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 (ITS90) 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 (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 T90 are defined. Several of these ranges or subranges 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 ITS90" (BIPM1990).
The ITS90 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 (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 (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 vapourpressure 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 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 T90 is defined in terms of the vapour pressure p of 3He and 4He using equations of the form:
9
T90/K = Ao+∑Ai[(in (p/Pa) —B)/C)i
i=1
The values of the constants A0, 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 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 3He or a 4He vapour pressure thermometer as specified in Sect. 3.1.
Table 1. Defining fixed points of the ITS90
Temperature  

Number  T_{90}/K  t_{90}/ºC  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 3He are of natural isotopic composition, eH2 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 (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
^{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 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 nonideality of the gas must be accounted for explicitly, using the appropriate second virial coefficient B3 (T90) or B4 (T90). In this range T90 is defined by the relation:
T90 = a + bp + cp2/1 + Bx(T90) NIV
where p is the pressure in the gas thermometer, a, b and c are coefficients the numerical values of which are obtained from measurements at three defining temperatures as given in Sect. 3.2, N/V is the gas density with N being the quantity of gas and V the volume of the bulb, X is 3 or 4 according to the isotope used, and the values of the second virial coefficients are given by the relations:
B(T90)/m3mol1={16,69 — 336,98(T90/K)1
+91,04(T90/K)2—13,82(T90/K)3} 106
For 4He
B4(T90)/m3mol1={15,708—374,05(T90/K)1
—383,53(T90/K)22 + 1799,2(T90/K)3
—4033,2(T90/K)4 + 3252,8 (T90/K)3} 106
Table 4. The constants A0, Ai; Bn, Bi; C0, Ci; D0 and Di 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 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 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 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:
W(T90)=R(T90)/IR(273,16K)
2 Note that this definition of W (T90) 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 0ºC, which since 1954 has itself been defined as 273.15 K
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(27,7646°C)=1,118,07
W)—38,8344°C)=0,844 235
An acceptable platinum resistance thermometer that is to be used up to the freezing point of silver must also satisfy the relation:
W(961,78°C)=4,2844
In each of the resistance thermometer ranges, T90 is obtained from W (T90) as given by the appropriate reference function {Eqs. (9b) or (10b)}, and the deviation W(T90)  Wr(T90). At the defining fixed points this deviation is obtained directly from the calibration of the thermometer: at intermediate temperatures it is obtained by means of the appropriate deviation function {Eqs. (12), (13) and (14)}.
(i)  For the range 13.8033 K to 273.16 K the following reference function is defined:
12
(9a.)In [Wr(T90)]=A0 + ?Ai[In (T90)/273,16K + 1,5/1,5]i
i=1
An inverse fnction, equivalent to Eq.(9a.) to within 0,1 mK, is:
15
(9b.) T90/273,16K = B0 + ? Bi[Wr(T90)1/6 —0,65/0,35]i
i=1
The values of the constants A0, Ai, B0 and Bi are given in Table 4.
A thermometer may be calibrated for use throughout this range or, using progressively fewer calibration points, for ranges with low temperature limits of 24.5561 K, 54.3584 K and 83.8058 K, all having an upper limit of 273.16 K.
(ii)  For the range 0 ºC to 961.78 ºC the following reference function is defined:
9
(10a.) Wr(T90) = C0 + ?Ci[T90/K — 754,15/481]i
i=1
An inverse function, equivalent to equation (10a.) to within 0,13 mK is:
9
(10b.) T90/K — 273,15 = D0 + ? Di[Wr(T90) — 2,64/1,64]i
i=1
The values of the constants C0, Ci, D0 and Di are given in Table 4.
A thermometer may be calibrated for use throughout this range or, using fewer calibration points, for ranges with upper limits of 660.323 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 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:
T90/K  17.035 = (p/kPa  33.3213)/13.32 (11a)
T90/K  20.27 = (p/kPa  101.292)/30 (11b)
(11a.) T90/K — 17,035 = (p/kPa — 33,3213)/13,32
(11b.) T90/K — 20,27 = (p/kPa — 101,292)/30
The deviation function is3
5
(12.) W(T90) — Wr(T90) = a[W(T90)—1] + b[W(T90)—]2 + ? ci[In W(T90)]i+n
i=1
3 This deviation function {and also those of Eqs. (13) and (14)} may be expressed in terms of Wr rather than W; for this procedure see "Supplementary Information for ITS90"
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 subranges 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  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 ºC  
Section  Lower temperature limit (t/ºC) 
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 ºC) to 29.7646 ºC  
3.3.3  As for 3.3.2 with c = d = 0  810 
* Calibration points 9, 1214 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:
(13.) W(T90) — Wr(T90) = a[W(T90)—1] + b[W(T90)—1] In W(T90)
with the values of a and b being obtained from measurements at the defining fixed points.
3.3.2. From 0 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:
(14.) W(T90) — Wr(T90) = a[W(T90)—1] + b[W(T90)—1]2 + c[W(T90)—1]3 + d[W(T90)—W(660,323 °C)]2
For temperatures below the freezing point of aluminium d = 0, with the values of a, b and c being determined from the measured deviations from 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 subranges 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:
(15.) L?(T90)/L?[(T90(X)]=exp(c2[?T90(X)]1)—1/exp(c2[?T90]1)—1
where T90(X) refers to any one of the silver {T90(Ag) = 1234.93 K}, the gold {T90(Au) = 1337.33 K} or the copper {T90(Cu) = 1357.77 K} freezing points4 and in which Llambda(T90) and Llambda[T90(X)] are the spectral concentrations of the radiance of a blackbody at the wavelength (in vacuo) lambda at T90 and at T90(X) respectively, and c2 = 0.014388 m · K
. For practical details and current good practice for optical pyrometry, see "Supplementary Information for the ITS90" (BIPM1990).
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 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 T90  T68. 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 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 IPTS68 is, in many areas, substantially worse than is implied by this number.
Table 6. Differences between ITS90 and EPT76, and between ITS90 and IPTS68 for specified values of T90 and t90.
Table 6. Differences between ITS90 and EPT76, and between ITS90 and IPTS68 for specified values of T90 and t90.
(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})/ºC  
t_{90}/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 
t_{90}/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 
t_{90}/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