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 CanadaReceived: 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 / ºC = T / K - 273.15 (1) The unit of Celsius temperature is the degree Celsius, symbol ºC, 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 / ºC = 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 ºC, 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 ºC) 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 (961.78ºC) 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:
The values of the constants A0, Ai, 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
Temperature Number T90/K t90/ºC Substancea Stateb Wr(T90) 1 3 to 5 -270.15
to -268.15He V 2 13.8033 -259.3467 e-H2 T 0.001 190 07 3 ~17 ~-256.15 e-H2
(or He)V
(or G)4 ~20.3 ~-252.85 e-H2
(or He)V
(or G)5 24.5561 -248.5939 Ne T 0.008 449 74 6 54.3584 -218.7916 O2 T 0.091 718 04 7 83.8058 -189.3442 Ar T 0.215 859 75 8 234.3156 -38.8344 Hg T 0.844 142 11 9 273.16 0.01 H2O T 1.000 000 00 10 302.9146 29.7646 Ga M 1.118 138 89 11 429.7485 156.5985 In F 1.609 801 85 12 505.078 231.928 Sn F 1.892 797 68 13 692.677 419.527 Zn F 2.568 917 30 14 933.473 660.323 Al F 3.376 008 60 15 1234.93 961.78 Ag F 4.286 420 53 16 1337.33 1064.18 Au F 17 1357.77 1084.62 Cu F (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+
Substance Assignment
value of
equilibrium
temperature
T90/KTemperature
with pressure, p
(dT/dp)/
(10-8K · Pa -1)*Variation
with depth, lambda
(dT/dl)/
(10-3K · m -1)**e-Hydrogen (T) 13.8033 34 0.25 Neon (T) 24.5561 16 1.9 Oxygen (T) 54.3584 12 1.5 Argon (T) 83.8058 25 3.3 Mercury (T) 234.3156 5.4 7.1 Water (T) 273.16 - 7.5 - 0.73 Gallium 302.9146 - 2.0 - 1.2 Indium 429.7485 4.9 3.3 Tin 505.078 3.3 2.2 Zinc 692.677 4.3 2.7 Aluminium 933.473 7.0 1.6 Silver 1234.93 6.0 5.4 Gold 1337.33 6.1 10 Copper 1357.77 3.3 2.6 * 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
3He
0.65 K to 3.2 K4He
1.25 K to 2.1768 K4He
2.1768 K to 5.0 KA0 1.053 447 1.392 408 3.146 631 A1 0.980 106 0.527 153 1.357 655 A2 0.676 380 0.166 756 0.413 923 A3 0.372 692 0.050 988 0.091 159 A4 0.151 656 0.026 514 0.016 349 A5 - 0.002 263 0.001 975 0.001 826 A6 0.006 596 - 0.017 976 - 0.00 4325 A7 0.088 966 0.005 409 - 0.00 4973 A8 - 0.004 770 0.013 259 0 A9 - 0.054 943 0 0 B 7.3 5.6 10.3 C 4.3 2.9 1.9
3.2.1. From 4.2 K to the Triple Point of Neon (24.5561 K) with 4He as the Thermometric Gas.
In this range T90 is defined by the relation:
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:
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:
Table 4. The constants A0, Ai; Bn, Bi; C0, Ci; D0 and Di in the reference functions of equations (9a); (10a); and (10b) respectively
A0 - 2.135 347 29 B0 0.183 324 722 C0 2.781 572 54 D0 439.932 854 A1 3.183 247 20 B1 0.240 975 303 C1 1.646 509 16 D1 472.418 020 A2 - 1.801 435 97 B2 0.209 108 771 C2 - 0.137 143 90 D2 37.684 494 A3 0.717 272 04 B3 0.190 439 972 C3 - 0.006 497 67 D3 7.472 018 A4 0.503 440 27 B4 0.142 648 498 C4 - 0.002 344 44 D4 2.920 828 A5 - 0.618 993 95 B5 0.077 993 465 C5 0.005 118 68 D5 0.005 184 A6 - 0.053 323 22 B6 0.012 475 611 C6 0.001 879 82 D6 - 0.963 864 A7 0.280 213 62 B7 - 0.032 267 127 C7 - 0.002 044 72 D7 - 0.188 732 A8 0.107 152 24 B8 - 0.075 291 522 C8 - 0.000 461 22 D8 0.191 203 A9 - 0.293 028 65 B9 - 0.056 470 670 C9 0.000 457 24 D9 0.049 025 A10 0.044 598 72 B10 0.076 201 285 A11 0.118 686 32 B11 - 0.123 893 204 A12 - 0.052 481 34 B12 - 0.029 201 193 B13 - 0.091 173 542 B14 0.001 317 696 B15 0.026 025 526
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 ºC): 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 ºC. 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 ºC.
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:
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 0ºC, 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:
An acceptable platinum resistance thermometer that is to be used up to the freezing point of silver must also satisfy the relation:
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:
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 ºC to 961.78 ºC the following reference function is defined:
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 ºC, 419.527 ºC, 231.928 ºC, 156.5985 ºC or 29.7646 ºC, all having a lower limit of 0 ºC.
(iii) - A thermometer may be calibrated for use in the range 234.3156 K ( - 38.8344 ºC) to 29.7646 ºC, 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 - 20.27 = (p/kPa - 101.292)/30 (11b)
3 This deviation function {and also those of Eqs. (13) and (14)} may be expressed in terms of Wr rather than W; for this procedure see "Supplementary Information for ITS-90" with values for the coefficients a, b and ci 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 Wr(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
a. Ranges with an upper limit of 273.16 K Section Lower
temperature
limit (T/K)Deviation functions Calibration
points (see
Table 1)3.3.1 13.8033 As equation (12), with n=2 2-9 3.3.1.1 24.5561 As for 3.3.1 with c4 = c5 = n = 0 2, 5-9 3.3.1.2 54.3584 As for 3.3.1 with c2 = c3 = c4 = c5 = 0, n = 1 6-9 3.3.1.3 83.8058 a[W (T90) - 1]+b[W (T90) - 1] ln W (T90) 7-9 b. Ranges with a lower limit of 0 ºC Section Lower
temperature
limit (t/ºC)Deviation functions Calibration
points (see
Table 1)3.3.2* 961.78 As equation (14) 9, 12-15 3.3.2.1 660.323 As for 3.3.2 with d = 0 9, 12 - 14 3.3.2.2 419.527 As for 3.3.2 with c = d = 0 9, 12, 13 3.3.2.3 231.928 As for 3.3.2 with c = d = 0 9, 11, 12 3.3.2.4 156.5982 As for 3.3.2 with b = c = d = 0 9, 11 3.3.2.5 29.7646 As for 3.3.2 with b = c = d = 0 9, 10 c. Range from 234.3156 K ( - 38.8344 ºC) to 29.7646 ºC 3.3.3 As for 3.3.2 with c = d = 0 8-10 * Calibration points 9, 12-14 are used with d = 0 for t90 <= 660.323 ºC; the values of a, b and c thus obtained are retained for t90 => 660.323 ºC 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:
with the values of a and b being obtained from measurements at the defining fixed points.
3.3.2. From 0 ºC to the Freezing Point of Silver (961.78 ºC).
The thermometer is calibrated at the triple point of water (0,01 ºC), and at the freezing points of tin (231.928 ºC), zinc (419.527 ºC), aluminium (660.323 ºC) and silver (961.78 ºC).
The deviation function is:
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 Wr(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 Wr(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 Wr(T90) are obtained from Eq. (10a) or from Table 1.
3.3.2.1. From 0 ºC to the Freezing Point of Aluminium (660.323 ºC).
The thermometer is calibrated at the triple point of water (0.01 ºC), and at the freezing points of tin (231.928 ºC), zinc (419.527 ºC) and aluminium (660.323 ºC).
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 ºC to the Freezing Point of Zinc (419.527 ºC).
The thermometer is calibrated at the triple point of water (0.0 ºC), and at the freezing points of tin (231.928 ºC). and zinc (419.527 ºC).
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 ºC to the Freezing Point of Tin (231.928 ºC).
The thermometer is calibrated at the triple point of water (0.01 ºC), and at the freezing points of indium (156.5985 ºC) and tin (231.928 ºC).
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 ºC to the Freezing Point of Indium (156,5985 ºC).
The thermometer is calibrated at the triple point of water (0.01 ºC), and at the freezing point of indium (156.5985 ºC).
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 ºC to the Melting Point of Gallium (29.7646 ºC).
The thermometer is calibrated at the triple point of water (0.01 ºC), and the melting point of gallium (29.7646 ºC).
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 ºC) to the Melting Point of Gallium (29.7646 ºC).
The thermometer is calibrated at the triple points of mercury (- 38.8344 ºC), and water (0.01 ºC), and at the melting point of gallium (29.7646 ºC).
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 Wr(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 ºC): Planck Radiation Law
Above the freezing point of silver the temperature T90 is defined by the equation:
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.
(T90 - T76)/mK T90/K 0 1 2 3 4 5 6 7 8 9 0 -0.1 -0.2 -0.3 -0.4 -0.5 10 -0.6 -0.7 -0.8 -1.0 -1.1 -1.3 -1.4 -1.6 -1.8 -2.0 20 -2.2 -2.5 -2.7 -3.0 -3.2 -3.5 -3.8 -4.1 (T90 - T68)/K T90/K 0 1 2 3 4 5 6 7 8 9 10 -0.006 -0.003 -0.004 -0.006 -0.008 -0.009 20 -0.009 -0.008 -0.007 -0.007 -0.006 -0.005 -0.004 -0.004 -0.005 -0.006 30 -0.006 -0.007 -0.008 -0.008 -0.008 -0.007 -0.007 -0.007 -0.006 -0.006 40 -0.006 -0.006 -0.006 -0.006 -0.006 -0.007 -0.007 -0.007 -0.006 -0.006 50 -0.006 -0.005 -0.004 -0.004 -0.003 -0.002 -0.001 0.000 0.001 0.002 60 0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006 0.007 0.007 70 0.007 0.007 0.007 0.007 0.007 0.008 0.008 0.008 0.008 0.008 80 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 90 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.009 0.009 0.009 T90/K 0 10 20 30 40 50 60 70 80 90 100 0.009 0.011 0.013 0.014 0.014 0.014 0.014 0.013 0.012 0.012 200 0.011 0.010 0.009 0.008 0.007 0.005 0.003 0.001 (t90 - t68)/ºC t90/ºC 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100 0.013 0.013 0.014 0.014 0.014 0.013 0.012 0.010 0.008 0.008 0 0.000 0.002 0.004 0.006 0.008 0.009 0.010 0.011 0.012 0.012 t90/ºC 0 10 20 30 40 50 60 70 80 90 0 0.000 -0.002 -0.005 -0.007 -0.010 -0.013 -0.016 -0.018 -0.021 -0.024 100 -0.026 -0.028 -0.030 -0.032 -0.034 -0.036 -0.037 -0.038 -0.039 -0.039 200 -0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.039 -0.039 -0.039 300 -0.039 -0.039 -0.039 -0.040 -0.040 -0.041 -0.042 -0.043 -0.045 -0.046 400 -0.048 -0.051 -0.053 -0.056 -0.059 -0.062 -0.065 -0.068 -0.072 -0.075 500 -0.079 -0.083 -0.087 -0.090 -0.094 -0.098 -0.101 -0.105 -0.108 -0.112 600 -0.115 -0.118 -0.122 - 0.125* -0.08 -0.03 0.02 0.06 0.11 0.16 700 0.20 0.24 0.28 0.31 0.33 0.35 0.36 0.36 0.36 0.35 800 0.34 0.32 0.29 0.25 0.22 0.18 0.14 0.10 0.06 0.03 900 -0.01 -0.03 -0.06 -0.08 -0.10 -0.12 -0.14 -0.16 -0.17 -0.18 1000 -0.19 -0.20 -0.21 -0.22 -0.23 -0.24 -0.25 -0.25 -0.26 -0.26 t90/ºC 0 100 200 300 400 500 600 700 800 900 1000 -0.26 -0.30 -0.35 -0.39 -0.44 -0.49 -0.54 -0.60 -0.66 2000 -0.72 -0.79 -0.85 -0.93 -1.00 -1.07 -1.15 -1.24 -1.32 -1.41 3000 -1.50 -1.59 -1.69 -1.78 -1.89 -1.99 -2.10 -2.21 -2.32 -2.43 * A discontinuity in the first derivative of (t90 - t68) occurs at a temperature of t90 = 630.6 ºC, at which (t90 - t68) = - 0.125 ºC
Appendix
The International Temperature Scale of 1927 (ITS-27)
The International Temperature Scale of 1927 was adopted by the seventh General Conference of Weights and Measures to overcome the practical difficulties of the direct realization of thermodynamic temperatures by gas thermometry, and as a universally acceptable replacement for the differing existing national temperature scales. The ITS-27 was formulated so as to allow measurements of temperature to be made precisely and reproducibly, with as close an approximation to thermodynamic temperatures as could be determined at that time. Between the oxygen boiling point and the gold freezing point it was based upon a number of reproducible temperatures, or fixed points, to which numerical values were assigned, and two standard interpolating instruments. Each of these interpolating instruments was calibrated at several of the fixed points, this giving the constants for the interpolating formula in the appropriate temperature range. A platinum resistance thermometer was used for the low part and a platinum rhodium/platinum thermocouple for temperatures above 660 ºC. For the region above the gold freezing point, temperatures were defined in terms of the Wien radiation law: in practice, this invariably resulted in the selection of an optical pyrometer as the realizing instrument.
The International Temperature Scale of 1948 (ITS-48)
The International Temperature Scale of 1948 was adopted by the ninth General Conference. Changes from the ITS-27 were: the lower limit of platinum resistance thermometer range was changed from -190 ºC to the defined oxygen boiling point of -182.97 ºC, and the junction of the platinum resistance thermometer range and the thermocouple range became the measured antimony freezing point (about 630 ºC) in place 660 ºC; the silver freezing point was defined as being 960.8 ºC instead of 960.5 ºC; the gold freezing point replaced the gold melting point (1063 ºC); the Planck radiation law replaced the Wien law; the value assigned to the second radiation constant became 1.438 x 10-2 m · K in place of 1,432 x 10-2 m · K the permitted ranges for the constants of the interpolation formula for the standard resistance thermometer and thermocouple were modified; the limitation on lT for optical pyrometry (lambda·T<3x10-3 m · K) was changed on the requirement that "visible" radiation be used.
The International Practical Temperature Scale of 1948 (Amended Edition of 1960) (IPTS-48)
The International Practical Temperature Scale of 1948, amended edition of 1960, was adopted by the eleventh General Conference: the tenth General Conference had already adopted the triple point of water as the sole point defining the kelvin, the unit of thermodynamic temperature. In addition to the introduction of the word "Practical", the modifications to the ITS-48 were: the triple point of water, defined as being 0.01 ºC, replaced the freezing point of zinc, defined as being 419.505 ºC, became a preferred alternative to the sulphur boiling point (444.6 ºC) as a calibration point; the permitted ranges for the constants of the interpolation formulae for the standard resistance thermometer and the thermocouple were further modified; the restriction to "visible" radiation for optical pyrometry was removed.
Inasmuch as the numerical values of temperature on the IPTS-48 were the same as on the ITS-48, the former was not a revision of the scale of 1948 but merely an amended form of it.
The International Practical Temperature Scale of 1968 (IPTS-68)
In 1968 the International Committee of Weights and Measures promulgated the International Practical Temperature Scale of 1968, having been empowered to do so by the thirteenth General Conference of 1967 - 1968. The IPTS-68 incorporated very extensive changes from the IPTS-48. These included numerical changes, designed to bring to more nearly in accord with thermodynamic temperatures, that were sufficiently large to be apparent to many users. Other changes were as follows: the lower limit of the scale was extended down to 13.81 K; at even lower temperatures (0.5 K to 5.2 K), the use of two helium vapour pressure scales was recommended; six new defining fixed points were introduced - the triple point of equilibrium hydrogen (13.81 K), an intermediate equilibrium hydrogen point (17.042 K), the normal boiling point of equilibrium hydrogen (20.28 K), the boiling point of neon (27.102 K), the triple point of oxygen (54.361 K), and the freezing point of tin (231.9681 ºC) which became a permitted alternative to the boiling point of water; the boiling point of sulphur was deleted; the values assigned to four fixed points were changed - the boiling point of oxygen (90.188 K), the freezing point of zinc (419.58 ºC), the freezing point of silver (961.93 ºC), and the freezing point of gold (1064.43 ºC): the interpolating formulae for the resistance thermometer range became much more complex; the value assigned to the second radiation constant c2 became 1.4388 x 10-2 m · K; the permitted ranges of the constants for the interpolation formulae for the resistance thermometer and thermocouple were again modified.
The International Practical Temperature Scale of 1968 (Amended Edition of 1975) (IPTS-68)
The International Practical Temperature Scale of 1968, amended edition of 1975, was adopted by the fifteenth General Conference in 1975. As was the case for the IPTS-48 with respect to the ITS-48, the IPTS-68 (75) introduced no numerical changes. Most of the extensive textural changes were; the oxygen point was defined as the condensation point rather than the boiling point; the triple point of argon (83.798 K) was introduced as a permitted alternative to the condensation point of oxygen; new values of the isotopic composition of naturally occurring neon were adopted; the recommendation to use values of T given by the 1958 4He and 1962 3He vapour-pressure scales was rescinded.
The 1976 Provisional 0.5 K to 30 K Temperature Scale (EPT-76)
The 1976 Provisional 0.5 K to 30 K Temperature Scale was introduced to meet two important requirements: these were to provide means of substantially reducing the errors (with respect to corresponding thermodynamic values) below 27 K that were then known to exist in the IPTS-68 and throughout the temperature ranges of the 4He and 3He vapour pressure scales of 1958 and 1962 respectively, and to bridge the gap between 5.2 K and 13.81 K in which there had not previously been an international scale. Other objectives in devising the ETP-76 were "that it should be thermodynamically smooth, that it should be continuous with the IPTS-68 at 27.1 K, and that is should agree with thermodynamic temperature T as closely as these two conditions allow". In contrast with the IPTS-68, and to ensure its rapid adoption, several methods of realizing the ETP-76 were approved. These included: using a thermodynamic interpolation instrument and one or more of eleven assigned reference points; taking differences from the IPTS-68 above 13.81 K; taking differences from certain well-established laboratory scales. Because there was a certain "lack of internal consistency" it was admitted that "slight ambiguities between realizations" might be introduced. However the advantages gained by adopting the EPT-76 as a working scale until such time as the IPTS-68 should be revised and extended were considered to outweigh the disadvantages.
