The International Temperature Scale of 1990
(ITS-90)

The International Temperature Scale of 1990 was adopted by the International Committee of Weights and Measures at its meeting in 1989. 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.

Also see the NIST ITS-90 Thermocouple Database.

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 water.

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 kelvin 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.

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 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 T 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.

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

Definition of the International Temperature Scale of 1990
Between 0.65 K and 5.0 K T₉₀ is defined in terms of the vapor-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.

From 0,65 K: Helium Vapor-Pressure Temperature Equations

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

 

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.

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 vapor 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 -268.15	He	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: vapor pressure point; T: triple point (temperature at which the solid liquid and vapor 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/K	Temperature 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
Aluminum	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 meter 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 vapor 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 K	4He 1.25 K to 2.1768 K	4He 2.1768 K to 5.0 K
A0	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

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.

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, A_i; B_n, B_i; C₀, C_i; D₀ and D_i 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".

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 accuracy, 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) - W_r(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.

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 vapor 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)

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 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.

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.

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.

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.

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), aluminum (660.323 ºC) and silver (961.78 ºC).

The deviation function is: 

For temperatures below the freezing point of aluminum 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 aluminum. From the freezing point of aluminum 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.

From 0 ºC to the Freezing Point of Aluminum (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 aluminum (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.

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.

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.

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.

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.

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

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 Lambda(T₉₀) and Lambda[T₉₀(X)] are the spectral concentrations of the radiance of a blackbody at the wavelength (in vacuum) 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.

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