Fundamental Definition
The International Temperature Scale of 1990 (ITS-90) is defined such that it approximates thermodynamic temperature as closely as possible throughout its range. The scale is based on assigned values of temperature for a number of reproducible equilibrium states (defining fixed points) and on prescribed algorithms and reference functions for interpolating between these fixed points.
Temperature Unit
The unit kelvin (K) is defined by fixing the numerical value of the Boltzmann constant k to 1.380 649 × 10⁻²³ J·K⁻¹; the triple point of water (273.16 K) is used as a practical realisation but no longer defines the kelvin.
Note: Before 2019 the kelvin was defined via the triple point of water; however, the definition was revised. The triple point remains important for realising the kelvin in practice but no longer defines its value.
Temperature differences may also be expressed in degrees Celsius, symbol °C. The numerical value of Celsius temperature t is related to thermodynamic temperature T by the equation:
where T₀ = 273.15 K
Temperature Ranges and Interpolation
ITS-90 extends from 0.65 K to the highest temperature practically measurable in terms of the Planck radiation law. The scale is divided into four primary ranges with specific interpolation instruments and methods. These ranges overlap to ensure continuity and allow for cross-validation of measurements at the boundaries:
Temperature Ranges
| Range | Temperature Limits | Interpolation Method |
|---|---|---|
| 1 | 0.65 K to 5.0 K | Helium vapor pressure thermometry |
| 2 | 3.0 K to 24.5561 K | Helium gas thermometry |
| 3 | 13.8033 K to 1,234.93 K | Platinum resistance thermometry |
| 4 | Above 1,234.93 K | Radiation thermometry |
Range Overlaps and Sub-ranges
The four primary ranges are designed with overlapping temperature regions to ensure measurement continuity and enable cross-validation between different thermometry methods:
- Low temperature overlap (3.0–5.0 K): Both helium vapor pressure and gas thermometry can be used
- Cryogenic overlap (13.8033–24.5561 K): Both helium gas thermometry and platinum resistance thermometry are applicable
- High temperature transition (1234.93 K): Platinum resistance thermometry meets radiation thermometry at the silver freezing point
Platinum Resistance Thermometry Sub-ranges
Within the platinum resistance thermometry range (13.8033 K to 1234.93 K), different interpolation equations are used for specific sub-ranges to optimize accuracy:
- 13.8033 K to 273.16 K: Uses a 12th-order polynomial in ln(T₉₀/273.16 K)
- 0°C to 660.323°C: Uses a quadratic equation in (T₉₀ - 273.16 K)
- 660.323°C to 961.78°C: Uses a modified quadratic with an additional term
Each sub-range requires calibration at specific fixed points, with the coefficients determined by the resistance ratios measured at these defining temperatures.
Helium Vapor Pressure Equations (0.65 K to 5.0 K)
Between 0.65 K and 5.0 K, ITS-90 is defined in terms of the vapor pressure relations for ³He and ⁴He. The defining equations are:
³He vapor pressure equation (0.65 K to 3.2 K):
⁴He vapor pressure equation (1.25 K to 2.1768 K and 2.1768 K to 5.0 K):
The coefficients A₀, Aᵢ, B, and C are tabulated in the official ITS-90 text and differ for each helium isotope and temperature range.
Helium Gas Thermometry (3.0 K to 24.5561 K)
In this range, ITS-90 is defined by means of a ³He or ⁴He constant volume gas thermometer calibrated at three fixed points. The defining equation is:
Where p is the pressure of the gas in the thermometer, and the coefficients a, b, and c are determined by calibration at the defining fixed points.
Platinum Resistance Thermometry (13.8033 K to 1,234.93 K)
This is the most commonly used range of ITS-90, employing standard platinum resistance thermometers (SPRTs). The defining equations vary by subrange:
13.8033 K to 273.16 K:
0°C to 660.323°C:
660.323°C to 961.78°C:
Where W(T₉₀) is the resistance ratio R(T₉₀)/R(273.16 K), and the coefficients are determined by calibration at the defining fixed points.
Radiation Thermometry (Above 1,234.93 K)
Above the freezing point of silver (1,234.93 K), ITS-90 is defined in terms of the Planck radiation law:
Where:
- Lλ(T) is the spectral radiance at wavelength λ
- Tₓ is the temperature of a reference fixed point
- c₂ = 0.014387774 m·K (second radiation constant)
- λ is the wavelength in vacuum
Implementation Note
These definitions provide the mathematical framework for ITS-90. Practical implementation requires careful attention to the specifications for reference instruments, calibration procedures, and uncertainty budgets. Consult the complete official ITS-90 text and relevant metrological guidelines for detailed implementation guidance.