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.

ii) — A thermometer may be calibrated for use in the
range 234,3156 K (—38,8344°C) to 29,7646°C, the cali-
bration 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 form
in Table 5.

3.3.4. 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 equi-
librium 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 deter-
mined 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 204K
respectively; or by using the vapour pressure-temperature
relation of equilibrium hydrogen, in which case the two
temperatures must lie within the ranges 17,025K to
17,045 K and 20,26 K to 20,28 K respectively, with the
precise values being determined from Eqs. (11 a) and (11 b)
respectively:

Too/K —17,035 = (p/kPa—33,3213)/13,32

Too/K —20,27 = (p/kPa—101,292)/30 .

_The deviation function is*:

W(Tyo)— W, (Too) = @[W (Tyo) —1] + [W (Too) —11?

+3 ella W (Tol (2)

(11a)
(11)

with values for the coefficients a, b and c, being obtained
from measurements at the defining fixed points and with
n=2.

For this range and for the sub-ranges 3.3.1.1 to 3.3.1.3
the required values of W, (To) 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,, c, and c, being obtained from
measurements at the defining fixed points and with
C4=Cs=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

3 This deviation function {and also those of Eqs. (13) and (14)} may
be expressed in terms of W, rather than W; for this procedure see
“Supplementary Information for ITS-90”

7

Table 5. Deviation functions and calibration points for platinum
resistance thermometers in the various ranges in which they define
Tyo

a Ranges with an upper limit of 273,16 K

Sec. Lower Deviation functions Calibration

tion temper- points
ature limit (sce Table 1)
T/K

331 13,8033 a[W(Toq)—1]+[W (Too)—1P 2~9

+ fla W (Toll, n=2
fort

24,5561 As for 3.3.1 with c,=cg=n=0 2,5-9
54,3584 As for 3.3.1 with -9
cp =CyCq=Cs=0, mel
3.3.1.3 83,8058 a[ PY (Too)~1] 1-9
+B{W (Toq)—1] In W (Tao)
b Ranges with a lower limit of 0°C
Sec- Upper _—_Deviation functions Calibration
tion temper- points
ature limit (see Table 1)
tec
33.2% 961,78 a[W(Too)—1]-+b[W (Toq)—1? 9, 12-15
+e [W Tyo) 1] +d (W (Too)
— W (660,323 °C)?
33.24 660,323 As for 3.3.2 with d= 9,12-14
33.22 419,527 As for 3.3.2 with 9, 12, 13
33.2.3 231,928 As for 3.3.2 with c= 9,11, 12
3.3.24 1565985 As for 3.3.2 with 9
3.3.2.5 29,7646 As for 3.3.2 with b= 9

¢ Range from 234,3156 K (—38,8344°C} to 29,7646°C
3.3.3 As for 3.3.2 with c=d=0 8-10

* Calibration points 9, 12-14 are used with d=0 for to<
660,323 °C; the values of @, 6 and c thus obtained are retained for
fo9 > 660,323°C, with d being determined from calibration point 15

calibrated at the triple points of oxygen (54,3584 K),
argon (83,8058 K), mercury (234,3156K) and water
(273,16 K).

The deviation function is given by Eq. (12) with values
for the coefficients a, b and c, being obtained from mea-
surements at the defining fixed points, with c,=c,;=
c,=¢s=0 and with n=1.

3.3.4.3. 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), mer-
cury (234,3156 K) and water (273,16 K).
The deviation function is:

W (Tyo) — W,(Too) = a[W (Too) — 1]

+b [W (Too)—1] In W (Too) (13)
with the values of a and b being obtained from measure-
ments at the defining fixed points.

3.3.2. From O°C to the Freezing Point of Silver
(961,78°C). The thermometer is calibrated at the triple



10

tion formulae for the standard resistance thermometer and thermo-
couple were modified; the limitation on AT for optical pyrometry
(AT-<3 x 1073 m - K) was changed to the requirement that “visible”
radiation be used.

The International Practical Temperature Scale
of 1948 (Amended Edition of 1960) (IPTS-48)

The International Practical Temperature Scale of 1948, amended
edition of 1960, was adopted by the eleventh Gencral Conference:
the tenth General Conference had already adopted the triple point
of water as the sole point defining the kelvin, the unit of thermody-
namic temperature. In addition to the introduction of the word
“Practical”, the modifications to the ITS-48 were: the triple point
of water, defined as being 0,01 °C, replaced the melting point of ice
as the calibration point in this region; 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 stan-
dard resistance thermometer and the thermocouple were further
modified; the restriction to “visible” radiation for optical pyrome-
try was removed.

Inasmuch as the numerical values of temperature on the IPTS-
48 were the same as on the ITS-48, the former was not a revision of
the scale of 1948 but merely an amended form of it.

The International Practical Temperature Scale
of 1968 (IPTS-68)

In 1968 the International Committee of Weights and Measures
promulgated the International Practical Temperature Scale of 1968,
having been empowered to do so by the thirteenth General Confer-
ence of 1967-1968. The IPTS-68 incoporated very extensive
changes from the IPTS-48. These included numerical changes, de-
signed to bring it more nearly in accord with thermodynamic tem-
peratures, 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
5,2K), the use of two helium vapour pressure scales was recom-
mended; six new defining fixed points were introduced ~ the triple
point of equilibrium hydrogen (13,81 K), an intermediate equilibri-
um hydrogen point (17,042 K), the normal boiling point of equilib-
rium 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 freez-
ing point of silver (961,93°C), and the freezing point of gold

(1064,43°C); the interpolating formulae for the resistance ther-
mometer range became much more complex; the value assigned to
the second radiation constant c, became 1,4388 x 107? m- K; the
permitted ranges of the constants for the interpolation formulae for
the resistance thermometer and thermocouple were again modified.

The International Practical Temperature Scale
of 1968 (Amended Edition of 1975) (IPTS-68)

The International Practical Temperature Scale of 1968, amended
edilion of 1975, was adopted by the fifteenth Gencral Conference in
1975. As was the case for the IPTS-48 with respect to the ITS-48,
the IPTS-68(75) introduced no numerical changes. Most of the
extensive textural changes were intended only to clarify and simplify
its use. More substantive changes were: the oxygen point was de-
fined 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 “He and 1962
3He vapour-pressure scales was rescinded.

The 1976 Provisional 0,5 K to 30 K Temperature Scale
(EPT-76)

The 1976 Provisional 0,5 K to 30 K Temperature Scale was intro-
duced to meet two important requirements: these were to provide
means of substantially reducing the errors (with respect to corre-
sponding thermodynamic values) below 27 K that were then known
to exist in the IPTS-68 and throughout the temperature ranges of
the *He and *He vapour pressure scales of 1958 and 1962 respective-
ly, and to bridge the gap between 5,2 K and 13,81 K in which there
had not previously been an international scale. Other objectives in
devising the ETP-76 were “that it should be thermodynamically
smooth, that it should be continuous with the IPTS-68 at 27,1 K,
and that is should agree with thermodynamic temperature T as
closely as these two conditions allow”. In contrast with the IPTS-68,
and to ensure its rapid adoption, several methods of realizing the
ETP-76 were approved. These included: using a thermodynamic
interpolation instrument and one or more of eleven assigned refer-
ence points; taking differences from the IPTS-68 above 13,81 K;
(aking differences from helium vapour pressure scales below 5 K;
and taking differences from certain well-established laboratory
scales. Because there was a certain “lack of internal consistency” it
was admitted that “slight ambiguities between realizations” might
be introduced, However the advantages gained by adopting the
EPT-76 as a working scale until such time as the IPTS-68 should be
revised and extended were considered to outweigh the disadvan-
tages.


6

Table 4. The constants Ag, Aj; By, B,; Co, C,3 Do and D, in the
reference functions of equations (9.); (9b); (10a); and (10b) respec-
tively

Ay —2,13534729 By
A, — 318324720 B,
A, —1,801 43597 B,
A; 0,71727204 By
As 0,503 44027 By
As —0,618 99395 Be
Ag —0,053 32322 Bg
A, — 0,28021362 B,

Ag 0,107 15224 Bg

0,183 324722 By; —0,091 173 542
0,240 975 303 By, 0,001 317 696
0,209 108771 By, 0,026 025 526
0,190 439 972

0,142 648 498
0,077 993 465
0,012 475 611
—0,032 267 127

—0,075 291 522

Ay —0,29302865 By —0,056 470 670
Aro 004459872 Big 0,076 201 285
Ay, 0,118 68632 By, 0,123 893 204

A,, —0,052 481 34 B,, —0,029 201 193

Co 2,781 57254 Dy 439,932 854
Cc, 1,646 50916 D, 472,418 020

C, —0,13714390 D, 37,684.494
Cs —0,006 49767 D,  7,472018
Cy, —0,002 34444 D, 2920828
Cs 0,005 11868 D, 0,005 184
Ce 0,001 879.82 Dg —0,963 864
C, —0,00204472 D, —0,188732
Cy —0,00046122 Dy 0,191 203
C. 0,000.45724 Dy 0,049 025

The accuracy with which T,, 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 Tg, is defined by means of a platinum resis-
tance 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 normaily 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
the ITS-90”. It is particularly important to take account
of the appropriate heat treatments that should be fol-
lowed 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 (Too) at a temperature T,, and the resis-

tance R (273,16 K) at the triple point of water. This ratio,
W (Too), i8?:

W (Too) = R (Too)/R 273,16 K). 1)

An acceptable platinum resistance thermometer must
be made from pure, strain-free platinum, and it must sat-
isfy at least one of the following two relations:

W (29,7646 °C)> 1,118 07, (8a)
W (—38,8344°C)<0,844 235. (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 . (80)

In each of the resistance thermometer ranges, To, is
obtained from W, (Tyo) as given by the appropriate refer-
ence function {Eqs.(9b) or (10b)}, and the deviation
W (Too)— W, (Too). At the defining fixed points this devia-
tion is obtained directly from the calibration of the ther-
mometer: 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:

tn [1% (Tool = Ao+ ¥ 4, [pnens 0+ 09

An inverse function, equivalent to Eq. (9a) to within
0,1 mK, is:

Tue. i
Tyo/273,16 K = Bot ©: B, [ze] 0b)
fest

0,35

The values of the constants 49, A;, By and B, 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 refer-
ence function is defined:

Tao Toss

81 (10a)

8
W, (Tag) = Cot al
An inverse function, equivalent to equation (10a) to with-
in 0,13 mK is:
9 -
TyolK-27315 = Do+ YD, [ze
ie

164 ] - (10)

The values of the constants Cy, C;, Dy and D, are given in
Table 4.

2 Note that this definition of W (Tq) differs from the corresponding
definition used in the ITS-27, ITS-48, IPTS-48, and IPTS-68: for all
of these earlier scales W(T) was defined in terms of a reference
temperature of 0°C, which since 1954 has itself been defined as
273,15 K



8

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 (Too) — W, (Too) = a1W (Too) H+ BIW (Too) AP (14)
+¢[W (Tyo)— 11 +4 [W (Too) — W (660,323 °C)P .

For temperatures below the freezing point of aluminium
d=0, with the values of a, b and ¢ being determined from
the measured deviations from W.(Tyo) 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 ¢ are retained and the value of d is
determined from the measured deviation from W, (Tyo) at
the freezing point of silver.

For this range and for the sub-ranges 3.3.2.1 to 3.3.2.5
the required values for W,(Tyo) 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 (0,01 °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 indi-
um (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 e=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 defin-
ing 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 at the melting point of galli-
um (29,7646 °C).

The deviation function is given by Eg. (14) with the
value of a being obtained from measurements at the defin-
ing 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,(Ty.) are obtained from
Egs. (9a) and (10a) for measurements below and above
273,16 K respectively, or from Table t.

3.4. The Range Above the Freezing Point of Silver
(961,78°C): Planck Radiation Law

Above the freezing point of silver the temperature Tyo is
defined by the equation:

_L, (Too) _ &xP (621A Ho) )—1
Ly [Too(X)] exp (c2[4 Too] ")~1

where Ty, (X) refers to any one of the silver {To (Ag)
= 1234,93K}, the gold {T5.(Au)=1337,33 K} or the
copper {Tyo (Cu)=1357,77 K} freezing points* and in
which L,(Too) and L,[Tyo(X)] are the spectral concen-
trations of the radiance of a blackbody at the wavelength
{in vacuo) A at Ty, and at T5,(X) respectively, and
c, =0,014388 m+ K.

For practical details and current good practice for
optical pyrometry, see “Supplementary Information for
the ITS-90” (BIPM-1990).

(15)

4, Supplementary Information and Differences
from Earlier Scales

The apparatus, methods and procedures that will serve to
realize the ITS-90 are given in “Supplementary Informa-
tion for the ITS-90”. This document also gives an account
of the earlier International Temperature Scales and the
numerical differences between successive scales that in-
clude, where practicable, mathematical functions for the
differences Ty —- T.g. A number of useful approximations
to the ITS-90 are given in “Techniques for Approximating
the ITS-90”.

These two documents have been prepared by the
Comité Consultatif de Thermométrie and are published
by the BIPM; they are revised and updated periodically.

The differences T,,—T,g are shown in Fig. 41 and
Table 6. The number of significant figures given in Table 6
allows smooth interpolations to be made. However, the
reproducibility of the IPTS-68 is, in many areas, substan-
tially worse than is implied by this number.

4 The Tyo 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 Jy9(X) will not result in significant differences in the
measured values of Tyo.


Metrologia 27, 3-10 (1990)

metrologia

© Springer-Verlag 1990

This copy incorporates textual corrections detailed in Metrologia 27,
107 (1990)

The International Temperature Scale of 1990 (ITS-90)

H. Preston-Thomas

President of the Comité Consultatif de Thermométrie and Vice-President of the Comité International des Poids et Mesures
Division of Physics, National Research Council of Canada, Ottawa, K1A 0S{ Canada

Received: October 24, 1989

Introductory Note

The official French text of the ITS-90 is published by the
BIPM as part of the Procés-verbaux of the Comité Inter-
national des Poids et Mesures (CIPM). However, the
English version of the text reproduced here has been au-
thorized 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 adopt-
ed by the International Committee of Weights and Mea-
sures at its mecting in 1989, in accordance with the re-
quest 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 Provi-
sional 0,5 K to 30 K Temperature Scale.

1. Units of Temperature

The unit of the fundamental physical quantity known as
thermodynamic temperature, symbol 7, is the kelvin,
symbol K, defined as the fraction 1/273,16 of the thermo-
dynamic temperature of the triple point of water '.

Because of the way earlier temperature scales were
defined, it remains common practice to express a temper-
ature 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:

tC = T/K ~273,15. (1)

* Comptes Rendus des Séances de la Treiziéme Conférence Géné-
tale des Poids ct Mesures (1967-1968), Resolutions 3 and 4, p. 104

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 kelvins or degrees Celsius.

The International Temperature Scale of 1990 (ITS-90)
defines both International Kelvin Temperatures, symbol
Tyo, and International Celsius Temperatures, symbol tg.
The relation between Ty) and too is the same as that
between T and ¢, ie.:

tgo/°C = Tyo /K ~273,15. (2)

The unit of the physical quantity 7, is the kelvin,
symbol K, and the unit of the physical quantity tg is the
degree Celsius, symbol °C, as is the case for the thermody-
namic temperature T and the Celsius temperature t.

2. Principles of the International Temperature Scale
of 1990 (ITS-90)

The ITS-90 extends upwards from 0,65 K to the highest
temperature practicably measurable in terms of the
Planck radiation law using monochromatic radiation.
The ITS-90 comprises a number of ranges and sub-ranges
throughout each of which temperatures Ty. are defined.
Several of these ranges or sub-ranges overlap, and where
such overlapping occurs, differing definitions of Tyg exist:
these differing definitions have equal status. For measure-
ments of the very highest precision there may be detect-
able numerical differences between measurements made
at the same temperature but in accordance with differing
definitions. Similarly, even using one definition, at a tem-
perature between defining fixed points two acceptable
interpolating instruments (e.g. resistance thermometers)
may give detectably differing numerical values of To). In
virtually all cases these differences are of negligible practi-
cal importance and are at the minimum level consistent
with a scale of no more than reasonable complexity: for
further information on this point, see “Supplementary
Information for the ITS-90” (BIPM-1990).


Table 6. Differences between ITS-90 and EPT-76, and between ITS-90 and IPTS-68 for specified values of Tyo and tog

{Tyo — The) K
Tao/K. 0 1 2 3 4 5 6 7 8 9
0 -0,i -02 —03 —04 —05
10 ~06 —08 -1.0 -11 =13 -14 -1,6 ~18 —20
20 22 27 —30 -3,2 ~35 —38 —44
(Too Tes VK
Tyo/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 0,005 —0,005 | 0,004 = 0,004. +» 0,005 —0,006
30 —0,006 —0,007 0,008 + —0,008 + 0,008 + —0,007 | 0007-0007 | 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 —0,005 0,004 0,003  -0002 -9,001 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
Too /K 0 10 20 30 40 50 60 70 80 90
100 0,009 0011 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
{too —fegh/°C
too /°C 0 —10 ~20 —30 —40 —50 —60 ~10 —80 -90
—100 0,013 0,013 0014 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 0012
tyg/°C 0 10 20 30 40 50 60 10 80 90
0 0,000 = —0,002 —0,005 0,007 0,010 -0,013 0016 = 0.018 += 0021 — 0,024
100 —0,026 —0,028 0,030 0032 -0034 0036  -0037 0038 0039  —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 0059-0062 —0,065 0.068 += —-0,072- —0,075
500 —0,079 —0,083 0,087 ~0,090 0094-0098» 0,101 0105 © 0,108» 0,112
600 0115  —0,118 0,122. 0,125 008 ~003 0,02 0,06 Ou 0,16
700 0,20 024 0,28 0331 0,33 0,35 036 0,36 0,36 0,35
800 0,34 032 0,29 0,25 0,22 0,18 014 0,10 0,06 0,03
900 —001 -003 0,06 008  ~010 012 014 -016  —017 —o18
1000 —0,19 -0,20 -0,21 = 0.22. 0.23 024 = 025 0.25 026 ©=— 026
tao fC 0 100 200 300 400 500 600 700 800 900
1000 026 0,30 035 039 044 049 —05¢ 060 0,66
2000 072-079-085 0,93 400 107,115. 424 182-1,
3000 -150 =159 1,69 1,78 189-199 210 221 232, 2.43.
* A discontinuity in the first derivative of (to9—teg) Occurs at a temperature of tg 630,6°C,at which (ts9—t54)= —0125°C

Appendix

The International Temperature Scale of 1927 (ITS-27)

The International Temperature Scale of 1927 was adopted by the
seventh General Conference of Weights and Measures to overcome
the practical difficulties of the direct realization of thermodynamic
temperatures by gas thermometry, and as a universally acceptable
replacement for the differing existing national temperature scales.
The ITS-27 was formulated so as to allow measurements of temper-
ature to be made precisely and reproducibly, with as close an ap-
proximation to thermodynamic temperatures as could be deter-
mined at that time. Between the oxygen boiling point and the gold
freezing point it was based upon a number of reproducible temper-
atures, 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 tem-
perature range. A platinum resistance thermometer was used for the
lower 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 (ITS-48)

The International Temperature Scale of 1948 was adopted by the
ninth General Conference. Changes from the ITS-27 were: the low-
er limit of the 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 of 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 radia-
tion law replaced the Wien law; the value assigned to the second
radiation constant became 1,438 x 10"? m-K in place of 1,432 x
10-? m - K; the permitted ranges for the constants of the interpola-



| T 7
—— 1 —1 —
0,02 4
C) ~
2 nl 4 04
2-002, 4
. |
2 -o04|
= I +92
8 poi fy gd
§ B00 0 200 400 4
s
3 ° °
§ ‘k i -° |
2 [ a
3
=
-oo1

& -O2- 70,2

L. -o0e| 4

N Fig. 1. The differences (to9—teg) a8 a
a aT ; i —t—h ! function of Celsius temperature t
=200 0 200 400 600 800 1000 Ps 90
tag /°C

The ITS-90 has been constructed in such a way that,
throughout its range, for any given temperature the nu-
merical value of Tyo is a close approximation to the nu-
merical value of T according to best estimates at the time
the scale was adopted. By comparison with direct mea-
surements of thermodynamic temperatures, measure-
ments of T,, are more easily made, are more precise and
are highly reproducible.

There are significant numerical differences between
the values of Tj) and the corresponding values of Ty,
measured on the International Practical Temperature
Scale of 1968 (IPTS-68), see Fig. 1 and Table 6. Similarly
there were differences between the IPTS-68 and the Inter-
national Practical Temperature Scale of 1948 (IPTS-48),
and between the International Temperature Scale of 1948
(ITS-48) and the International Temperature Scale of 1927
(ITS-27). See the Appendix and, for more detailed infor-
mation, “Supplementary Information for the ITS-90”.

3. Definition of the International Temperature Scale
of 1990

Between 0,65 K and 5,0 K 1,, is defined in terms of the
vapour-pressure temperature relations of *He and “He.

Between 3,0K and the triple point of neon
(24,5561 K) Tyo is defined by means of a helium gas ther-
mometer 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
(43,8033 K) and the freezing point of silver (961,78°C) Tyo
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) Tyo is
defined in terms of a defining fixed point and the Planck
radiation law.

The defining fixed points of the ITS-90 are listed in
Table 1. The effects of pressure, arising from significant
depths of immersion of the sensor or from other causes,
on the temperature of most of these points are given in
Table 2.

3.1. From 0,65 K to 5,0 K: Helium Vapour-Pressure
Temperature Equations

In this range Tyo is defined in terms of the vapour pressure

p of 5He and *He using equations of the form:
9 :

TaolK = Agt 2 A: (in (p/Pa)— BY/C]. 3)

The values of the constants Ay, A;, B and C are given in

Table 3 for *He in the range of 0,65 K to 3,2 K, and for

“He in the ranges 1,25 K to 2,1768 K (the 4 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 Tyo is defined in terms of a *He or a “He gas
thermometer of the constant-volume type that has been
calibrated at three temperatures. These are the triple
point of neon (24,5561 K), the triple point of equilibrium
hydrogen (13,8033 K), and a temperature between 3,0 K.
and 5,0K. This last temperature is determined using a
He or a *He vapour pressure thermometer as specified in
Sect. 3,1.



Table 1. Defining fixed points of the ITS-90

Num- Temperature Sub- State? W,(Ty9)
ber ———_ | stance*
Too/K tgofC
1 3 to 5 —27015to He v
— 268,15
2 13,8033 —259,3467 eH, T 0,001 190 07
3 wT we — 256,15 eH, V
(or He) (or G)
4 20,3 —252,85 eH, V
(or He) (or G)

5 24,5561 —248,5939 Ne T 0,008 449 74
6 54,3584 —218,7916 O, 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,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

* All substances except *He are of natural isotopic composition,
e-H, is hydrogen at the equilibrium concentration of the ortho- and
pata-molecular forms

° For complete definitions and advice on the realization of these
various states, see “Supplementary Information for the ITS-90”. The
symbols have the following meanings: V: vapour pressure point;
T: triple point (temperature at which the solid, liquid and vapour
phases are in equilibrium); G: gas thermometer point; M, F: melting
point, freezing point (temperature, at a pressure of 101 325 Pa, at
which the solid and liquid phases are in equilibrium)

Table 2. Effect of pressure on the temperatures of some defining
fixed points *

Substance Assigned Temperature Variation
value of with pressure, p_ with depth, {
equilibrium (d7/dp)/ (anan/
temperature (10-®K-Pa7*)* (1073 K-m7)**
Tyo /K

e-Hydrogen (T) 13,8033 34 0,25

Neon (T) 24,5561 16 19

Oxygen (T) 54,3584 12 1,5

Argon (T) 83,8058 25 33

Mercury (T) 2343156 54 1M

Water (T) 27316 —7,5 -0,73

Gallium 302,9146  ~2,0 —12

Indium 429,7485 4,9 33

Tin 505,078 3,3 22

Zine 692,677 43 27

Aluminium 933,473 10 1,6

Silver 1234,93 60 54

Gold 1337,33 61 10

Copper 1357,77 33 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 (py =101 325 Pa). For triple points (T) the
pressure effect is a consequence only of the hydrostatic head of
liquid in the cell

5

Table 3. Values of the constants for the helium vapour pressure
Eqs. (3), and the temperature range for which each equation, identi-
fied by its set of constants, is valid

He *He He

0,65 K to3,2K 1,25 K to 21768 K 2,1768 K to 50K
Ag 1,053 447 1,392 408 3,146 631
A, 0,980 106 0,527 153 1,357 655
Az 0,676 380 0,166 756 0,413 923
A; 0,372 692 0,050 988 0,091 159
Ag 0,151 656 0,026 514 0,016 349
As —0,002 263 0,001 975 0,001 826
Ag 0,006 596 —0,017 976 —0,00 4325
A, 0,088 966 0,005 409 —0,00 4973
Ag 0,004 770 0,013 259 9
Ag —0,054 943 0 0
B 73 5,6 10,3
Cc 4,3 2,9 19

3.2.1. From 4,2 K to the Triple Point of Neon (24,5561 K)
with “He as the Thermometric Gas. In this range Tyq is
defined by the relation:

Ty =a+bptep’, (2)

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 restric-
tion 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 *He or “He as the Thermometric Gas. For a *He gas
thermometer, and for a *He gas thermometer used below
4,2 K, the non-ideality of the gas must be accounted for
explicitly, using the appropriate second virial coefficient
By (Too) or By (Too). In this range Tq is defined by the
relation:

__ atbptep®
ToT BB) NIV i)

where p is the pressure in the gas thermometer, a, b and
c are coefficients the numerical values of which are ob-
tained 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 *He,
By(Tgo)m? mol! = {16,69—336,98 (Tyo/K)"* (6a)
$:91,04 (Tyo/K}"? 13,82 (Too/K)~ >} 1078.
For *He,
Ba (Tyo)/m? mol”! = {16,708 — 374,05 (Tyo/K)"* (6b)
383,53 (Tyq/K)-?+ 1799,2 (Tyo/K)~?
~4033,2 (Tyo/K)~* + 3252,8 (Too/K)~ >} 107°.