The
International Temperature 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 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.:
t_{90} / ºC = T_{90} / 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 T_{90} is defined in terms of the vapour pressure
p of ^{3}He and ^{4}He using equations of the
form:
9 
T_{90}/K = A_{o}+∑A_{i}[(in (p/Pa) —B)/C)^{i} 
i=1 
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 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 ^{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 (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 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 B3 (T_{90}) or B4 (T_{90}). In this
range T_{90} is defined by the relation:
T_{90} = a + bp + cp^{2}/1 + B_{x}(T_{90}) NIV
where
p is the pressure in the gas thermometer, a, b and c are coefficients
the numerical values of which are obtained from measurements at
three defining temperatures as given in Sect. 3.2, N/V is the
gas density with N being the quantity of gas and V the volume
of the bulb, X is 3 or 4 according to the isotope used, and the
values of the second virial coefficients are given by the relations:
For ^{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}
For ^{4}He
B_{4}(T_{90})/m^{3}mol^{1}={15,708—374,05(T_{90}/K)^{1}
—383,53(T_{90}/K)^{2}^{2} + 1799,2(T_{90}/K)^{3}
—4033,2(T_{90}/K)^{4} + 3252,8 (T_{90}/K)^{3}} 10^{6}
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 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(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})/IR(273,16K)
^{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 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, 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})
 Wr(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:
_{12} (9a.)In [W_{r}(T_{90})]=A_{0} + ∑A_{i}[In (T_{90})/273,16K + 1,5/1,5]^{i} ^{i=1}
An inverse fnction, equivalent to Eq.(9a.) to within 0,1 mK, is:
_{15} (9b.) T_{90}/273,16K = B_{0} + ∑ B_{i}[W_{r}(T_{90})^{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.) W_{r}(T_{90}) = C_{0} + ∑C_{i}[T_{90}/K — 754,15/481]^{i} ^{i=1}
An inverse function, equivalent to equation (10a.) to within 0,13 mK is:
_{9} (10b.) T_{90}/K — 273,15 = D_{0} + ∑ D_{i}[W_{r}(T_{90}) — 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:
T_{90}/K
 17.035 = (p/kPa  33.3213)/13.32 (11a)
T_{90}/K
 20.27 = (p/kPa  101.292)/30 (11b)
(11a.) T_{90}/K — 17,035 = (p/kPa — 33,3213)/13,32
(11b.) T_{90}/K — 20,27 = (p/kPa — 101,292)/30
The deviation function is^{3}
_{5} (12.) W(T_{90}) — W_{r}(T_{90}) = a[W(T_{90})—1] + b[W(T_{90})—]^{2} + ∑ c_{i}[In W(T_{90})]^{i+n}
^{i=1}
^{3}
This deviation function {and also those of Eqs. (13) and (14)}
may be expressed in terms of W_{r} rather than W; for
this procedure see "Supplementary Information for ITS90"
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
thermometers in 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 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 t_{90}
<= 660.323 ºC; the values of a, b and c thus obtained are retained
for t_{90} => 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(T_{90}) — W_{r}(T_{90}) = a[W(T_{90})—1] + b[W(T_{90})—1] In W(T_{90})
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(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}
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 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 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 ºC): Planck
Radiation Law
Above
the freezing point of silver the temperature T90 is defined by
the equation:
(15.) Lλ(T_{90})/Lλ[(T_{90}(X)]=exp(c_{2}[λT_{90}(X)]^{1})—1/exp(c_{2}[λT_{90}]^{1})—1
where
T_{90}(X) refers to any one of the silver {T90(Ag) = 1234.93
K}, the gold {T_{90}(Au) = 1337.33 K} or the copper {T90(Cu)
= 1357.77 K} freezing points4 and in which Llambda(T_{90})
and Llambda[T_{90}(X)] are the spectral concentrations
of the radiance of a blackbody at the wavelength (in vacuo) lambda
at T_{90} and at T_{90}(X) respectively, and c_{2}
= 0.014388 m · K
.
For practical details and current good practice for optical pyrometry,
see "Supplementary Information for the ITS90" (BIPM1990).
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}.
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}  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 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 ITS90 and EPT76, and between ITS90 and
IPTS68 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})/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 (t_{90}  t_{68})
occurs at a temperature of t90 = 630.6 ºC, at which (t_{90}
 t_{68}) =  0.125 ºC
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 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 (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
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 102 m · K in place of 1,432 x 102 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<3x103
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 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 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 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 102 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 4He and 1962 3He 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 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 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.
