melting points, and freezing points:

**Triple Point:**The triple point of a substance is the unique temperature and pressure at which the three phases of a substance – solid, liquid, and gas – can exist in equilibrium. At this specific combination of temperature and pressure, a substance can exist simultaneously as a solid, liquid, and gas. A well-known example of a triple point is that of water, which is reached at a temperature of 0.01 °C (273.16 K) and a specific pressure of 611.657 Pascal.**Melting Point:**The melting point is the temperature at which a solid substance begins to melt and transitions into a liquid state. This temperature is specific to each substance and is measured under standard pressure. For example, the ITS-90 uses the melting point of gallium, which is at 29.7646 °C.**Freezing Point:**The freezing point is the temperature at which a liquid begins to freeze and transitions into a solid state. For example, the freezing point of aluminum is at 660.323 °C.

Here are the key temperature fixed points used by the ITS-90:

## The calibration ranges of the ITS-90

The International Temperature Scale of 1990 (ITS-90) not only defines the fixed points with their corresponding temperatures at which thermometers are calibrated, but also the corresponding calibration ranges.

By definition, there are two ranges: one for the negative temperature range, which starts at approximately 13 K and extends to the water triple point at 0.01 °C, and one for the positive temperature range. The latter begins at the water triple point at 0.01 °C (or in the range from the mercury triple point at -38.8344 °C to the gallium melting point at 29.7646 °C) and extends to the silver freezing point at 961.78 °C.

Depending on the temperature range, the parameters for the ITS-90 deviation function are defined. In the range from the argon triple point to the freezing of silver, the parameters a, b, c, and d are used. This temperature range is also the practical range used in calibration laboratories to calibrate thermometers. In extreme ranges at very low temperatures, such as the oxygen triple point, there is an additional parameter ci, which, however, is only used at these extreme temperatures.

The graph provides a visual representation of the corresponding defining ITS-90 temperatures at the fixed points and the associated temperatures. For example, the temperature of the aluminum freezing point is 660.323 °C.

It is important to know that with thermometers calibrated at the ITS-90 temperature fixed points, one cannot extrapolate, but only interpolate.

This means, if a temperature of about 500 °C is to be measured, then the highest calibration point must be the aluminum freezing point at 660.323 °C and not the zinc freezing point at 419.527 °C. Because at 419 °C, one would have to extrapolate to 500 °C. Therefore, the range is always selected so that the temperature to be measured can be calculated by interpolation.

The graph shows the corresponding calibration ranges schematically. In our example, this would mean that if a temperature of 500 °C is to be measured, we would use the calibration range up to the aluminum freezing point at 660.323 °C and calibrate accordingly at aluminum, zinc, tin, and the water triple point. This would be the second calibration range from the right in the representation.

The white dots represent the necessary fixed points for calibration. Therefore, the temperature fixed points at the freezing of indium and at the gallium melting point would not be necessary. They do not contribute to the calibration and the subsequent calculation of the characteristic curve – i.e., the deviation function and reference function of the International Temperature Scale of 1990 (ITS-90).

## Applying the ITS-90 in Everyday Life

The International Temperature Scale of 1990 (ITS-90) is applied almost daily in the routine of a temperature calibration laboratory. However, users are often not aware of this fact as the mathematics of the ITS-90 are embedded in temperature measuring devices and bridges, running in the background.

It is important to understand that temperature cannot be directly measured but is calculated, for example, based on the resistance of a material. The ITS-90 contains the mathematical foundations for calculating temperatures from the resistance measurements of Standard Platinum Resistance Thermometers (SPRT) of the ITS-90.

The question often comes as to how the ITS-90 can be meaningfully used as a characteristic curve in the everyday work of a laboratory.

Therefore, in this blog post, I will demonstrate with an example how the corresponding temperature can be calculated using the ITS-90 from measured resistances. I like to explain this example in detail in my seminars.

The ITS-90 uses so-called W-values, which represent the ratio of the measured resistance to the most recent known value of the water triple point. Using this calculated W-value and the reference and deviation functions derived from the ITS-90, temperatures can be determined. The calculation of the W-value is done according to the following formula:

Where R(T90) represents the measured resistance at temperature T90, and R(273.16 K) represents the resistance at the water triple point (specifically at 273.16 Kelvin).

In the next calculation step, the reference functions (10a and 10b) as well as the deviation function (14) defined according to the ITS-90 (International Temperature Scale of 1990) are needed. We only use the functions relevant to our temperature range.

### Reference functions:

### The reference function is used with the following parameters:

### The deviation function is as follows:

The equations and tables are taken from the publication of the ITS-90 by Walter Blanke (see references).

## ITS-90 Calculation Example

Let’s assume you measure a resistance value of 31.1428 ohms. From the calibration certificate, you find the following information:

*R(0,01°C) = 25,1648 ohms*

*a = -1,6093e-03*

*b = 1,9911e-03*

First, you calculate the W-value:

*W(t90) = R(t90) / R(0,01°C)*

*W(t90) = 31,1428 ohms / 25,1648 ohms*

*W(t90) = 1,23755404*

Using the deviation function (14), you can then calculate the Wr(t90) value:

*Wr(t90) = 1,237824*

With the determined value, you can now calculate the temperature t90 using the reference function (10b):

*t90 = 60,1873°C*

In this way, the corresponding temperature can be calculated from the measured resistance value.

## Sources:

- Walter Blanke: Die Internationale Temperaturskala von 1990: ITS-90
- Thomas Klasmeier: Handbook “Temperature”