The International Temperature Scale of 1990 (ITS-90)

H. Preston-Thomas
President of the Comité Consultatif de Thermométrie and Vice-President of the Comité International des Poids et Mesures Division of Physics, National Research Council of Canada, Ottawa, K1A OS1 Canada

Received: October 24, 1989

Introductory Note
The official French text of the ITS-90 is published by the BIPM as part of the Prochès-verbaux of the Comité International des Poids et Mesures (CIPM). However, the English version of the text reproduced here has been authorized by the Comité Consultatif de Thermométrie (CCT) and approved by the CIPM.

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 / șC = T / K - 273.15 (1)

The unit of Celsius temperature is the degree Celsius, symbol șC, 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 / șC = 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 șC, as is the case for the thermodynamic temperature T and the Celsius temperature t.

2. Principles of the International Temperature Scale of 1990 (ITS-90)

The ITS-90 extends upwards from 0.65 K to the highest temperature practicably measurable in terms of the Planck radiation law using monochromatic radiation. The ITS-90 comprises a number of ranges and sub-ranges throughout each of which temperatures T90 are defined. Several of these ranges or sub-ranges overlap, and where such overlapping occurs, differing definitions of T90 exist: these differing definitions have equal status. For measurements of the very highest precision there may be detectable numerical differences between measurements made at the same temperature but in accordance with differing definitions. Similarly, even using one definition, at a temperature between defining fixed points two acceptable interpolating instruments (e.g. resistance thermometers) may give detectably differing numerical values of T90. In virtually all cases these differences are of negligible practical importance and are at the minimum level consistent with a scale of no more than reasonable complexity; for further information on this point see "Supplementary information for the ITS-90" (BIPM-1990).

The ITS-90 has been constructed in such a way that, throughout its range, any given temperature the numerical value of T90 is a close approximation to the numerical value of T90 according to best estimates at the time the scale was adopted. By comparison with direct measurements of thermodynamic temperatures, measurements of T90 are more easily made, are more precise and are highly reproducible.

There are significant numerical differences between the values of T90 and the corresponding values of T90 measured on the International Practical Temperature Scale of 1968 (IPTS-68), see Fig. 1 and Table 6. Similarly there were differences between the IPTS-68 and the International Practical Temperature Scale of 1948 (IPTS-48), and between the International Temperature Scale of 1948 (ITS-48) and the International Temperature Scale of 1927 (ITS-27). See the Appendix, and, for more detailed information, "Supplementary Information for the ITS-90."

FIG. 1. The differences (t90 - t68) as a function of Celsius temperature t90.

3. Definition of the International Temperature Scale of 1990

Between 0.65 K and 5.0 K T90 is defined in terms of the vapour-pressure temperature relations 3He and 4He.

Between 3.0 K and the triple point of neon (24.5561 K) T90 is defined by means of a helium gas thermometer calibrated at three experimentally realizable temperatures having assigned numerical values (defining fixed points) and using specified interpolation procedures.

Between the triple point of equilibrium hydrogen (13.8033 K) and the freezing point of silver (961.78 șC) T90 is defined by means of platinum resistance thermometers calibrated at specified sets of defining fixed points and using specified interpolation procedures.

Above the freezing point of silver (961.78șC) T90 is defined in terms of a defining fixed point and the Planck radiation law.

The defining fixed points of the ITS-90 are listed in Table 1. The effects of pressure, arising from significant depths of immersion of the sensor or from other causes, on the temperature of most of these points are given in Table 2.

3.1. From 0,65 K: Helium Vapour-Pressure Temperature Equations

In this range T₉₀ is defined in terms of the vapour pressure p of ³He and ⁴He using equations of the form:

9

T90/K = Ao+∑Ai[(in (p/Pa) —B)/C)i

i=1

The values of the constants A₀, A_i, B and C are given in Table 3 for ³He in the range of

0.65 K to 3.2 K, and for ⁴He in the ranges 1.25 K to 2.1768 K (the lambda point) and 2.1768 K to 5.0 K.

3.2 From 3.0 K to the Triple Point of Neon (24.5561 K): Gas Thermometer

In this range T₉₀ is defined in terms of a ³He or a ⁴He gas thermometer of the constant-volume type that has been calibrated at three temperatures. These are the triple point of neon (24.5561 K), the triple point of equilibrium hydrogen (13.8033 K), and a temperature is between 3.0 K and 5.0 K. This last temperature is determined using a 3He or a 4He vapour pressure thermometer as specified in Sect. 3.1.

Table 1. Defining fixed points of the ITS-90

(a) All substances except ³He are of natural isotopic composition, e-H₂ is hydrogen at the equilibrium concentration of the ortho- and para-molecular forms

(b) For complete definitions and advice on the realization of these various states, see "Supplementary Information for the ITS-90". The symbols have the following meanings: V: vapour pressure point; T: triple point (temperature at which the solid liquid and vapour phases are in equilibrium); G: gas thermometer point; M, F: melting point, freezing point (temperature, at a pressure of 101 325 Pa, at which the solid and liquid phases are in equilibrium)

Table 2. Effect of pressure on the temperatures of some defining fixed points⁺

* Equivalent to millikelvins per standard atmosphere

** Equivalent to millikelvins per metre of liquid

+ The Reference pressure for melting and freezing points is the standard atmosphere (p0=101 325 Pa). For triple points (T) the pressure effect is a consequence only of the hydrostatic head of liquid in the cell

Table 3. Values of the constants for the helium vapour pressure Eqs. (3), and the temperature range for which each equation, identified by its set of constants, is valid

T₉₀ = a + bp +cp², (4)

where p is the pressure in the gas thermometer and a, b and c are coefficients the numerical values of which are obtained from measurements made at the three defining fixed points given in Sect. 3.2. but with the further restriction that the lowest one of these points lies between 4.2 K and 5.0 K.

3.2.2. From 3.0 K to the Triple Point of Neon (24.5561 K) with ³He or ⁴He as the Thermometric Gas.

For a ³He gas thermometer, and for a ⁴He gas thermometer used below 4.2 K, the non-ideality of the gas must be accounted for explicitly, using the appropriate second virial coefficient B3 (T₉₀) or B4 (T₉₀). In this range T₉₀ is defined by the relation:

T₉₀ = a + bp + cp²/1 + B_x(T₉₀) NIV

where p is the pressure in the gas thermometer, a, b and c are coefficients the numerical values of which are obtained from measurements at three defining temperatures as given in Sect. 3.2, N/V is the gas density with N being the quantity of gas and V the volume of the bulb, X is 3 or 4 according to the isotope used, and the values of the second virial coefficients are given by the relations:

For ³He
B(T₉₀)/m³mol^-1={16,69 — 336,98(T₉₀/K)^-1
      +91,04(T₉₀/K)^-2—13,82(T₉₀/K)^-3} 10^-6
For ⁴He
B₄(T₉₀)/m³mol^-1={15,708—374,05(T₉₀/K)^-1
    —383,53(T₉₀/K)^-2-2 + 1799,2(T₉₀/K)^-3
—4033,2(T₉₀/K)^-4 + 3252,8 (T₉₀/K)^-3} 10^-6

Table 4. The constants A₀, A_i; B_n, B_i; C₀, C_i; D₀ and D_i in the reference functions of equations (9a); (10a); and (10b) respectively

The accuracy with which T₉₀ can be realized using Eqs. (4) and (5) depends on the design of the gas thermometer and the gas density used. Design criteria and current good practice required to achieve a selected accuracy are given in "Supplementary Information for the ITS -90".

3.3. The Triple Point of Equilibrium Hydrogen (13.8033 K) to the Freezing Point of Silver (961.78 șC): Platinum Resistance Thermometer

In this range T90 is defined by means of a platinum resistance thermometer calibrated at specified sets of defining fixed points, and using specified reference and deviation functions for interpolation at intervening temperatures.

No single platinum resistance thermometer can provide high accuracy, or is even likely to be usable, over all of the temperature range 13,8033 K to 961.78 șC. The choice of temperature range, or ranges, from among those listed below for which a particular thermometer can be used is normally limited by its construction.

For practical details and current good practice, in particular concerning types of thermometer available, their acceptable operating ranges, probable accuracies, permissible leakage resistance, resistance values, and thermal treatment, see "Supplementary Information for ITS-90". It is particularly important to take account of the appropriate heat treatments that should be followed each time a platinum resistance thermometer is subjected to a temperature above about 420 șC.

Temperatures are determined in terms of the ratio of the resistance R(T₉₀) at a temperature T₉₀ and the resistance R (273.16 K) at the triple point of water.

This ratio, W (T₉₀), is ²:

W(T₉₀)=R(T₉₀)/IR(273,16K)

² Note that this definition of W (T₉₀) differs from the corresponding definition used in the ITS-27, ITS-48, IPTS-48, and IPTS-68: for all of these earlier scales W (T) was defined in terms of reference temperature of 0șC, which since 1954 has itself been defined as 273.15 K

An acceptable platinum resistance thermometer must be made from pure, strain-free platinum, and it must satisfy at least one of the following two relations:

W(27,7646°C)≥1,118,07
W)—38,8344°C)≥0,844 235

An acceptable platinum resistance thermometer that is to be used up to the freezing point of silver must also satisfy the relation:

W(961,78°C)≥4,2844

In each of the resistance thermometer ranges, T₉₀ is obtained from W (T₉₀) as given by the appropriate reference function {Eqs. (9b) or (10b)}, and the deviation W(T₉₀) - Wr(T₉₀). At the defining fixed points this deviation is obtained directly from the calibration of the thermometer: at intermediate temperatures it is obtained by means of the appropriate deviation function {Eqs. (12), (13) and (14)}.

(i) - For the range 13.8033 K to 273.16 K the following reference function is defined:

₁₂         
(9a.)In [W_r(T₉₀)]=A₀ + ∑A_i[In (T₉₀)/273,16K + 1,5/1,5]^i
i=1         

An inverse fnction, equivalent to Eq.(9a.) to within 0,1 mK, is:

₁₅  
(9b.) T₉₀/273,16K = B₀ + ∑ B_i[W_r(T₉₀)^1/6 —0,65/0,35]^i
i=1  

The values of the constants A0, Ai, B0 and Bi are given in Table 4.

A thermometer may be calibrated for use throughout this range or, using progressively fewer calibration points, for ranges with low temperature limits of 24.5561 K, 54.3584 K and 83.8058 K, all having an upper limit of 273.16 K.

(ii) - For the range 0 șC to 961.78 șC the following reference function is defined:

₉  
(10a.) W_r(T₉₀) = C₀ + ∑C_i[T₉₀/K — 754,15/481]^i
i=1  

An inverse function, equivalent to equation (10a.) to within 0,13 mK is:

        ₉
(10b.) T₉₀/K — 273,15 = D₀ + ∑ D_i[W_r(T₉₀) — 2,64/1,64]^{i
        i=1}

The values of the constants C0, Ci, D0 and Di are given in Table 4.

A thermometer may be calibrated for use throughout this range or, using fewer calibration points, for ranges with upper limits of 660.323 șC, 419.527 șC, 231.928 șC, 156.5985 șC or 29.7646 șC, all having a lower limit of 0 șC.

(iii) - A thermometer may be calibrated for use in the range 234.3156 K ( - 38.8344 șC) to 29.7646 șC, the calibration being made at these temperatures and at the triple point of water. Both reference functions {Eqs. (9) and (10)} are required to cover this range.

The defining fixed points and deviation functions for the various ranges are given below, and in summary from in Table 5.

3.3.1. The Triple Point of Equilibrium Hydrogen (13.8033 K) to the Triple Point of Water (273.16 K).

The thermometer is calibrated at the triple points of equilibrium hydrogen (13.8033 K), neon (24.5561 K), oxygen (54.3584 K), argon (83.8058 K), mercury (234.3156 K), and water (273.16 K), and at two additional temperatures close to 17.0 K and 20.3 K. These last two may be determined either: by using a gas thermometer as described in Sect. 3.2, in which case the two temperatures must lie within the ranges 16.9 K to 17.1 K and 20.2 K to 20.4 K respectively; or by using the vapour pressure-temperature relation of equilibrium hydrogen, in which case the tow temperatures must lie within the ranges 17.025 K to 17.045 K and 20.26 K to 20.28 K respectively, with the precise values being determined from Eqs. (11a) and (11b) respectively:

T₉₀/K - 17.035 = (p/kPa - 33.3213)/13.32 (11a)

T₉₀/K - 20.27 = (p/kPa - 101.292)/30 (11b)

(11a.) T₉₀/K — 17,035 = (p/kPa — 33,3213)/13,32
(11b.) T₉₀/K — 20,27 = (p/kPa — 101,292)/30

The deviation function is³
                                                          ₅
(12.) W(T₉₀) — W_r(T₉₀) = a[W(T₉₀)—1] + b[W(T₉₀)—]² + ∑ c_i[In W(T₉₀)]^{i+n
                                                         i=1}

³ This deviation function {and also those of Eqs. (13) and (14)} may be expressed in terms of W_r rather than W; for this procedure see "Supplementary Information for ITS-90"

with values for the coefficients a, b and c_i being obtained from measurements at the defining fixed points and with n = 2.

For this range and for the sub-ranges 3.3.1.1 to 3.3.1.3 the required values W_r(T₉₀) are obtained from Eq. (9a) or from Table 1.

3.3.1.1. The Triple Point of Neon (24.5561 K) to the Triple Point of Water (273.16 K).

The thermometer is calibrated at the triple points of equilibrium hydrogen (13.8033 K), neon (24.5561 K), oxygen (54.3584 K), argon (83.8058 K), mercury (234.3156 K) and water (273.16 K).

The deviation function is given by Eq. (12) with values for the coefficients a, b, c₁, c₂ and c₃ being obtained from measurements at the defining fixed points and with c₄ = c₅ = n = 0.

3.3.1.2 The Triple Point of Oxygen (54.3584 K) to the Triple Point of Water (273.16 K).

The thermometer is calibrated at the triple points of oxygen (54.3584 K), argon (83.8058 K), mercury (234.3156 K) and water (273.16 K).

Table 5. Deviation functions and calibration points for platinum resistance thermometers in the various ranges in which they define T₉₀

* Calibration points 9, 12-14 are used with d = 0 for t₉₀ <= 660.323 șC; the values of a, b and c thus obtained are retained for t₉₀ => 660.323 șC with d being determined from calibration point 15

The deviation function is given by Eq. (12) with values for the coefficients a, b and c1 being obtained from measurements at the defining fixed points, with c2 = c3 = c4 = c5 = 0 and with n = 1.

3.3.1.3. The Triple Point of Argon (83.8058 K) to the Triple Point of Water (273.16 K).

The thermometer is calibrated at the triple points of argon (83,8058 K), mercury (234,3156 K) and water (273,16 K).

The deviation function is:

(13.) W(T₉₀) — W_r(T₉₀) = a[W(T₉₀)—1] + b[W(T₉₀)—1] In W(T₉₀)

with the values of a and b being obtained from measurements at the defining fixed points.

3.3.2. From 0 șC to the Freezing Point of Silver (961.78 șC).

The thermometer is calibrated at the triple point of water (0,01 șC), and at the freezing points of tin (231.928 șC), zinc (419.527 șC), aluminium (660.323 șC) and silver (961.78 șC).

The deviation function is:

(14.) W(T₉₀) — W_r(T₉₀) = a[W(T₉₀)—1] + b[W(T₉₀)—1]² + c[W(T₉₀)—1]³ + d[W(T₉₀)—W(660,323 °C)]²

For temperatures below the freezing point of aluminium d = 0, with the values of a, b and c being determined from the measured deviations from W_r(T₉₀) at the freezing points of tin, zinc and aluminium. From the freezing point of aluminium to the freezing point of silver the above values of a, b and c are retained and the value of d is determined from the measured deviation from W_r(T₉₀) at the freezing point of silver.

For this range and for the sub-ranges 3.3.2.1 to 3.3.2.5 the required values for W_r(T₉₀) are obtained from Eq. (10a) or from Table 1.

3.3.2.1. From 0 șC to the Freezing Point of Aluminium (660.323 șC).

The thermometer is calibrated at the triple point of water (0.01 șC), and at the freezing points of tin (231.928 șC), zinc (419.527 șC) and aluminium (660.323 șC).

The deviation function is given by Eq. (14), with the values of a, b and c being determined from measurements at the defining fixed points and with d = 0.

3.3.2.2. From 0 șC to the Freezing Point of Zinc (419.527 șC).

The thermometer is calibrated at the triple point of water (0.0 șC), and at the freezing points of tin (231.928 șC). and zinc (419.527 șC).

The deviation function is given by Eq. (14), with the values of a and b being obtained from measurements at the defining fixed points and with c = d = 0.

3.3.2.3. From 0 șC to the Freezing Point of Tin (231.928 șC).

The thermometer is calibrated at the triple point of water (0.01 șC), and at the freezing points of indium (156.5985 șC) and tin (231.928 șC).

The deviation function is given by Eq. (14), with the values of a and b being obtained from measurements at the defining fixed points and with c = d = 0.

3.3.2.4.From 0 șC to the Freezing Point of Indium (156,5985 șC).

The thermometer is calibrated at the triple point of water (0.01 șC), and at the freezing point of indium (156.5985 șC).

The deviation function is given by Eq. (14) with the value of a being obtained from measurements at the defining fixed points and with b = c = d = 0.

3.3.2.5. From 0 șC to the Melting Point of Gallium (29.7646 șC).

The thermometer is calibrated at the triple point of water (0.01 șC), and the melting point of gallium (29.7646 șC).

The deviation function is given by Eq. (14) with the value of a being obtained from measurements at the defining fixed points and with b = c = d = 0.

3.3.3. The Triple Point of Mercury (-38.8344 șC) to the Melting Point of Gallium (29.7646 șC).

The thermometer is calibrated at the triple points of mercury (- 38.8344 șC), and water (0.01 șC), and at the melting point of gallium (29.7646 șC).

The deviation function is given by Eq. (14) with the values of a and b being obtained from measurements at the defining fixed points and with c = d = 0.

The required values of W_r(T₉₀) are obtained from Eqs. (9a) and (10a) for measurements below and above 273.16 K respectively, or from Table 1.

3.4. The Range Above the Freezing Point of Silver (961,78 șC): Planck Radiation Law

Above the freezing point of silver the temperature T90 is defined by the equation:

(15.) Lλ(T₉₀)/Lλ[(T₉₀(X)]=exp(c₂[λT₉₀(X)]^-1)—1/exp(c₂[λT₉₀]^-1)—1

where T₉₀(X) refers to any one of the silver {T90(Ag) = 1234.93 K}, the gold {T₉₀(Au) = 1337.33 K} or the copper {T90(Cu) = 1357.77 K} freezing points4 and in which Llambda(T₉₀) and Llambda[T₉₀(X)] are the spectral concentrations of the radiance of a blackbody at the wavelength (in vacuo) lambda at T₉₀ and at T₉₀(X) respectively, and c₂ = 0.014388 m · K

. For practical details and current good practice for optical pyrometry, see "Supplementary Information for the ITS-90" (BIPM-1990).

4 The T₉₀ values of the freezing points of silver, gold and copper are believed to be self consistent to such a degree that the substitution of any one of them in place of one of the other two as the reference temperature T₉₀(X) will not result in significant differences in the measured values of T₉₀.

4. Supplementary Information and Differences from Earlier Scales

The apparatus, methods and procedures that will serve to realize the ITS-90 are given in "Supplementary Information for the ITS-90". This document also gives an account of the earlier International Temperature Scales and the numerical differences between successive scales that include, where practicable, mathematical functions for differences T₉₀ - T68. A number of useful approximations to the ITS-90 are given in "Techniques for Approximating the ITS-90".

These two documents have been prepared by the Comité Consultatif de Thermométrie and are published by the BIPM; they are revised and updated periodically. The differences T₉₀ - T₆₈ are shown in Fig. 1 and Table 6. The number of significant figures given in Table 6 allows smooth interpolations to be made. However, the reproducibility of the IPTS-68 is, in many areas, substantially worse than is implied by this number.

Table 6. Differences between ITS-90 and EPT-76, and between ITS-90 and IPTS-68 for specified values of T₉₀ and t₉₀.