The International Temperature Scale of 1990
The International Temperature Scale of 1990 was adopted by the International Committee of Weights and Measures at its meeting in 1989, in accordance with the request embodied in Resolution 7 of the 18th General Conference of Weights and Measures of 1987. This scale supersedes the International Practical Temperature Scale of 1968 (amended edition of 1975) and the 1976 Provisional 0.5 K to 30 K Temperature Scale.

1. Units of Temperature
The unit of the fundamental physical quantity known as thermodynamic temperature, symbol T, is the kelvin, symbol K, defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water1.

Because of the way earlier temperature scales were defined, it remains common practice to express a temperature in terms of its difference from 273.15 K, the ice point. A thermodynamic temperature, T, expressed in this way is known as a Celsius temperature, symbol t, defined by:

t / °C = T/K - 273.15 . (1)

The unit of Celsius temperature is the degree Celsius, symbol °C, which is by definition equal in magnitude to the kelvin. A difference of temperature may be expressed in kelvins or degrees Celsius.

The International Temperature Scale of 1990 (ITS-90) defines both International Kelvin Temperatures, symbol T90, and International Celsius Temperatures, symbol t90. The relation between T90 and t90, is the same as that between T and t, i.e.:

t90 / °C = T90/K - 273.15 . (2)

The unit of the physical quantity T90 is the kelvin, symbol K, and the unit of the physical quantity t90, is the degree Celsius, symbol °C, as is the case for the thermodynamic temperature T and the Celsius temperature t.
ITS 90 Fixed points include:
Boiling point of Nitrogen -195.798°C
Mercury triple point -38.8344°C
Triple point of water 0.01°C
Melting point of Gallium 29.7646°C
Freezing point of Indium 156.5985°C
Freezing point of Tin 231.928°C
Freezing point of Lead 327.462°C
Freezing point of Zinc 419.527°C
Freezing point of Antimony 630.63°C
Freezing point of Aluminium 660.323°C
Freezing point of Silver 961.78°C

Resistance temperature detectors (RTDs) operate on the inherent propensity of metals to exhibit a change in electrical resistance as a result of a change in temperature. We are all aware that metals are conductive materials. It is actually the inverse of a metal's conductivity, or its resistivity, that brought about the development of RTDs. Each metal has a specific and unique resistivity that can be determined experimentally. This resistance, R, is directly proportional to a metal wire's length, L, and inversely proportional to the cross-sectional area, A:

R =ρL/A     (1)

where:

ρ = the constant of proportionality, or the resistivity of the material

Principle of Operation

RTDs are manufactured from metals whose resistance increases with temperature. Within a limited temperature range, this resistivity increases linearly with temperature:

ρ_t = ρ₀ [1 + a (t – t ₀ )]     (2)

where:

ρ_t = resistivity at temperature, t

ρ₀ = resistivity at a standard temperature, t ₀

a = temperature coefficient of resistance (°C ^–1 )

Combining Equations 1 and 2, setting t ₀ to 0°C, and rearranging to the standard linear y = mx + b form, it is clear that resistance vs. temperature is linear with a slope equal to a:

R/R₀ = αt + 1     (3)

In theory, any metal could be used to measure temperature. The metal selected should have a high melting point and an ability to withstand the effects of corrosion. Platinum has therefore become the metal of choice for RTDs. Its desirable characteristics include chemical stability, availability in a pure form, and electrical properties that are highly reproducible.

Platinum RTDs are made of either IEC/DIN-grade platinum or reference-grade platinum. The difference lies in the purity of the platinum. The IEC/DIN standard is pure platinum that is intentionally contaminated with other platinum group metals. The reference-grade platinum is made from 99.99% pure platinum. Both probes will read 100 Ω at 0°C, but at 100°C the DIN grade platinum RTD will read 138.5 Ω and the reference grade will read 139.02 Ω. International committees have been established to develop standard curves for RTDs. The committees have defined a mean temperature coefficient to be between 0°C and 100°C. Solving Equation (3) for a:

α = (R ₁₀₀ – R ₀ ) / R ₀ t     (4)

IEC/DIN grade platinum: a = 0.00385 Ω/Ω/°C

reference grade platinum: a = 0.003926 Ω/Ω/°C (max.)

The relationship between resistance and temperature can be approximated by the Callendar-Van Dusen equation:

where:

T = temperature (°C)

R = resistance at temperature T

R₀ = resistance at the ice point

α = constant (gives the linear approximation to the R vs. T curve)

δ= constant

β= constant (b = 0 when T is >0°C)

The actual values for the coefficients,α, δ, and β are determined by testing the RTD at four temperatures and solving the equations. The Callendar-Van Dusen equation can be simplified to:

R_t = R₀ [1 + At + Bt² + C(t – 100°C)]t ³     (6)

In the positive quadrant, temperatures over 0°C, the behavior of a PRT may be described by a quadratic equation in the form:

R_t = R₀ (1 + At + Bt² )     (7)

As written, the above implies that valid equations may be generated from empirical data taken using 0°C plus two arbitrarily selected positive temperatures. For a single PRT, the constants A and B could be slightly different, depending on the temperatures selected.

Callendar resolved the issue by defining two additional fixed points:

• The boiling point of water, 100°C
• The triple point of zinc, 419.58°

The coefficients A, B, and C depend on the wire material (i.e., platinum) and its purity. International standard IEC 751 describes the specifications that permit universal interchangeability among platinum RTDs.

The coefficients for platinum RTDs according to the IEC 751-2 (ITS90) Standard are:

A = 3.9083 × 10^–3 C^–1

B = –5.775 × 10^–7 C^–2

C = –4.183 × 10^–12 C^–3

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