The International Temperatures Scale of 1990 (ITS90)
H. PrestonThomas
President of the Comité Consultatif de Thermométrie and VicePresident 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 ITS90 is published by the BIPM as part of the Prochèsverbaux 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 water^{1}.
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 kelvin or degrees Celsius.
The International Temperature Scale of 1990 (ITS90) defines both International Kelvin Temperatures, symbol T_{90}, and International Celsius Temperatures, symbol T_{90}. The relation between T_{90} and T_{90} is the same as that between T and t, i.e.:
t_{90} / °C = T_{90} / K  273.15 (2)
The unit of the physical quantity T_{90} is the kelvin, symbol K, and the unit of the physical quantity T_{90} is the degree Celsius, symbol °C, as is the case for the thermodynamic temperature T and the Celsius temperature t.
2. Principles of the International Temperature Scale of 1990 (ITS90)
The ITS90 extends upwards from 0.65 K to the highest temperature practicably measurable in terms of the Planck radiation law using monochromatic radiation. The ITS90 comprises a number of ranges and subranges throughout each of which temperatures T_{90} are defined. Several of these ranges or subranges overlap, and where such overlapping occurs, differing definitions of T_{90} 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 T_{90}. 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 ITS90" (BIPM1990).
The ITS90 has been constructed in such a way that, throughout its range, any given temperature the numerical value of T_{90} is a close approximation to the numerical value of T_{90} according to best estimates at the time the scale was adopted. By comparison with direct measurements of thermodynamic temperatures, measurements of T_{90} are more easily made, are more precise and are highly reproducible.
There are significant numerical differences between the values of T_{90} and the corresponding values of T_{90} measured on the International Practical Temperature Scale of 1968 (IPTS68), see Fig. 1 and Table 6. Similarly there were differences between the IPTS68 and the International Practical Temperature Scale of 1948 (IPTS48), and between the International Temperature Scale of 1948 (ITS48) and the International Temperature Scale of 1927 (ITS27). See the Appendix, and, for more detailed information, "Supplementary Information for the ITS90."
FIG. 1. The differences (t_{90}  t_{68}) as a function of Celsius temperature t_{90}
3. Definition of the International Temperature Scale of 1990
Between 0.65 K and 5.0 K T_{90} is defined in terms of the vapourpressure temperature relations ^{3}He and ^{4}He.
Between 3.0 K and the triple point of neon (24.5561 K) T_{90} 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 °C) T_{90} 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 (961.78°C) T_{90} is defined in terms of a defining fixed point and the Planck radiation law.
The defining fixed points of the ITS90 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 VapourPressure Temperature Equations
In this range T_{90} is defined in terms of the vapour pressure p of ^{3}He and ^{4}He using equations of the form:
T_{90}/K = A_{0} + Sigma_{i}^{9}_{= 1}(A_{i}[(ln(p / Pa)  B ) / C )^{i} (3)
The values of the constants A_{0}, A_{i}, B and C are given in Table 3 for ^{3}He in the range of 0.65 K to 3.2 K, and for ^{4}He 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 T_{90} is defined in terms of a ^{3}He or a ^{4}He gas thermometer of the constantvolume 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 ^{3}He or a ^{4}He vapour pressure thermometer as specified in Sect. 3.1
1. Defining fixed points of the ITS90

Temperature


Number

T_{90}/K

t_{90}/°C

Substance^{a}

State^{b}

W_{r}(T_{90})

1

3 to 5

270.15 to 268.15

He

V

.

2

13.8033

259.3467

eH_{2}

T

0.001 190 07

3

~17

~256.15

eH_{2} (or He)

V (or G)

.

4

~20.3

~252.85

eH_{2} (or He)

V (or G)

.

5

24.5561

248.5939

Ne

T

0.008 449 74

6

54.3584

218.7916

O_{2}

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

H_{2}O

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 ^{3}He are of natural isotopic composition, eH_{2} is hydrogen at the equilibrium concentration of the ortho and paramolecular forms.
(b) For complete definitions and advice on the realization of these various states, see "Supplementary Information for the ITS90". 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 T_{90}/K

Temperature with pressure,
p (dT/dp)/ (10^{8}K.Pa^{1})^{*}

Variation with depth, lambda
(dT/dl)/(10^{3}K.m^{1})^{**}

eHydrogen (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 (p_{0}=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

^{3}He
0.65 K to 3.2 K

^{4}He
1.25 K to 2.1768 K

^{4}He
2.1768 K to 5.0 K

A_{0}

1.053 447

1.392 408

3.146 631

A_{1}

0.980 106

0.527 153

1.357 655

A_{2}

0.676 380

0.166 756

0.413 923

A_{3}

0.372 692

0.050 988

0.091 159

A_{4}

0.151 656

0.026 514

0.016 349

A_{5}

 0.002 263

0.001 975

0.001 826

A_{6}

0.006 596

 0.017 976

 0.00 4325

A_{7}

0.088 966

0.005 409

 0.00 4973

A_{8}

 0.004 770

0.013 259

0

A_{9}

 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 ^{4}He as the Thermometric Gas.
In this range T_{90} is defined by the relation:
T_{90} = a + bp +cp^{2} (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 ^{3}He or ^{4}He as the Thermometric Gas.
For a ^{3}He gas thermometer, and for a ^{4}He gas thermometer used below 4.2 K, the nonideality of the gas must be accounted for explicitly, using the appropriate second virial coefficient B_{3} (T_{90}) or B_{4} (T_{90}). In this range T_{90} is defined by the relation:
T_{90} = (a + bp + cp^{2}) / (1 + B_{X}(T_{90})N/V) (5)
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 ^{3}He,
B(T_{90})/m^{3}mol^{1} = {16.69  336.98(T_{90}/K)^{1}
+ 91.04(T_{90}/K)^{2}  13.82(T_{90}/K)^{3}}10^{6} (6a)
For ^{4}He,
B(T_{90})/m^{3}mol^{1} = {16.708  374.05(T_{90}/K)^{1
}  383.53 (T_{90}/K)^{2} + 1799.2 (T_{90}/K)^{3
}  4033.2 (T_{90}/K)^{4} + 3252.8 (T_{90}/K)^{3}}10^{6} (6b)
Table 4. The constants A_{0}, A_{i}; B_{n}, B_{i}; C_{0}, C_{i}; D_{0} and D_{i} in the reference functions of equations (9a); (10a); and (10b) respectively
A_{0}

 2.135 347 29

B_{0}

0.183 324 722

C_{0}

2.781 572 54

D_{0}

439.932 854

A_{1}

3.183 247 20

B_{1}

0.240 975 303

C_{1}

1.646 509 16

D_{1}

472.418 020

A_{2}

 1.801 435 97

B_{2}

0.209 108 771

C_{2}

 0.137 143 90

D_{2}

37.684 494

A_{3}

0.717 272 04

B_{3}

0.190 439 972

C_{3}

 0.006 497 67

D_{3}

7.472 018

A_{4}

0.503 440 27

B_{4}

0.142 648 498

C_{4}

 0.002 344 44

D_{4}

2.920 828

A_{5}

 0.618 993 95

B_{5}

0.077 993 465

C_{5}

0.005 118 68

D_{5}

0.005 184

A_{6}

 0.053 323 22

B_{6}

0.012 475 611

C_{6}

0.001 879 82

D_{6}

 0.963 864

A_{7}

0.280 213 62

B_{7}

 0.032 267 127

C_{7}

 0.002 044 72

D_{7}

 0.188 732

A_{8}

0.107 152 24

B_{8}

 0.075 291 522

C_{8}

 0.000 461 22

D_{8}

0.191 203

A_{9}

 0.293 028 65

B_{9}

 0.056 470 670

C_{9}

0.000 457 24

D_{9}

0.049 025

A_{10}

0.044 598 72

B_{10}

0.076 201 285


A_{11}

0.118 686 32

B_{11}

 0.123 893 204

A_{12}

 0.052 481 34

B_{12}

 0.029 201 193


B_{13}

 0.091 173 542

B_{14}

0.001 317 696

B_{15}

0.026 025 526

The accuracy with which T_{90} 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 °C): Platinum Resistance Thermometer
In this range T_{90} 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 °C. 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 ITS90". 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 °C.
Temperatures are determined in terms of the ratio of the resistance R(T_{90}) at a temperature T_{90} and the resistance R (273.16 K) at the triple point of water.
This ratio, W (T_{90}), is ^{2}:
W(T_{90}) = R(T_{90}) / R(2173.15K) (7)
An acceptable platinum resistance thermometer must be made from pure, strainfree platinum, and it must satisfy at least one of the following two relations:
W(29.7646°C) ? 1.11807 (8a)
W(38.8344°C) ? 0.844235 (8b)
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 (8c)
In each of the resistance thermometer ranges, T_{90} is obtained from W (T_{90}) as given by the appropriate reference function {Eqs. (9b) or (10b)}, and the deviation W(T_{90})  W_{r}(T_{90}). 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:
In[W_{r}(T_{90})] = A_{0}+sigma_{i}^{12}_{= 1}{A_{i}[(ln( T_{90}/273.16K)+1.5)/1.5]^{i} } (9a)
An inverse function equivalent to Eq. (9a) to within 0.1mK is:
T_{90}/273.16K = B_{0}+sigma_{i}^{15}_{= 1}{B_{i}[(W_{r}(T_{90})2.64)/0.35 ]^{i }} (9b)
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 °C to 961.78 °C the following reference function is defined:
W_{r}(T_{90}) = C_{0} + sigma_{i}^{9}_{= 1}{C_{i}[( T_{90} / K  754.15) / 481 ]^{i}} (10a)
An inverse function equivalent to Eq. (10a) to within 0.13mK is:
T_{90}/K  273.16 = D_{0}+sigma_{i}^{9}_{= 1}{D_{i}[( W_{r}(T_{90})2.64)/1.64 ]^{i }} (10b)
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 °C, 419.527 °C, 231.928 °C, 156.5985 °C or 29.7646 °C, all having a lower limit of 0 °C.
(iii)  A thermometer may be calibrated for use in the range 234.3156 K (  38.8344 °C) to 29.7646 °C, 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 pressuretemperature 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:
T_{90}/K  17.035 = (p/kPa  33.3213)/13.32 (11a)
T_{90}/K  20.27 = (p/kPa  101.292)/30 (11b)
the deviation function is ^{3}
W(T_{90})  W_{r}(T_{90}) = a[W(T_{90})  1] + b[W(T_{90})  1]^{2}
+ sigma_{i}^{5}_{= 1}{c_{i}[ln (W(T_{90})) ]^{i+n} } (12)
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 subranges 3.3.1.1 to 3.3.1.3 the required values W_{r}(T_{90}) 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, c_{1}, c_{2} and c_{3} being obtained from measurements at the defining fixed points and with c_{4} = c_{5} = 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 thermometersin
the various ranges in which they define T_{90}
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

29

3.3.1.1

24.5561

As for 3.3.1 with c_{4} = c_{5} = n = 0

2, 59

3.3.1.2

54.3584

As for 3.3.1 with c_{2} = c_{3} = c_{4} = c_{5} = 0, n = 1

69

3.3.1.3

83.8058

a[W (T_{90})  1]+b[W (T_{90})  1] ln W (T_{90})

79


b. Ranges with a lower limit of 0 °C

Section

Lower temperature limit (t/°C)

Deviation functions

Calibration points
(see Table 1)

3.3.2*

961.78

As equation (14)

9, 1215

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 °C) to 29.7646 °C

3.3.3

.

As for 3.3.2 with c = d = 0

810

* Calibration points 9, 1214 are used with d = 0 for t_{90} <= 660.323 °C; the values of a, b and c thus obtained are retained for t_{90} => 660.323 °C with d being determined from calibration point 15
The deviation function is given by Eq. (12) with values for the coefficients a, b and c_{1} being obtained from measurements at the defining fixed points, with c_{2} = c_{3} = c_{4} = c_{5} = 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:
W(T_{90})  W_{r}(T_{90}) = a[W(T_{90})  1] + b[W(T_{90})  1] ln W(T_{90}) (13)
with the values of a and b being obtained from measurements at the defining fixed points.
3.3.2. From 0 °C to the Freezing Point of Silver (961.78 °C).
The thermometer is calibrated at the triple point of water (0,01 °C), and at the freezing points of tin (231.928 °C), zinc (419.527 °C), aluminium (660.323 °C) and silver (961.78 °C). The deviation function is:
W(T_{90})  W_{r}(T_{90}) = a[W(T_{90})  1] + b[W(T_{90})  1]^{2
}+ c[W(T_{90})  1]^{3} + d[W(T_{90})  W(660.323°C)]^{2} (14)
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}(T_{90}) 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}(T_{90}) at the freezing point of silver. For this range and for the subranges 3.3.2.1 to 3.3.2.5 the required values for W_{r}(T_{90}) are obtained from Eq. (10a) or from Table 1.
3.3.2.1. From 0 °C to the Freezing Point of Aluminium (660.323 °C).
The thermometer is calibrated at the triple point of water (0.01 °C), and at the freezing points of tin (231.928 °C), zinc (419.527 °C) and aluminium (660.323 °C).
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 °C to the Freezing Point of Zinc (419.527 °C).
The thermometer is calibrated at the triple point of water (0.0 °C), and at the freezing points of tin (231.928 °C). and zinc (419.527 °C).
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 °C to the Freezing Point of Tin (231.928 °C).
The thermometer is calibrated at the triple point of water (0.01 °C), and at the freezing points of indium (156.5985 °C) and tin (231.928 °C).
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 °C to the Freezing Point of Indium (156,5985 °C).
The thermometer is calibrated at the triple point of water (0.01 °C), and at the freezing point of indium (156.5985 °C).
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 °C to the Melting Point of Gallium (29.7646 °C).
The thermometer is calibrated at the triple point of water (0.01 °C), and the melting point of gallium (29.7646 °C).
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 °C) to the Melting Point of Gallium (29.7646 °C).
The thermometer is calibrated at the triple points of mercury ( 38.8344 °C), and water (0.01 °C), and at the melting point of gallium (29.7646 °C).
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}(T_{90}) 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 °C): Planck Radiation Law
Above the freezing point of silver the temperature T_{90} is defined by the equation:
L(T_{90}) / L(T_{90}(X)) = (exp(c_{2}[y T_{90 }(X)]^{1})  1)
/ (exp(c_{2}[y T_{90}(X)]^{1})  1) (15)
where T_{90}(X) refers to any one of the silver {T_{90}(Ag) = 1234.93 K}, the gold {T_{90}(Au) = 1337.33 K} or the copper {T_{90}(Cu) = 1357.77 K} freezing points^{4} and in which L_{lambda}(T_{90}) and L_{lambda}[T_{90}(X)] are the spectral concentrations of the radiance of a black body at the wavelength (in vacuo) lambda at T_{90} and at T_{90}(X) respectively, and c_{2} = 0.014388 m · K. (Transcribers note: y = lamba symbol which is missing in the standard www fonts).
For practical details and current good practice for optical pyrometry, see "Supplementary Information for the ITS90" (BIPM1990).
4. Supplementary Information and Differences from Earlier Scales
The apparatus, methods and procedures that will serve to realize the ITS90 are given in "Supplementary Information for the ITS90". 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 T_{90}  T_{68}. A number of useful approximations to the ITS90 are given in "Techniques for Approximating the ITS90".
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 T_{90}  T_{68} 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 IPTS68 is, in many areas, substantially worse than is implied by this number.
Table 6. Differences between ITS&endash;90 and EPT&endash;76, and betweenITS&endash;90
and IPTS&endash;68 for specified values of T_{90} and t_{90}.
(T_{90}  T_{76})/mK

T_{90}/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

.

.


(T_{90}  T_{68})/K

T_{90}/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


T_{90}/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

.

.


(t_{90}  t_{68})/°C

t_{90}/°C

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


t_{90}/°C

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


t_{90}/°C

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 (t_{90}  t_{68}) occurs at a temperature of t_{90} = 630.6 °C, at which (t_{90}  t_{68}) =  0.125 °C
Foot Notes
^{1 }Comptes Rendus des Séances de la Treiziéme Conférence Générale des Poids es Mesures (1967  1968), Resolutions 3 and 4, p.104
^{2}Note that this definition of W (T_{90}) differs from the corresponding definition used in the ITS27, ITS48, IPTS48, and IPTS68: for all of these earlier scales W (T) was defined in terms of reference temperature of 0°C, which since 1954 has itself been defined as 273.15 K
^{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 ITS90"
^{4 }The T_{90} 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 T_{90}(X) will not result in significant differences in the measured values of T_{90}.
Appendix
The International Temperature Scale of 1927 (ITS27)
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 ITS27 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 °C. 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 (ITS48)
The International Temperature Scale of 1948 was adopted by the ninth General Conference. Changes from the ITS27 were: the lower limit of platinum resistance thermometer range was changed from 190 °C to the defined oxygen boiling point of 182.97 °C, and the junction of the platinum resistance thermometer range and the thermocouple range became the measured antimony freezing point (about 630 °C) in place 660 °C; the silver freezing point was defined as being 960.8 °C instead of 960.5 °C; the gold freezing point replaced the gold melting point (1063 °C); 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) (IPTS48)
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 ITS48 were: the triple point of water, defined as being 0.01 °C, replaced the freezing point of zinc, defined as being 419.505 °C, became a preferred alternative to the sulphur boiling point (444.6 °C) 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 IPTS48 were the same as on the ITS48, 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 (IPTS68)
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 IPTS68 incorporated very extensive changes from the IPTS48. 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 °C) 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 °C), the freezing point of silver (961.93 °C), and the freezing point of gold (1064.43 °C): the interpolating formulae for the resistance thermometer range became much more complex; the value assigned to the second radiation constant c_{2} 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) (IPTS68)
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 IPTS48 with respect to the ITS48, the IPTS68 (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 ^{4}He and 1962 ^{3}He vapourpressure scales was rescinded.
The 1976 Provisional 0.5 K to 30 K Temperature Scale (EPT76)
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 IPTS68 and throughout the temperature ranges of the ^{4}He and ^{3}He 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 ETP76 were "that it should be thermodynamically smooth, that it should be continuous with the IPTS68 at 27.1 K, and that is should agree with thermodynamic temperature T as closely as these two conditions allow". In contrast with the IPTS68, and to ensure its rapid adoption, several methods of realizing the ETP76 were approved. These included: using a thermodynamic interpolation instrument and one or more of eleven assigned reference points; taking differences from the IPTS68 above 13.81 K; taking differences from certain wellestablished 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 EPT76 as a working scale until such time as the IPTS68 should be revised and extended were considered to outweigh the disadvantages.
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