Editing Thermometer (section)

==Physical principles of thermometry==
[[File:Oldthermometers.jpg|thumb|upright|left|Various thermometers from the 19th century.]]
[[File:Thermometer CF.svg|thumb|upright|Comparison of the Celsius and Fahrenheit scales]]

Thermometers may be described as empirical or absolute. Absolute thermometers are calibrated numerically by the thermodynamic absolute temperature scale. Empirical thermometers are not in general necessarily in exact agreement with absolute thermometers as to their numerical scale readings, but to qualify as thermometers at all they must agree with absolute thermometers and with each other in the following way: given any two bodies isolated in their separate respective thermodynamic equilibrium states, all thermometers agree as to which of the two has the higher temperature, or that the two have equal temperatures.<ref>Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing Company, Amsterdam, {{ISBN|0-444-41806-7}}, page 29.</ref> For any two empirical thermometers, this does not require that the relation between their numerical scale readings be linear, but it does require that relation to be [[Monotonic function|strictly monotonic]].<ref name="Thomsen 1962">{{cite journal | last1 = Thomsen | first1 = J.S. | year = 1962 | title = A restatement of the zeroth law of thermodynamics | journal = Am. J. Phys. | volume = 30 | issue = 4| pages = 294–296 | doi=10.1119/1.1941991|bibcode = 1962AmJPh..30..294T | doi-access = free }}</ref> This is a fundamental character of temperature and thermometers.<ref>[[Ernst Mach|Mach, E.]] (1900). ''Die Principien der Wärmelehre. Historisch-kritisch entwickelt'', Johann Ambrosius Barth, Leipzig, section 22, pages 56-57. English translation edited by McGuinness, B. (1986), ''Principles of the Theory of Heat, Historically and Critically Elucidated'', D. Reidel Publishing, Dordrecht, {{ISBN|90-277-2206-4}}, section 5, pp. 48–49, section 22, pages 60–61.</ref><ref name="Truesdell 1980">Truesdell, C.A. (1980). ''The Tragicomical History of Thermodynamics, 1822-1854'', Springer, New York, {{ISBN|0-387-90403-4}}.</ref><ref>Serrin, J. (1986). Chapter 1, 'An Outline of Thermodynamical Structure', pages 3-32, especially page 6, in ''New Perspectives in Thermodynamics'', edited by J. Serrin, Springer, Berlin, {{ISBN|3-540-15931-2}}.</ref>

As it is customarily stated in textbooks, taken alone, the so-called "[[zeroth law of thermodynamics]]" fails to deliver this information, but the statement of the zeroth law of thermodynamics by [[James Serrin]] in 1977, though rather mathematically abstract, is more informative for thermometry: "Zeroth Law – There exists a topological line <math>M</math> which serves as a coordinate manifold of material behaviour. The points <math>L</math> of the manifold <math>M</math> are called 'hotness levels', and <math>M</math> is called the 'universal hotness manifold'."<ref>Serrin, J. (1978). The concepts of thermodynamics, in ''Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August 1977'', edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, {{ISBN|0-444-85166-6}}, pages 411-451.</ref> To this information there needs to be added a sense of greater hotness; this sense can be had, independently of [[calorimetry]], of [[thermodynamics]], and of properties of particular materials, from [[Wien's displacement law#Frequency-dependent formulation|Wien's displacement law]] of [[thermal radiation]]: the temperature of a bath of thermal radiation is [[Proportionality (mathematics)|proportional]], by a universal constant, to the frequency of the maximum of its [[Frequency spectrum#Light|frequency spectrum]]; this frequency is always positive, but can have values that [[Third law of thermodynamics|tend to zero]]. Another way of identifying hotter as opposed to colder conditions is supplied by [[Planck's principle]], that when a process of isochoric adiabatic work is the sole means of change of internal energy of a closed system, the final state of the system is never colder than the initial state; except for phase changes with latent heat, it is hotter than the initial state.<ref>[[Max Planck|Planck, M.]] (1926). Über die Begründung des zweiten Hauptsatzes der Thermodynamik, ''S.-B. Preuß. Akad. Wiss. phys. math. Kl.'': 453–463.</ref><ref>Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, London, pp. 42–43.</ref><ref name="L&Y 56">{{cite journal | last1 = Lieb | first1 = E.H. | last2 = Yngvason | first2 = J. | year = 1999 | title = The physics and mathematics of the second law of thermodynamics | journal = Physics Reports | volume = 314 | issue = 1–2 | pages = 1–96 [56] |arxiv = hep-ph/9807278 |bibcode = 1999PhR...314....1L |doi = 10.1016/S0370-1573(98)00128-8 | s2cid = 119517140 }}</ref>

There are several principles on which empirical thermometers are built, as listed in the section of this article entitled "Primary and secondary thermometers". Several such principles are essentially based on the constitutive relation between the state of a suitably selected particular material and its temperature. Only some materials are suitable for this purpose, and they may be considered as "thermometric materials". Radiometric thermometry, in contrast, can be only slightly dependent on the constitutive relations of materials. In a sense then, radiometric thermometry might be thought of as "universal". This is because it rests mainly on a universality character of thermodynamic equilibrium, that it has the universal property of producing [[blackbody]] radiation.

===Thermometric materials===
[[File:Thermometers in pitcher.jpg|thumb|Bi-metallic stem thermometers used to measure the temperature of steamed milk]]
[[File:Backofenthermometer.jpg|thumb|upright|Bi-metallic thermometer for cooking and baking in an oven]]
There are various kinds of empirical thermometer based on material properties.

Many empirical thermometers rely on the constitutive relation between pressure, volume and temperature of their thermometric material. For example, mercury expands when heated.

If it is used for its relation between pressure and volume and temperature, a thermometric material must have three properties:

(1) Its heating and cooling must be rapid. That is to say, when a quantity of heat enters or leaves a body of the material, the material must expand or contract to its final volume or reach its final pressure and must reach its final temperature with practically no delay; some of the heat that enters can be considered to change the volume of the body at constant temperature, and is called the [[Calorimetry|latent heat of expansion at constant temperature]]; and the rest of it can be considered to change the temperature of the body at constant volume, and is called the [[Calorimetry|specific heat at constant volume]]. Some materials do not have this property, and take some time to distribute the heat between temperature and volume change.<ref name="Truesdell Bharatha 1977 20">Truesdell, C., Bharatha, S. (1977). ''The Concepts and Logic of Classical Thermodynamics as a Theory of Heat Engines. Rigorously Constructed upon the Foundation Laid by S. Carnot and F. Reech'', Springer, New York, {{ISBN|0-387-07971-8}}, page 20.</ref>

(2) Its heating and cooling must be reversible. That is to say, the material must be able to be heated and cooled indefinitely often by the same increment and decrement of heat, and still return to its original pressure, volume and temperature every time. Some plastics do not have this property;<ref name="Ziegler 1983">Ziegler, H., (1983). ''An Introduction to Thermomechanics'', North-Holland, Amsterdam, {{ISBN|0-444-86503-9}}.</ref>

(3) Its heating and cooling must be monotonic.<ref name="Thomsen 1962"/><ref>Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience Publishers, New York, page 17.</ref> That is to say, throughout the range of temperatures for which it is intended to work,

:(a) at a given fixed pressure,

::either (i) the volume increases when the temperature increases, or else (ii) the volume decreases when the temperature increases;

::but not (i) for some temperatures and (ii) for others; or

:(b) at a given fixed volume,

::either (i) the pressure increases when the temperature increases, or else (ii) the pressure decreases when the temperature increases;

::but not (i) for some temperatures and (ii) for others.

At temperatures around about 4&nbsp;°C, water does not have the property (3), and is said to behave anomalously in this respect; thus water cannot be used as a material for this kind of thermometry for temperature ranges near 4&nbsp;°C.<ref name="Truesdell 1980"/><ref>Maxwell, J.C. (1872). ''Theory of Heat'', third edition, Longmans, Green, and Co., London, pages 232-233.</ref><ref>Lewis, G.N., Randall, M. (1923/1961). ''Thermodynamics'', second edition revised by K.S Pitzer, L. Brewer, McGraw-Hill, New York, pages 378-379.</ref><ref>{{cite journal | last1 = Thomsen | first1 = J.S. | last2 = Hartka | first2 = T.J. | year = 1962 | title = Strange Carnot cycles; thermodynamics of a system with a density extremum | journal = Am. J. Phys. | volume = 30 | issue = 1| pages = 26–33 | doi=10.1119/1.1941890|bibcode = 1962AmJPh..30...26T }}</ref><ref name="Truesdell Bharatha 1977">Truesdell, C., Bharatha, S. (1977). ''The Concepts and Logic of Classical Thermodynamics as a Theory of Heat Engines. Rigorously Constructed upon the Foundation Laid by S. Carnot and F. Reech'', Springer, New York, {{ISBN|0-387-07971-8}}, pages 9-10, 15-18, 36-37.</ref>

Gases, on the other hand, all have the properties (1), (2), and (3)(a)(α) and (3)(b)(α). Consequently, they are suitable thermometric materials, and that is why they were important in the development of thermometry.<ref>Planck, M. (1897/1903). ''[https://archive.org/details/treatiseonthermo00planrich Treatise on Thermodynamics]'', translated by A. Ogg, Longmans, Green & Co., London.</ref>

===Constant volume thermometry===
According to Preston (1894/1904), [[Henri Victor Regnault|Regnault]] found constant pressure air thermometers unsatisfactory, because they needed troublesome corrections. He therefore built a constant volume air thermometer.<ref>Preston, T. (1894/1904). ''The Theory of Heat'', second edition, revised by J.R. Cotter, Macmillan, London, Section 92.0</ref> Constant volume thermometers do not provide a way to avoid the problem of anomalous behaviour like that of water at approximately 4&nbsp;°C.<ref name="Truesdell Bharatha 1977"/>

===Radiometric thermometry===
[[Planck's law]] very accurately quantitatively describes the power spectral density of electromagnetic radiation, inside a rigid walled cavity in a body made of material that is completely opaque and poorly reflective, when it has reached thermodynamic equilibrium, as a function of absolute thermodynamic temperature alone. A small enough hole in the wall of the cavity emits near enough blackbody radiation of which the [[spectral radiance]] can be precisely measured. The walls of the cavity, provided they are completely opaque and poorly reflective, can be of any material indifferently.