MadSci Network: Physics
Query:

Re: WHY ON THE KELVIN TEMPERATURE SCALE IS THERE NO DEGREE SYMBOL?

Date: Mon Jan 29 12:36:59 2001
Posted By: Jaime Valencia-Rodríguez, Staff, Chemical Science and Technology Lab, NIST
Area of science: Physics
ID: 980626799.Ph
Message:

This is a very interesting question, and its answer calls for some 
antecedents:

First it is necessary to talk about the International System of Units, and 
in doing so, we need to mention the Convention of the Metre and the Bureau 
International des Poids et Mesures (http://www.bipm.fr)

The Convention of the Metre 
(Convention du Mčtre)
The Convention of the Metre is a diplomatic treaty between 
forty-nine nations which gives authority to the Conférence Générale des 
Poids et Mesures (CGPM), the Comité International des Poids et Mesures 
(CIPM) and the Bureau International des Poids et Mesures (BIPM) to act in 
matters of world metrology, particularly concerning the demand for 
measurement standards of ever increasing accuracy, range and diversity, and 
the need to demonstrate equivalence between national measurement standards. 
The Convention was signed in Paris in 1875 by representatives of seventeen 
nations. As well as founding the BIPM and laying down the way in which the 
activities of the BIPM should be financed and managed, the Metre Convention 
established a permanent organizational structure for member governments to 
act in common accord on all matters relating to units of measurement. 
The Convention, modified slightly in 1921, remains the basis of all 
international agreement on units of measurement. There are now forty-nine 
Member States, including all the major industrialized countries.

The International System of Units (SI)
The 11th Conférence Générale des Poids et Mesures (1960) adopted the name 
Systčme International d'Unités (International System of Units, 
international abbreviation SI), for the recommended practical system of 
units of measurement. 
The 11th CGPM laid down rules for the prefixes, the derived units, and 
other matters. The base units are a choice of seven well-defined units 
which by convention are regarded as dimensionally independent: the metre, 
the kilogram, the second, the ampere, the kelvin, the mole, and the 
candela. Derived units are those formed by combining base units according 
to the algebraic relations linking the corresponding quantities. The names 
and symbols of some of the units thus formed can be replaced by special 
names and symbols which can themselves be used to form expressions and 
symbols of other derived units. 
The SI is not static but evolves to match the world's increasingly 
demanding requirements for measurement.

It is clear now, I hope, that in order to ensure that the measurements we 
are making will be accepted by everybody, it is necessary for us to follow 
the BIPM rules and recommendations. This is more so because at the very end 
all measurements do have some economic impact (bad measurements mean bad 
products).

We are closer now to the answer you need. We need to know some 
organizational details of the BIPM:

Committee structure of the Metre Convention
Under the terms of the Metre Convention, the BIPM operates under the 
exclusive supervision of the Comité International des Poids et Mesures 
(CIPM), which itself comes under the authority of the Conférence Générale 
des Poids et Mesures (CGPM). The GPM elects the members of the CIPM and 
brings together periodically, at present once every four years, 
representatives of the governments of Member States. The CIPM has 
established a number of Consultative Committees, which bring together 
the world's experts in their specified fields as advisers on 
scientific and technical matters.
 
One of this Committees is the Consultative Committee for Thermometry whose 
main task is to provide sound basis for temperature measurements. It was 
established in 1937, and this year will hold its 21st meeting. During the 
first of those meetings the CCT organized all the work that had been made 
during the 60 previous years, ad over the following years it has been 
studying the reliability of the different versions of the International 
Temperature Scale.

Now it is necessary to talk a little about temperature and thermometers.
Temperature is the quantity more often measured in science and technology: 
nearly 35% of the money spent in metrology activities worldwide is invested 
in temperature measurement and its control.
Nevertheless temperature is not an easy thing to define or to measure. 
Temperature is a quantity that establishes the thermal equilibrium between 
two bodies or systems, and it can not be measured directly. In practice we 
always measure some other quantity (the thermometric property of a 
thermometer) that varies according to a known function with temperature. 
Among the most used thermometric properties are: pressure of a gas (gas 
thermometers), length of a liquid column (mercury thermometers), 
electromotive force (thermocouples), electric resistance (resistance 
thermometers) and spectral radiance (radiation thermometers).
If the response of a thermometer (its state equation) can be described 
using a function in which there are no quantities that depend on 
temperature in a unknown way, we say that the thermometer is a 
thermodynamic thermometer. Those thermometers need not to be calibrated, 
because its response is always known.
In the other hand, if the behavior of a thermometer is described using 
constants or variables that depends on temperature, we say that the 
thermometer is a practical one. Those thermometers require to be calibrated 
in order to provide meaningful responses.
Examples of thermodynamic thermometers are the gas thermometer and the 
radiation thermometer.
Mercury and alcohol thermometers, thermocouples, PRTs (Platinum Resistance 
Thermometers), RTDs (Resistance Temperature Devices) and thermistors are 
examples of practical thermometers.
Since the measurement of temperatures using a gas thermometer (which was 
the only thermodynamic thermometer available in the 19 century) is a 
cumbersome and very slow procedure, many efforts were performed in order to 
define reliable practical thermometers. Therefore at the end of the 19 
century and the beginning of the 20 century it was possible to speak of a 
thermodynamic temperature scale (obtained by means of a gas thermometer), 
and a practical temperature scale (obtained using mercury-in-glass 
thermometers).
It is considered that the modern thermometry was started by Chappius in 
1888 (see Quinn, T. J. Temperature, Academic Press, 1983). The overall aim 
of his work was to relate the readings of the very best mercury-in-glass 
thermometers to absolute (i.e. thermodynamic) temperature.
In 1899 Callendar made a proposal for a practical temperature scale (one 
based on the precise assignation of temperature to several equilibrium 
states, or fixed points, and an interpolating instrument possesing a well 
studied interpolating equation that describes its response). Callendar 
proposed also the use of a platinum resistance thermometer as the defining 
(interpolating) thermometer.
The advantages of such practical temperature scale were twofold: a platinum 
thermometer is a (relatively) easy to use instrument with fast response, 
and its reproducibility is much better than that of the best gas 
thermometers.
The first Temperature Scale was officially adopted in 1927. It covered the 
range from -182,97 °C (Note: According to the SI recommendations it is 
improper to write 182.97 °C) to 1063 °C.
New versions appeared on 1948, 1968 and 1990. This last version, the 
International Temperature Scale of 1990 is the only scale accepted 
internationally, it superseded all the previous Scales (see:Preston-Thomas, 
H. The International Temperature Scale of 1990 (ITS-90), Metrologia 27,3-10 
(1990)). It covers the range from 0,65 k to the highest temperature that 
could be measured using radiation thermometry.

We are almost there now, so pay attention. 
Now I will follow very closely the discussion in the book of Quinn already 
cited:
In 1960 an important change was made on the definition of the unit of 
thermodynamic temperature: the 1854 proposal of Kelvin was finally adopted, 
namely that the unit of thermodynamic temperature be defined in terms of 
the interval between the absolute zero and a single fixed point. The 
temperature of the triple point of water was fixed at exactly 0,01 °K (note 
that we are speaking of degrees Kelvin here) above the ice point, which in 
turn was assigned the thermodynamic temperature of 273,15 °K. This proposal 
was already been made in 1948 but at that time, there was still a 
divergence of view as to whether the absolute zero should be assigned a 
temperature of -273,15 °C or -273,16°C. The question was finally resolved 
in 1954 (and accepted by the CIPM in 1955), and the new definition of the 
degree Kelvin adopted by the 10th CGPM en 1960. This resulted in the 
curious situation that thermodynamic temperatures were defined in quite a 
different way to International Practical Temperatures (in which two fixed 
points were used for the definition of the degree Kelvin, and whose unit 
was also the degree Kelvin). It therefore became necessary to distinguish 
between the degree Kelvin (unit of thermodynamic temperature) and the 
International Practical degree Kelvin (unit of International Practical 
Kelvin Temperature, obtained from the International Practical Temperature 
Scale of 1948). The two were almost certainly not identically equal  since 
°K(Int-1948) was defined in terms of an interval of exactly 100 
°K(Int-1948) between the ice and the steam points, while °K(thermodynamic) 
was defined in terms of an interval of exactly 273,16 °K between the 
absolute zero and the triple point of water. Since the number 273,16 
resulted from experimental measurements using gas thermometers which have 
been calibrated at the ice (whose temperature was 0 °C by definition) and 
steam points (100 °C, also by definition), the two units °K(Int-1948) and 
°K(thermodynamic) would be identical if, and only if, these experiments had 
been exactly right in giving a temperature of -273,15 °C to the absolute 
zero.
This awkward situation was resolved in the 1968 revision of the Temperature 
Scale, when both thermodynamic and Practical units were defined to be 
identical and equal to 1/273,16 of the thermodynamic temperature of the 
triple point of water. The unit itself was renamed "the kelvin" in place of 
"degree Kelvin" and designated "K" instead of "°K". This left the interval 
between the ice and the steam points as an experimental quantity to be 
decided upon the basis of the best measurements of the thermodynamic 
temperature of the steam point (the best value is now of 99,975 °C). In the 
other hand, using an interval of 100 °C between the ice and the steam 
points leads to a value of -273,22 °C for the absolute zero.



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