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| {{About|the thermodynamic property||Temperature (disambiguation)}}
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| [[File:MonthlyMeanT.gif|thumb|right|300px|A map of global long term monthly average surface air temperatures in Mollweide projection.]]
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| A '''temperature''' is a numerical measure of hot and cold. Its measurement is by detection of heat radiation or particle velocity or kinetic energy, or by the bulk behavior of a [[thermometer|thermometric]] material. It may be [[calibration|calibrated]] in any of various [[Temperature conversion formulas|temperature scales]], Celsius, Fahrenheit, Kelvin, etc. The fundamental physical definition of temperature is provided by [[thermodynamics]].
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| Measurements with a small thermometer, or by detection of heat radiation, can show that the temperature of a body of material can vary from time to time and from place to place within it. For example, a lightning bolt can heat a small portion of the atmosphere hotter than the surface of the sun.<ref>http://thunder.msfc.nasa.gov/primer/primer2.html</ref> If changes happen too fast, or with too small a spacing, within a body, it may be impossible to define its temperature.
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| Within a body that exchanges no energy or matter with its surroundings, temperature tends to become spatially uniform as time passes. When a path permeable only to heat is open between two bodies, energy always transfers [[Spontaneous process|spontaneously]] as heat from a hotter body to a colder one. The transfer rate depends on the [[thermal conductivity]] of the path or boundary between them. Between two bodies with the same temperature, no heat flows. These bodies are said to be in [[thermal equilibrium]].
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| The [[kinetic theory]] offers a valuable but limited account of the behavior of the materials of macroscopic systems. It indicates the [[#Kinds of temperature scale|absolute temperature]] as proportional to the average kinetic energy of the random microscopic motions of their constituent microscopic particles such as electrons, atoms, and molecules.
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| [[File:Thermally Agitated Molecule.gif|280px|thumb|right|Thermal vibration of a segment of [[protein]] [[alpha helix]]. The amplitude of the vibrations increases with temperature.]]
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| The coldest theoretical temperature is called [[absolute zero]]. It can be approached but not reached in any actual physical system. It is denoted by 0 K on the Kelvin scale, −273.15 °C on the Celsius scale, and −459.67 °F on the Fahrenheit scale. In matter at absolute zero, the motions of microscopic constituents are minimal. | |
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| Temperature is important in all fields of natural science, including [[physics]], [[geology]], [[chemistry]], [[atmospheric sciences]] and [[biology]].
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| ==Use in science==
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| {{refimprove section|date=January 2013}}
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| [[File:Annual Average Temperature Map.jpg|thumb|400px|Annual mean temperature around the world]]
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| Many things depend on temperature, such as
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| *physical properties of materials including the [[Phases of matter|phase]] ([[solid]], [[liquid]], [[gas]]eous or [[Plasma (physics)|plasma]]), [[density]], [[solubility]], [[vapor pressure]], [[electrical conductivity]]
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| *rate and extent to which [[chemical reaction]]s occur
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| *the amount and properties of [[thermal radiation]] emitted from the surface of an object
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| *[[speed of sound]] is a function of the square root of the absolute temperature
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| ==Temperature scales==
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| {{see also|Scale of temperature}}
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| {{refimprove section|date=August 2013}}
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| Temperature scales differ in two ways: the point chosen as zero degrees, and the magnitudes of incremental units or degrees on the scale.
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| The [[Celsius]] scale (°C) is used for common temperature measurements in most of the world. It is an empirical scale. It developed by a historical progress, which led to its zero point {{gaps|0|°C}} being defined by the freezing point of water, with additional degrees defined so that {{gaps|100|°C}} was the boiling point of water, both at sea-level atmospheric pressure. Because of the 100 degree interval, it is called a centigrade scale.<ref>Middleton, W.E.K. (1966), pp. 89–105.</ref> Since the standardization of the kelvin in the International System of Units, it has subsequently been redefined in terms of the equivalent fixing points on the Kelvin scale, and so that a temperature increment of one degree celsius is the same as an increment of one kelvin, though they differ by an additive offset of 273.15.
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| The United States commonly uses the [[Fahrenheit]] scale, on which water freezes at 32 °F and boils at 212 °F at sea-level atmospheric pressure. | |
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| Many scientific measurements use the [[kelvin temperature scale]] (unit symbol K), named in honor of the Scottish physicist who first defined it. It is a thermodynamic or [[absolute temperature]] scale. Its zero point, {{gaps|0|K}}, is defined to coincide with coldest physically-possible temperature (called [[absolute zero]]). Its degrees are defined [[#Definition of the Kelvin scale|through thermodynamics]]. The temperature of absolute zero occurs at {{gaps|0|K}} = {{gaps|-273.15|°C}} (or −459.67 °F), and the freezing point of water at sea-level atmospheric pressure occurs at {{gaps|273.15|K}} ={{gaps|0|°C}}.
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| The [[International System of Units]] (SI) defines a scale and unit for the kelvin or [[thermodynamic temperature]] by using the reliably reproducible temperature of the [[triple point]] of water as a second reference point (the first reference point being 0 K at absolute zero). The triple point is a singular state with its own unique and invariant temperature and pressure, along with, for a fixed mass of water in a vessel of fixed volume, an autonomically and stably self-determining partition into three mutually contacting phases, vapour, liquid, and solid, dynamically depending only on the total internal energy of the mass of water. For historical reasons, the triple point temperature of water is fixed at 273.16 units of the measurement increment.
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| ==Thermodynamic approach to temperature==
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| Temperature is one of the principal quantities in the study of [[thermodynamics]].
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| ===Kinds of temperature scale===
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| There is a variety of kinds of temperature scale. It may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in the middle of the nineteenth century.<ref name="Truesdell 1980"/><ref>Quinn, T.J. (1983).</ref>
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| ====Empirically based scales====
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| Empirically based temperature scales rely directly on measurements of simple physical properties of materials. For example, the length of a column of mercury, confined in in a glass-walled capillary tube, is dependent largely on temperature, and is the basis of the very useful mercury-in-glass thermometer. Such scales are valid only within convenient ranges of temperature. For example, above the boiling point of mercury, a mercury-in-glass thermometer is impracticable. Most materials expand with temperature increase, but some materials, such as water, contract with temperature increase over some specific range, and then they are hardly useful as thermometric materials. A material is of no use as a thermometer near one of its phase-change temperatures, for example its boiling-point.
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| In spite of these restrictions, most generally used practical thermometers are of the empirically based kind. Especially, it was used for [[calorimetry]], which contributed greatly to the discovery of thermodynamics. Nevertheless, empirical thermometry has serious drawbacks when judged as a basis for theoretical physics. Empirically based thermometers, beyond their base as simple direct measurements of ordinary physical properties of thermometric materials, can be re-calibrated, by use of theoretical physical reasoning, and this can extend their range of adequacy.
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| ====Theoretically based scales====
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| Theoretically based temperature scales are based directly on theoretical arguments, especially those of thermodynamics, of kinetic theory, and of quantum mechanics. They rely on theoretical properties of idealized devices and materials. They are more or less comparable with practically feasible physical devices and materials. Theoretically based temperature scales are used to provide calibrating standards for practical empirically based thermometers.
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| The accepted fundamental thermodynamic temperature scale is the Kelvin scale, based on an ideal cyclic process envisaged for a [[Carnot heat engine]].
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| An ideal material on which a temperature scale can be based is the [[ideal gas]]. The pressure exerted by a fixed volume and mass of an ideal gas is directly proportional to its temperature. Some natural gases show so nearly ideal properties over suitable temperature ranges that they can be used for thermometry; this was important during the development of thermodynamics, and is still of practical importance today.<ref>Quinn, T.J. (1983), pp. 61–83.</ref><ref>Schooley, J.F. (1986), pp. 115–138.</ref>
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| Measurement of the spectrum of electromagnetic radiation from an ideal three dimensional [[black body]] can provide an accurate temperature measurement because the frequency of maximum spectral radiance of black-body radiation is directly proportional to the temperature of the black body; this is known as [[Wien's displacement law]], and has a theoretical explanation in [[Planck's law]] and the [[Bose–Einstein statistics|Bose–Einstein law]].
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| Measurement of the spectrum of noise-power produced by an electrical resistor can also provide an accurate temperature measurement. The resistor has two terminals and is in effect a one-dimensional body. The Bose-Einstein law for this case indicates that the noise-power is directly proportional to the temperature of the resistor and to the value of its resistance and to the noise band-width. In a given frequency band, the noise-power has equal contributions from every frequency, and is called [[Johnson noise]]. If the value of the resistance is known then the temperature can be found.<ref>Quinn, T.J. (1983), pp. 98–107.</ref><ref>Schooley, J.F. (1986), pp. 138–143.</ref>
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| If molecules, or atoms, or electrons, are emitted from a material and their velocities are measured, the spectrum of their velocities often nearly obeys a theoretical law called the [[Maxwell–Boltzmann distribution]], which gives a well-founded measurement of temperatures for which the law holds.<ref>Zeppenfeld, M., Englert, B.G.U., Glöckner, R., Prehn, A., Mielenz, M., Sommer, C., van Buuren, L.D., Motsch, M., Rempe, G. (2012).</ref> There have not yet been successful experiments of this same kind that directly use the [[Fermi–Dirac statistics|Fermi–Dirac distribution]] for thermometry, but perhaps that will be achieved in future.<ref>Miller, J. (2013).</ref>
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| ====Absolute thermodynamic scale====
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| The Kelvin scale is called '''absolute''' for two reasons. One is Kelvin's, that its formal character is independent of the properties of particular materials. The other reason is that its zero is in a sense absolute, in that it indicates absence of microscopic classical motion of the constituent particles of matter, so that they have a limiting specific heat of zero for zero temperature, according to the third law of thermodynamics. Nevertheless, a Kelvin temperature has a definite numerical value, that has been arbitrarily chosen by tradition. This numerical value also depends on the properties of water, which has a [[Triple point#Triple points of water|gas–liquid–solid triple point]] that can be reliably reproduced as a standard experimental phenomenon. The choice of this triple point is also arbitrary and by convention. The Kelvin scale is also called the '''thermodynamic scale'''.
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| ===Definition of the Kelvin scale===
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| The thermodynamic definition of temperature is due to Kelvin.
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| It is framed in terms of an idealized device called a [[Carnot engine]], imagined to define a continuous cycle of states of its working body. The cycle is imagined to run so slowly that at each point of the cycle the working body is in a state of thermodynamic equilibrium. There are four limbs in such a [[Carnot cycle]]. The engine consists of four bodies. The main one is called the working body. Two of them are called heat reservoirs, so large that their respective non-deformation variables are not changed by transfer of energy as heat through a wall permeable only to heat to the working body. The fourth body is able to exchange energy with the working body only through adiabatic work; it may be called the work reservoir. The substances and states of the two heat reservoirs should be chosen so that they are not in thermal equilibrium with one another. This means that they must be at different fixed temperatures, one, labeled here with the number 1, hotter than the other, labeled here with the number 2. This can be tested by connecting the heat reservoirs successively to an auxiliary empirical thermometric body that starts each time at a convenient fixed intermediate temperature. The thermometric body should be composed of a material that has a strictly monotonic relation between its chosen empirical thermometric variable and the amount of adiabatic isochoric work done on it. In order to settle the structure and sense of operation of the Carnot cycle, it is convenient to use such a material also for the working body; because most materials are of this kind, this is hardly a restriction of the generality of this definition. The Carnot cycle is considered to start from an initial condition of the working body that was reached by the completion of a reversible adiabatic compression. From there, the working body is initially connected by a wall permeable only to heat to the heat reservoir number 1, so that during the first limb of the cycle it expands and does work on the work reservoir. The second limb of the cycle sees the working body expand adiabatically and reversibly, with no energy exchanged as heat, but more energy being transferred as work to the work reservoir. The third limb of the cycle sees the working body connected, through a wall permeable only to heat, to the heat reservoir 2, contracting and accepting energy as work from the work reservoir. The cycle is closed by reversible adiabatic compression of the working body, with no energy transferred as heat, but energy being transferred to it as work from the work reservoir.
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| With this set-up, the four limbs of the reversible Carnot cycle are characterized by amounts of energy transferred, as work from the working body to the work reservoir, and as heat from the heat reservoirs to the working body. The amounts of energy transferred as heat from the heat reservoirs are measured through the changes in the non-deformation variable of the working body, with reference to the previously known properties of that body, the amounts of work done on the work reservoir, and the first law of thermodynamics. The amounts of energy transferred as heat respectively from reservoir 1 and from reservoir 2 may then be denoted respectively {{math|''Q''<sub>1</sub>}} and {{math|''Q''<sub>2</sub>}}. Then the absolute or thermodynamic temperatures, {{math|''T''<sub>1</sub>}} and {{math|''T''<sub>2</sub>}}, of the reservoirs are defined so that to be such that
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| :<math>T_1 / T_2 = - Q_1 / Q_2 \,\,\,.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)</math>
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| Kelvin's original work postulating absolute temperature was published in 1848. It was based on the work of Carnot, before the formulation of the first law of thermodynamics. Kelvin wrote in his 1848 paper that his scale was absolute in the sense that it was defined "independently of the properties of any particular kind of matter." His definitive publication, which sets out the definition just stated, was printed in 1853, a paper read in 1851.<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W. (Lord Kelvin)]] (1848).</ref><ref>[[William Thomson, 1st Baron Kelvin|Thomson, W. (Lord Kelvin)]] (1851).</ref><ref>[[J. R. Partington|Partington, J.R.]] (1949), pp. 175–177.</ref>
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| This definition rests on the physical assumption that there are readily available walls permeable only to heat. In his detailed definition of a wall permeable only to heat, [[Constantin Carathéodory|Carathéodory]] includes several ideas. The non-deformation state variable of a closed system is represented as a real number. A state of thermal equilibrium between two closed systems connected by a wall permeable only to heat means that a certain mathematical relation holds between the state variables, including the respective non-deformation variables, of those two systems (that particular mathematical relation is regarded by Buchdahl as a preferred statement of the zeroth law of thermodynamics).<ref>Buchdahl, H.A (1986). On the redundancy of the zeroth law of thermodynamics, ''J. Phys. A, Math. Gen.'', '''19''': L561–L564.</ref> Also, referring to thermal contact equilibrium, "whenever each of the systems {{math|''S''<sub>1</sub>}} and {{math|''S''<sub>2</sub>}} is made to reach equilibrium with a third system {{math|''S''<sub>3</sub>}} under identical conditions, the systems {{math|''S''<sub>1</sub>}} and {{math|''S''<sub>2</sub>}} are in mutual equilibrium."<ref name="Carathéodory 1909">{{cite journal
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| |author=C. Carathéodory
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| |author-link=Constantin Carathéodory
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| |title=Untersuchungen über die Grundlagen der Thermodynamik
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| |year=1909
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| |journal=Mathematische Annalen
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| |volume=67
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| |pages=355–386
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| |doi=10.1007/BF01450409}} A partly reliable translation is to be found at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA.</ref> It may viewed as a re-statement of the principle stated by [[James Clerk Maxwell|Maxwell]] in the words: "All heat is of the same kind."<ref>[[James Clerk Maxwell|Maxwell, J.C.]] (1871). ''Theory of Heat'', Longmans, Green, and Co., London, p. 57.</ref> This physical idea is also expressed by Bailyn as a possible version of the zeroth law of thermodynamics: "All diathermal walls are equivalent."<ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, ISBN 0-88318-797-3, page 24.</ref> Thus the present definition of thermodynamic temperature rests on the zeroth law of thermodynamics. Explicitly, this present definition of thermodynamic temperature also rests on the first law of thermodynamics, for the determination of amounts of energy transferred as heat.
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| Implicitly for this definition, the second law of thermodynamics provides information that establishes the virtuous character of the temperature so defined. It provides that any working substance that complies with the requirement stated in this definition will lead to the same ratio of thermodynamic temperatures, which in this sense is universal, or absolute. The second law of thermodynamics also provides that the thermodynamic temperature defined in this way is positive, because this definition requires that the heat reservoirs not be in thermal equilibrium with one another, and the cycle can be imagined to operate only in one sense if net work is to be supplied to the work reservoir.
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| Numerical details are settled by making one of the heat reservoirs a cell at the triple point of water, which is defined to have an absolute temperature of 273.16 K.<ref>Quinn, T.J. (1983). ''Temperature'', Academic Press, London, ISBN0-12-569680-9, pp. 160–162.</ref> The zeroth law of thermodynamics allows this definition to be used to measure the absolute or thermodynamic temperature of an arbitrary body of interest, by making the other heat reservoir have the same temperature as the body of interest.
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| ===Temperature an intensive variable===
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| In thermodynamic terms, temperature is an [[Intensive and extensive properties|intensive variable]] because it is equal to a [[differential coefficient]] of one [[Intensive and extensive properties|extensive variable]] with respect to another, for a given body. It thus has the [[Dimensional analysis|dimensions]] of a [[ratio]] of two extensive variables. In thermodynamics, two bodies are often considered as connected by contact with a common wall, which has some specific permeability properties. Such specific permeability can be referred to a specific intensive variable. An example is a diathermic wall that is permeable only to heat; the intensive variable for this case is temperature. When the two bodies have been in contact for a very long time, and have settled to a permanent steady state, the relevant intensive variables are equal in the two bodies; for a diathermal wall, this statement is sometimes called the zeroth law of thermodynamics.<ref>Tisza, L. (1966). ''Generalized Thermodynamics'', M.I.T. Press, Cambridge MA, pp. 47,57.</ref><ref name="Munster 49 69">Münster, A. (1970), ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, ISBN 0-471-62430-6, pp. 49, 69.</ref><ref name="Bailyn 14 214">Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, ISBN 0-88318-797-3, pp. 14–15, 214.</ref>
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| In particular, when the body is described by stating its internal energy {{math|''U''}}, an extensive variable, as a function of its entropy {{math|''S''}}, also an extensive variable, and other state variables {{math|''V'', ''N''}}, with {{math|''U'' {{=}} ''U'' (''S'', ''V'', ''N''}}), then the temperature is equal to the partial derivative of the internal energy with respect to the entropy:
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| :<math>T = \left ( \frac{\partial U}{\partial S} \right )_{V, N} \, .\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)</math><ref name="Munster 49 69"/><ref name="Bailyn 14 214"/><ref name="Callen 146–148">[[Herbert Callen|Callen, H.B.]] (1960/1985), ''Thermodynamics and an Introduction to Thermostatistics'', (first edition 1960), second edition 1985, John Wiley & Sons, New York, ISBN 0–471–86256–8, pp. 146–148.</ref>
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| Likewise, when the body is described by stating its entropy {{math|''S''}} as a function of its internal energy {{math|''U''}}, and other state variables {{math|''V'', ''N''}}, with {{math|''S'' {{=}} ''S'' (''U'', ''V'', ''N'')}}, then the reciprocal of the temperature is equal to the partial derivative of the entropy with respect to the internal energy:
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| :<math>\frac {1}{T} = \left ( \frac{\partial S}{\partial U} \right )_{V, N} \, .\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(3)</math><ref name="Munster 49 69"/><ref name="Callen 146–148"/><ref>Kondepudi, D., [[Ilya Prigogine|Prigogine, I.]] (1998). ''Modern Thermodynamics. From Heat Engines to Dissipative Structures'', John Wiley, Chichester, ISBN 0-471-97394-7, pp. 115–116.</ref>
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| The above definition, equation (1), of the absolute temperature is due to Kelvin. It refers to systems closed to transfer of matter, and has special emphasis on directly experimental procedures. A presentation of thermodynamics by Gibbs starts at a more abstract level and deals with systems open to the transfer of matter; in this development of thermodynamics, the equations (2) and (3) above are actually alternative definitions of temperature.<ref>Tisza, L. (1966). ''Generalized Thermodynamics'', M.I.T. Press, Cambridge MA, p. 58.</ref>
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| ===Temperature local when local thermodynamic equilibrium prevails===
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| Real world bodies are often not in thermodynamic equilibrium and not homogeneous. For study by methods of classical irreversible thermodynamics, a body is usually spatially and temporally divided conceptually into 'cells' of small size. If classical thermodynamic equilibrium conditions for matter are fulfilled to good approximation in such a 'cell', then it is homogeneous and a temperature exists for it. If this is so for every 'cell' of the body, then [[Thermodynamic equilibrium#Local and global equilibrium|local thermodynamic equilibrium]] is said to prevail throughout the body.<ref>[[Edward Arthur Milne|Milne, E.A.]] (1929). The effect of collisions on monochromatic radiative equilibrium, [http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1928MNRAS..88..493M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf ''Monthly Notices of the Royal Astronomical Society'', '''88''': 493–502].</ref><ref>Gyarmati, I. (1970). ''Non-equilibrium Thermodynamics. Field Theory and Variational Principles'', translated by E. Gyarmati and W.F. Heinz, Springer, Berlin, pp. 63–66</ref><ref>Glansdorff, P., [[Ilya Prigogine|Prigogine, I.]], (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley, London, ISBN 0-471-30280-5, pp. 14–16.</ref><ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, ISBN 0-88318-797-3, pp. 133–135.</ref><ref>[[Herbert Callen|Callen, H.B.]] (1960/1985), ''Thermodynamics and an Introduction to Thermostatistics'', (first edition 1960), second edition 1985, John Wiley & Sons, New York, ISBN 0–471–86256–8, pp. 309–310.</ref>
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| It makes good sense, for example, to say of the extensive variable {{math|''U''}}, or of the extensive variable {{math|''S''}}, that it has a density per unit volume, or a quantity per unit mass of the system, but it makes no sense to speak of density of temperature per unit volume or quantity of temperature per unit mass of the system. On the other hand, it makes no sense to speak of the internal energy at a point, while when local thermodynamic equilibrium prevails, it makes good sense to speak of the temperature at a point. Consequently, temperature can vary from point to point in a medium that is not in global thermodynamic equilibrium, but in which there is local thermodynamic equilibrium.
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| Thus, when local thermodynamic equilibrium prevails in a body, temperature can be regarded as a spatially varying local property in that body, and this is because temperature is an intensive variable.
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| ==Kinetic theory approach to temperature==
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| A more thorough account of this is below at [[#Theoretical foundation|Theoretical foundation]].
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| [[Kinetic theory]] provides a microscopic explanation of temperature, based on macroscopic systems' being composed of many microscopic particles, such as [[molecule]]s and [[ion]]s of various species, the particles of a species being all alike. It explains macroscopic phenomena through the [[classical mechanics]] of the microscopic particles. The [[equipartition theorem]] of kinetic theory asserts that each classical [[Degrees of freedom (physics and chemistry)|degree of freedom]] of a freely moving particle has an average kinetic energy of {{math|''k''<sub>B</sub>''T''/2}} where {{math|''k''<sub>B</sub>}} denotes [[Boltzmann's constant]]. The translational motion of the particle has three degrees of freedom, so that, except at very low temperatures where quantum effects predominate, the average translational kinetic energy of a freely moving particle in a system with temperature {{math|''T''}} will be {{math|3''k''<sub>B</sub>''T''/2}}.
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| It is possible to measure the average kinetic energy of constituent microscopic particles if they are allowed to escape from the bulk of the system. The spectrum of velocities has to be measured, and the average calculated from that. It is not necessarily the case that the particles that escape and are measured have the same velocity distribution as the particles that remain in the bulk of the system, but sometimes a good sample is possible.
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| [[Molecule]]s, such as oxygen (O<sub>2</sub>), have more [[Degrees of freedom (physics and chemistry)|degrees of freedom]] than single spherical atoms: they undergo rotational and vibrational motions as well as translations. Heating results in an increase in temperature due to an increase in the average translational kinetic energy of the molecules. Heating will also cause, through [[equipartition]]ing, the energy associated with vibrational and rotational modes to increase. Thus a [[diatomic]] gas will require more energy input to increase its temperature by a certain amount, i.e. it will have a greater [[heat capacity]] than a monatomic gas.
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| The process of cooling involves removing internal energy from a system. When no more energy can be removed, the system is at absolute zero, though this cannot be achieved experimentally. Absolute zero is the null point of the [[thermodynamic temperature]] scale, also called absolute temperature. If it were possible to cool a system to absolute zero, all classical motion of its particles would cease and they would be at complete rest in this classical sense. Microscopically in the description of quantum mechanics, however, matter still has [[zero-point energy]] even at absolute zero, because of the [[uncertainty principle]].
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| ==Basic theory==
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| Temperature is a measure of a [[Categories (Aristotle)#The Praedicamenta|quality]] of a state of a material <ref>Bryan, G.H. (1907). ''Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications'', B.G. Teubner, Leipzig, page 3.[http://www.e-booksdirectory.com/details.php?ebook=6455]</ref> The quality may be regarded as a more abstract entity than any particular temperature scale that measures it, and is called ''hotness'' by some writers. The quality of hotness refers to the state of material only in a particular locality, and in general, apart from bodies held in a steady state of thermodynamic equilibrium, hotness varies from place to place. It is not necessarily the case that a material in a particular place is in a state that is steady and nearly homogeneous enough to allow it to have a well-defined hotness or temperature. Hotness may be represented abstractly as a one-dimensional manifold. Every valid temperature scale has its own one-to-one map into the hotness manifold.<ref name="Mach 1900">Mach, E. (1900). ''Die Principien der Wärmelehre. Historisch-kritisch entwickelt'', Johann Ambrosius Barth, Leipzig, section 22, pages 56-57.</ref><ref name="Serrin 1986">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>
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| When two systems in thermal contact are at the same temperature no heat transfers between them. When a temperature difference does exist heat flows spontaneously from the warmer system to the colder system until they are in [[thermal equilibrium]]. Heat transfer occurs by conduction or by thermal radiation.<ref name="Maxwell 1872">Maxwell, J.C. (1872). ''Theory of Heat'', third edition, Longmans, Green, London, page 32.</ref><ref name="Tait 1884 39-40">Tait, P.G. (1884). ''Heat'', Macmillan, London, Chapter VII, pages 39-40.</ref><ref name="Planck 1897">Planck, M. (1897/1903). ''Treatise on Thermodynamics'', translated by A. Ogg, Longmans, Green, London, pages 1-2.</ref><ref>Planck, M. (1914), [http://openlibrary.org/books/OL7154661M/The_theory_of_heat_radiation ''The Theory of Heat Radiation''], second edition, translated into English by M. Masius, Blakiston's Son & Co., Philadelphia, reprinted by Kessinger.</ref><ref name=dugdale>{{cite book
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| |author=J. S. Dugdale
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| |title=Entropy and its Physical Interpretation
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| |publisher=Taylor & Francis
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| |year=1996, 1998
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| |isbn=978-0-7484-0569-5
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| |page=13
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| }}</ref><ref name=reif>{{cite book
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| |author=F. Reif
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| |title=Fundamentals of Statistical and Thermal Physics
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| |year=1965
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| |publisher=McGraw-Hill
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| |page=102
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| }}</ref><ref name=Moran>{{cite book
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| |author=M. J. Moran, H. N. Shapiro
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| |title=Fundamentals of Engineering Thermodynamics
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| |edition=5
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| |page=14
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| |section=1.6.1
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| |publisher=John Wiley & Sons, Ltd.
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| |year=2006
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| |isbn=978-0-470-03037-0
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| }}</ref><ref>{{cite web
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| |author=T.W. Leland, Jr.
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| |title=Basic Principles of Classical and Statistical Thermodynamics
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| |page=14
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| |url=http://www.uic.edu/labs/trl/1.OnlineMaterials/BasicPrinciplesByTWLeland.pdf
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| |quote=Consequently we identify temperature as a driving force which causes something called heat to be transferred.
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| }}</ref>
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| Experimental physicists, for example [[Galileo Galilei#Technology|Galileo]] and [[Newtons law of cooling|Newton]],<ref>Tait, P.G. (1884). ''Heat'', Macmillan, London, Chapter VII, pages 42, 103-117.</ref> found that there are indefinitely many [[Scale of temperature|empirical temperature scales]]. Nevertheless, the zeroth law of thermodynamics says that they all measure the same quality.
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| ===Temperature for bodies in thermodynamic equilibrium===
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| For experimental physics, hotness means that, when comparing any two given bodies in their respective separate [[Thermodynamic equilibrium|thermodynamic equilibria]], any two suitably given empirical thermometers with numerical scale readings will agree as to which is the hotter of the two given bodies, or that they have the same temperature.<ref>Beattie, J.A., Oppenheim, I. (1979). ''Principles of Thermodynamics'', Elsevier Scientific Publishing Company, Amsterdam, 0–444–41806–7, page 29.</ref> This does not require the two thermometers to have a linear relation between their numerical scale readings, but it does require that the relation between their numerical readings shall be [[monotonic|strictly monotonic]].<ref>Landsberg, P.T. (1961). ''Thermodynamics with Quantum Statistical Illustrations'', Interscience Publishers, New York, page 17.</ref><ref>{{cite journal | last1 = Thomsen | first1 = J.S. | year = 1962 | title = A restatement of the zeroth law of thermodynamics | url = | journal = Am. J. Phys. | volume = 30 | issue = | pages = 294–296 |bibcode = 1962AmJPh..30..294T |doi = 10.1119/1.1941991 }}</ref> A definite sense of greater hotness 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]]. Thermal radiation is initially defined for a cavity in thermodynamic equilibrium. These physical facts justify a mathematical statement that hotness exists on an ordered one-dimensional [[manifold]]. This is a fundamental character of temperature and thermometers for bodies in their own thermodynamic equilibrium.<ref name="Truesdell 1980"/><ref name="Mach 1900"/><ref name="Serrin 1986"/><ref>Maxwell, J.C. (1872). ''Theory of Heat'', third edition, Longman's, Green & Co, London, page 45.</ref><ref name="Pitteri 1984">Pitteri, M. (1984). On the axiomatic foundations of temperature, Appendix G6 on pages 522-544 of ''Rational Thermodynamics'', C. Truesdell, second edition, Springer, New York, ISBN 0-387-90874-9.</ref>
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| Except for a system undergoing a [[order parameter|first-order]] [[phase transition|phase change]] such as the melting of ice, as a closed system receives heat, without change in its volume and without change in external force fields acting on it, its temperature rises. For a system undergoing such a phase change so slowly that departure from thermodynamic equilibrium can be neglected, its temperature remains constant as the system is supplied with [[latent heat]]. Conversely, a loss of heat from a closed system, without phase change, without change of volume, and without change in external force fields acting on it, decreases its temperature.<ref>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>
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| ===Temperature for bodies in a steady state but not in thermodynamic equilibrium===
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| While for bodies in their own thermodynamic equilibrium states, the notion of temperature requires that all empirical thermometers must agree as to which of two bodies is the hotter or that they are at the same temperature, this requirement is not safe for bodies that are in steady states though not in thermodynamic equilibrium. It can then well be that different empirical thermometers disagree about which is the hotter, and if this is so, then at least one of the bodies does not have a well defined absolute thermodynamic temperature. Nevertheless, any one given body and any one suitable empirical thermometer can still support notions of empirical, non-absolute, hotness and temperature, for a suitable range of processes. This is a matter for study in [[non-equilibrium thermodynamics]].
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| ===Temperature for bodies not in a steady state===
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| When a body is not in a steady state, then the notion of temperature becomes even less safe than for a body in a steady state not in thermodynamic equilibrium. This is also a matter for study in [[non-equilibrium thermodynamics]].
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| ===Thermodynamic equilibrium axiomatics===
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| For axiomatic treatment of thermodynamic equilibrium, since the 1930s, it has become customary to refer to a [[zeroth law of thermodynamics]]. The customarily stated minimalist version of such a law postulates only that all bodies, which when thermally connected would be in thermal equilibrium, should be said to have the same temperature by definition, but by itself does not establish temperature as a quantity expressed as a real number on a scale. A more physically informative version of such a law views empirical temperature as a chart on a hotness manifold.<ref name="Mach 1900"/><ref name="Pitteri 1984"/><ref name="Serrin 1978">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 Janiero, 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> While the zeroth law permits the definitions of many different empirical scales of temperature, the [[second law of thermodynamics]] selects the definition of a single preferred, [[absolute temperature]], unique up to an arbitrary scale factor, whence called the [[thermodynamic temperature]].<ref name="Truesdell 1980">Truesdell, C.A. (1980), Sections 11 B, 11H, pages 306–310, 320-332.</ref><ref name="Mach 1900"/><ref name="Maxwell 1872 155-158">Maxwell, J.C. (1872). ''Theory of Heat'', third edition, Longmans, Green, London, pages 155-158.</ref><ref name="Tait 1884 68-69">Tait, P.G. (1884). ''Heat'', Macmillan, London, Chapter VII, Section 95, pages 68-69.</ref><ref name=buchdahl>{{cite book
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| |author=H.A. Buchdahl
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| |title=The Concepts of Classical Thermodynamics
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| |year=1966
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| |publisher=Cambridge University Press
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| |page=73
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| }}</ref><ref>Kondepudi, D. (2008). ''Introduction to Modern Thermodynamics'', Wiley, Chichester, ISBN 978-0-470-01598-8, Section 32., pages 106-108.</ref> If [[internal energy]] is considered as a function of the volume and entropy of a homogeneous system in thermodynamic equilibrium, thermodynamic absolute temperature appears as the partial derivative of [[internal energy]] with respect the [[entropy]] at constant volume. Its natural, intrinsic origin or null point is [[absolute zero]] at which the entropy of any system is at a minimum. Although this is the lowest absolute temperature described by the model, the [[third law of thermodynamics]] postulates that absolute zero cannot be attained by any physical system.
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| ==Heat capacity==
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| {{see also|Heat capacity|Calorimetry}}
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| When a sample is heated, meaning it receives thermal energy from an external source, some of the introduced [[heat]] is converted into kinetic energy, the rest to other forms of internal energy, specific to the material. The amount converted into kinetic energy causes the temperature of the material to rise. The introduced heat (<math>\Delta Q</math>) divided by the observed temperature change is the [[heat capacity]] (''C'') of the material.
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| : <math> C = \frac{\Delta Q}{\Delta T} </math>
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| If heat capacity is measured for a well defined [[amount of substance]], the [[specific heat]] is the measure of the heat required to increase the temperature of such a unit quantity by one unit of temperature. For example, to raise the temperature of water by one kelvin (equal to one degree Celsius) requires 4186 [[joules]] per [[kilogram]] (J/kg)..
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| ==Temperature measurement==
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| [[File:Pakkanen.jpg|thumb|right|A typical Celsius thermometer measures a winter day temperature of {{gaps|-17|°C}}.]]
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| {{See also|Timeline of temperature and pressure measurement technology|International Temperature Scale of 1990|Comparison of temperature scales}}
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| [[Temperature measurement]] using modern scientific [[thermometer]]s and temperature scales goes back at least as far as the early 18th century, when [[Gabriel Fahrenheit]] adapted a thermometer (switching to [[mercury (element)|mercury]]) and a scale both developed by [[Ole Rømer|Ole Christensen Rømer]]. Fahrenheit's scale is still in use in the United States for non-scientific applications.
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| Temperature is measured with [[thermometers]] that may be [[calibration|calibrated]] to a variety of [[Temperature conversion formulas|temperature scales]]. In most of the world (except for [[Belize]], [[Myanmar]], [[Liberia]] and the [[United States]]), the Celsius scale is used for most temperature measuring purposes. Most scientists measure temperature using the Celsius scale and thermodynamic temperature using the [[Kelvin]] scale, which is the Celsius scale offset so that its null point is {{gaps|0|K}} = {{gaps|−273.15|°C}}, or [[absolute zero]]. Many engineering fields in the U.S., notably high-tech and US federal specifications (civil and military), also use the Kelvin and Celsius scales. Other engineering fields in the U.S. also rely upon the [[Rankine scale]] (a shifted Fahrenheit scale) when working in thermodynamic-related disciplines such as [[combustion]].
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| ===Units===
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| The basic unit of temperature in the [[International System of Units]] (SI) is the [[kelvin]]. It has the symbol K.
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| For everyday applications, it is often convenient to use the Celsius scale, in which {{gaps|0|°C}} corresponds very closely to the [[freezing point]] of water and {{gaps|100|°C}} is its [[boiling point]] at sea level. Because liquid droplets commonly exist in clouds at sub-zero temperatures, {{gaps|0|°C}} is better defined as the melting point of ice. In this scale a temperature difference of 1 degree Celsius is the same as a {{gaps|1|kelvin}} increment, but the scale is offset by the temperature at which ice melts (273.15 K).
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| By international agreement<ref>[http://www1.bipm.org/en/si/si_brochure/chapter2/2-1/2-1-1/kelvin.html The kelvin in the SI Brochure]</ref> the Kelvin and Celsius scales are defined by two fixing points: [[absolute zero]] and the [[triple point]] of [[Vienna Standard Mean Ocean Water]], which is water specially prepared with a specified blend of hydrogen and oxygen isotopes. Absolute zero is defined as precisely {{gaps|0|K}} and {{gaps|−273.15|°C}}. It is the temperature at which all classical translational motion of the particles comprising matter ceases and they are at complete rest in the classical model. Quantum-mechanically, however, zero-point motion remains and has an associated energy, the [[zero-point energy]]. Matter is in its [[ground state]],<ref>{{cite web
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| |url=http://www.calphad.com/absolute_zero.html
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| |title=Absolute Zero
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| |publisher=Calphad.com
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| |accessdate=2010-09-16
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| }}</ref> and contains no [[thermal energy]]. The triple point of water is defined as {{gaps|273.16|K}} and {{gaps|0.01|°C}}. This definition serves the following purposes: it fixes the magnitude of the kelvin as being precisely 1 part in 273.16 parts of the difference between absolute zero and the triple point of water; it establishes that one kelvin has precisely the same magnitude as one degree on the Celsius scale; and it establishes the difference between the null points of these scales as being {{gaps|273.15|K}} ({{gaps|0|K}} = {{gaps|−273.15|°C}} and {{gaps|273.16|K}} = {{gaps|0.01|°C}}).
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| In the United States, the Fahrenheit scale is widely used. On this scale the freezing point of water corresponds to 32 °F and the boiling point to 212 °F. The Rankine scale, still used in fields of chemical engineering in the U.S., is an absolute scale based on the Fahrenheit increment.
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| ====Conversion====
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| The following table shows the [[temperature conversion formulas]] for conversions to and from the Celsius scale.
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| {{temperature|C}}
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| ====Plasma physics====
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| The field of [[plasma physics]] deals with phenomena of [[Electromagnetic radiation|electromagnetic]] nature that involve very high temperatures. It is customary to express temperature in [[electronvolt]]s (eV) or kiloelectronvolts (keV), where 1 eV = {{gaps|11|605|K}}. In the study of [[QCD matter]] one routinely encounters temperatures of the order of a few hundred [[MeV]], equivalent to about {{gaps|10<sup>12</sup>|K}}.
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| ==Theoretical foundation==
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| {{see also|Thermodynamic temperature}}
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| Historically, there are several scientific approaches to the explanation of temperature: the classical thermodynamic description based on macroscopic empirical variables that can be measured in a laboratory; the [[kinetic theory of gases]] which relates the macroscopic description to the probability distribution of the energy of motion of gas particles; and a microscopic explanation based on [[statistical physics]] and [[quantum mechanics]]. In addition, rigorous and purely mathematical treatments have provided an axiomatic approach to classical thermodynamics and temperature.<ref name=caratheodory>{{cite journal
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| |author=C. Caratheodory
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| |title=Untersuchungen über die Grundlagen der Thermodynamik
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| |year=1909
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| |journal=Mathematische Annalen
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| |volume=67
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| |pages=355–386
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| |doi=10.1007/BF01450409
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| |issue=3
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| }}</ref> Statistical physics provides a deeper understanding by describing the atomic behavior of matter, and derives macroscopic properties from statistical averages of microscopic states, including both classical and quantum states. In the fundamental physical description, using [[natural units]], temperature may be measured directly in units of energy. However, in the practical systems of measurement for science, technology, and commerce, such as the modern [[metric system]] of units, the macroscopic and the microscopic descriptions are interrelated by the [[Boltzmann constant]], a proportionality factor that scales temperature to the microscopic mean kinetic energy.
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| The microscopic description in [[statistical mechanics]] is based on a model that analyzes a system into its fundamental particles of matter or into a set of classical or [[quantum mechanics|quantum-mechanical]] oscillators and considers the system as a [[Statistical ensemble (mathematical physics)|statistical ensemble]] of [[State of matter|microstates]]. As a collection of classical material particles, temperature is a measure of the mean energy of motion, called [[kinetic energy]], of the particles, whether in solids, liquids, gases, or plasmas. The kinetic energy, a concept of [[classical mechanics]], is half the [[mass]] of a particle times its [[speed]] squared. In this mechanical interpretation of thermal motion, the kinetic energies of material particles may reside in the velocity of the particles of their translational or vibrational motion or in the inertia of their rotational modes. In monatomic [[perfect gas]]es and, approximately, in most gases, temperature is a measure of the mean particle kinetic energy. It also determines the probability distribution function of the energy. In condensed matter, and particularly in solids, this purely mechanical description is often less useful and the oscillator model provides a better description to account for quantum mechanical phenomena. Temperature determines the statistical occupation of the microstates of the ensemble. The microscopic definition of temperature is only meaningful in the [[thermodynamic limit]], meaning for large ensembles of states or particles, to fulfill the requirements of the statistical model.
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| In the context of thermodynamics, the kinetic energy is also referred to as [[thermal energy]]. The thermal energy may be partitioned into independent components attributed to the [[Degrees of freedom (physics and chemistry)|degrees of freedom]] of the particles or to the modes of oscillators in a [[thermodynamic system]]. In general, the number of these degrees of freedom that are available for the [[equipartition theorem|equipartitioning]] of energy depend on the temperature, i.e. the energy region of the interactions under consideration. For solids, the thermal energy is associated primarily with the [[Atom vibrations|vibrations]] of its atoms or molecules about their equilibrium position. In an [[ideal gas|ideal monatomic gas]], the kinetic energy is found exclusively in the purely translational motions of the particles. In other systems, [[vibration]]al and [[rotation]]al motions also contribute degrees of freedom.
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| ===Kinetic theory of gases===
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| [[File:Translational motion.gif|thumb|right|500px|The temperature of an ideal [[monatomic]] [[gas]] is related to the average [[kinetic energy]] of its [[atom]]s. In this animation, the [[Bohr radius|size]] of [[helium]] atoms relative to their spacing is shown to scale under 1950 [[Atmosphere (unit)|atmospheres]] of pressure. These atoms have a certain, average speed (slowed down here two [[1000000000000 (number)|trillion]] times from room temperature).]]
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| The [[James_Clerk_Maxwell|Maxwell]]-[[Ludwig_Boltzmann|Boltzmann]] [[kinetic theory]] of gases contributes to a fundamental understanding of temperature.<ref>{{cite journal|last=Swendsen|first=Robert|title=Statistical mechanics of colloids and Boltzmann's definition of entropy|journal=American Journal of Physucs|date=March 2006|volume=74|issue=3|pages=187-190}}</ref>
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| It also explains the [[ideal gas]] law, and under certain circumstances, the heat capacity of gases (especially [[Monatomic gas|monatomic]] or [[Noble_gas|'noble']] gases.) An important result of the [[kinetic theory]] of gases is that it relates temperature to the average translational kinetic energy of the molecules in a container of gas in thermodynamic equilibrium.<ref>Balescu, R. (1975). ''Equilibrium and Nonequilibrium Statistical Mechanics'', Wiley, New York, ISBN 0-471-04600-0, pages 148-154.</ref><ref name="K&K 391 397">{{cite book
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| |title=Thermal Physics
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| |last=Kittel |first=Charles
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| |authorlink=Charles Kittel
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| |coauthors=[[Herbert Kroemer|Kroemer, Herbert]]
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| |year=1980
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| |edition=2nd
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| |publisher=W. H. Freeman Company
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| |isbn=0-7167-1088-9
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| |pages=391–397
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| }}</ref><ref>{{cite journal | last1 = Kondepudi | first1 = D.K. | year = 1987 | title = Microscopic aspects implied by the second law | url = | journal = Foundations of Physics | volume = 17 | issue = | pages = 713–722 |bibcode = 1987FoPh...17..713K |doi = 10.1007/BF01889544 }}</ref>
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| The [[ideal gas law]] is based on observed [[empirical relationship]]s between pressure (''p'') and volume (''V''), and temperature (''T'') of a gas. It had been recognized long before the kinetic theory of gases was developed (see [[Boyle's law|Boyle's]] and [[Charles's law|Charles's]] laws). The ideal gas law states:<ref>[[Richard Feynman|Feynman]], R.P., Leighton, R.B., Sands, M. (1963). ''The Feynman Lectures on Physics'', Addison–Wesley, Reading MA, volume 1, pages 39–6 to 39–12.</ref>
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| :<math>pV = nRT\,\!</math>
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| where ''n'' is the number of [[mole unit|mole]]s of gas and R = {{val|8.314472|(15)|u=Jmol<sup>−1</sup>K<sup>−1</sup>}} is the [[gas constant]].
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| The ideal gas law gives us our first hint that there is an [[absolute zero]] on the temperature scale, because it only holds if the temperature is measured on an [[absolute temperature|absolute]]scale such as Kelvins. Moreover, the ideal gas law allows one to measure temperature on this [[absolute temperature|absolute]] scale using the [[gas thermometer]]. Thus, one can define a scale for temperature based on the corresponding pressure and volume of the gas: the temperature in kelvins is the pressure in pascals of one mole of gas in a container of one cubic metre, divided by the gas constant.
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| [[File:Gas thermometer and absolute zero.jpg|thumb|left|240px|Plots of pressure vs temperature for three different gas samples extrapolate to absolute zero.]]
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| Although it is not a particularly convenient device, the [[gas thermometer]] provides an essential theoretical basis by which all thermometers can be calibrated. The pressure, volume, and the number of moles of a substance are all inherently greater than or equal to zero, suggesting that temperature must also be [[Non-negative#non-negative_and_non-positive|non-negative]]. As a practical matter it is not possible to use a gas thermometer to measure absolute zero temperature since the gases tend to condense into a liquid long before the temperature reaches zero. It is possible, however, to extrapolate to absolute zero by using the ideal gas law, as shown in the figure to the left.
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| By showing that the force associated with pressure is caused by collisions of individual atoms with the walls of a container, the kinetic theory is able to relate temperature to energy for an ideal gas. For simplicity, we shall consider only the monatomic ideal gas, for which all energy is translational [[kinetic energy]]. From [[classical mechanics]], we have, <math> E_\text{k} = \begin{matrix} \frac 1 2 \end{matrix} mv^2,\,</math> where ''m'' is the particle mass and ''v'' its speed, the magnitude of its velocity.
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| The distribution of the speeds (which determine the translational kinetic energies) of the particles in a classical ideal gas is called the [[Maxwell-Boltzmann distribution]].<ref name="K&K 391 397"/> The temperature of a classical ideal gas is related to its average kinetic energy per [[degrees of freedom (physics and chemistry)|degree of freedom]] {{math|{{var|{{overline|E}}}}{{sub|k}}}} via the equation:<ref>Tolman, R.C. (1938). ''The Principles of Statistical Mechanics'', Oxford University Press, London, pp. 93, 655.</ref>
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| :<math> \overline{E}_\text{k} = \begin{matrix} \frac 1 2 \end{matrix} kT,</math>
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| where the [[Boltzmann constant]] <math> k = R/n </math> ({{var|n}} = [[Avogadro number]], {{var|R}} = [[ideal gas constant]]). This relation is valid in the ideal gas regime, i.e. when the particle density is much less than <math>1/\Lambda^{3}</math>, where <math>\Lambda</math> is the [[thermal de Broglie wavelength]]. A [[monoatomic gas]] has only the three translational degrees of freedom.
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| Reformulating the pressure-volume term as the sum of classical mechanical particle energies in terms of particle mass, ''m'', and root-mean-square particle speed ''v'', the ideal gas law directly provides the relationship between kinetic energy and temperature:<ref name=atkins>{{cite book
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| |title=Physical Chemistry
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| |author=Peter Atkins, Julio de Paula
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| |page=9
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| |edition=8
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| |publisher=Oxford University Press
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| |year=2006
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| }}</ref>
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| :<math> \displaystyle \frac 1 2 mv_\mathrm{rms}^2 = \frac 3 2 k T.</math>
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| In a mixture of particles of various masses, lighter particles move faster than do heavier particles, but have the same average kinetic energy. A [[neon]] atom moves slowly relative to a [[hydrogen]] molecule of the same kinetic energy. A pollen particle suspended in water moves in a slow [[Brownian motion]] among fast-moving water molecules.
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| It should be noted that this direct proportionality between temperature and energy does not hold for all substances. It is, however, generally true that energy is an [[Monotonic function|increasing function]] of temperature.
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| ===Zeroth law of thermodynamics===
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| {{main|Zeroth law of thermodynamics}}
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| Energy can be transferred between two bodies by a wide variety of processes that include [[thermal conduction|conduction]], [[convective heat transfer|convection]], [[thermal radiation|radiation]], [[phase changes]], and [[Joule heating|Joule]] (ohmic) heating. (See [[heat transfer]].) While all these processes can be called [[heat]], for our purposes it is best to view heat as the transfer of energy via between [[thermal conduction|conduction]] two bodies in [[thermal contact]]. Energy transfer due to compression/decompression is not heat, but is instead called [[work (physics)|work]].
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| The exchange of energy will, in turn, cause other state variables to change. For example, if one of the two bodies is a thermometer, an important state variable that changes is the volume. Left isolated from other bodies, the two connected bodies eventually reach a state of [[thermal equilibrium]] in which no further changes occur.
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| One statement of the [[zeroth law of thermodynamics]] is that if two systems are each in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other. This statement is taken to justify a statement that all three systems have the same temperature, but, by itself, it does not justify the idea of temperature as a numerical scale for a concept of hotness which exists on a one-dimensional manifold with a sense of greater hotness. Sometimes the zeroth law is stated to provide the latter justification.<ref name="Serrin 1978"/> For suitable systems, an empirical temperature scale may be defined by the variation of one of the other state variables, such as pressure, when all other coordinates are fixed. The [[second law of thermodynamics]] is used to define an absolute thermodynamic temperature scale for systems in thermal equilibrium.
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| | |
| ===Second law of thermodynamics===
| |
| {{main|Second law of thermodynamics}}
| |
| In the previous section certain properties of temperature were expressed by the zeroth law of thermodynamics. It is also possible to define temperature in terms of the [[second law of thermodynamics]] which deals with [[entropy]]. Entropy is often thought of as a measure of the disorder in a system. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability.
| |
| | |
| For example, in a series of coin tosses, a perfectly ordered system would be one in which either every toss comes up heads or every toss comes up tails. This means that for a perfectly ordered set of coin tosses, there is only one set of toss outcomes possible: the set in which 100% of tosses come up the same. On the other hand, there are multiple combinations that can result in disordered or mixed systems, where some fraction are heads and the rest tails. A disordered system can be 90% heads and 10% tails, or it could be 98% heads and 2% tails, et cetera. As the number of coin tosses increases, the number of possible combinations corresponding to imperfectly ordered systems increases. For a very large number of coin tosses, the combinations to ~50% heads and ~50% tails dominates and obtaining an outcome significantly different from 50/50 becomes extremely unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy.
| |
| | |
| It has been previously stated that temperature governs the transfer of heat between two systems and it was just shown that the universe tends to progress so as to maximize entropy, which is expected of any natural system. Thus, it is expected that there is some relationship between temperature and entropy. To find this relationship, the relationship between heat, work and temperature is first considered. A [[heat engine]] is a device for converting thermal energy into mechanical energy, resulting in the performance of work, and analysis of the [[Carnot heat engine]] provides the necessary relationships. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, ''q<sub>H</sub>'' and the heat ejected at the low temperature, ''q<sub>C</sub>''. The efficiency is the work divided by the heat put into the system or:
| |
| :<math>
| |
| \textrm{efficiency} = \frac {w_{cy}}{q_H} = \frac{q_H-q_C}{q_H} = 1 - \frac{q_C}{q_H} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(4)</math>
| |
| | |
| where ''w<sub>cy</sub>'' is the work done per cycle. The efficiency depends only on ''q<sub>C</sub>''/''q<sub>H</sub>''. Because ''q<sub>C</sub>'' and ''q<sub>H</sub>'' correspond to heat transfer at the temperatures ''T<sub>C</sub>'' and ''T<sub>H</sub>'', respectively, ''q<sub>C</sub>''/''q<sub>H</sub>'' should be some function of these temperatures:
| |
| :<math>
| |
| \frac{q_C}{q_H} = f(T_H,T_C) \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(5)</math>
| |
| | |
| [[Carnot's theorem (thermodynamics)|Carnot's theorem]] states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between ''T''<sub>1</sub> and ''T''<sub>3</sub> must have the same efficiency as one consisting of two cycles, one between ''T''<sub>1</sub> and ''T''<sub>2</sub>, and the second between ''T''<sub>2</sub> and ''T''<sub>3</sub>. This can only be the case if:
| |
| :<math>
| |
| q_{13} = \frac{q_1 q_2} {q_2 q_3}
| |
| </math>
| |
| | |
| which implies:
| |
| :<math>
| |
| q_{13} = f(T_1,T_3) = f(T_1,T_2)f(T_2,T_3)
| |
| </math>
| |
| | |
| Since the first function is independent of ''T''<sub>2</sub>, this temperature must cancel on the right side, meaning ''f''(''T''<sub>1</sub>,''T''<sub>3</sub>) is of the form ''g''(''T''<sub>1</sub>)/''g''(''T''<sub>3</sub>) (i.e. ''f''(''T''<sub>1</sub>,''T''<sub>3</sub>) = ''f''(''T''<sub>1</sub>,''T''<sub>2</sub>)''f''(''T''<sub>2</sub>,''T''<sub>3</sub>) = ''g''(''T''<sub>1</sub>)/''g''(''T''<sub>2</sub>)· ''g''(''T''<sub>2</sub>)/''g''(''T''<sub>3</sub>) = ''g''(''T''<sub>1</sub>)/''g''(''T''<sub>3</sub>)), where ''g'' is a function of a single temperature. A temperature scale can now be chosen with the property that:
| |
| | |
| :<math>
| |
| \frac{q_C}{q_H} = \frac{T_C}{T_H}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(6)</math>
| |
| | |
| Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in terms of temperature:
| |
| :<math>
| |
| \textrm{efficiency} = 1 - \frac{q_C}{q_H} = 1 - \frac{T_C}{T_H}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(7)
| |
| </math>
| |
| | |
| Notice that for ''T<sub>C</sub>'' = 0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K. Since an efficiency greater than 100% violates the first law of thermodynamics, this implies that 0 K is the minimum possible temperature. In fact the lowest temperature ever obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 5 from the middle portion and rearranging gives:
| |
| :<math>
| |
| \frac {q_H}{T_H} - \frac{q_C}{T_C} = 0
| |
| </math>
| |
| | |
| where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, ''S'', defined by:
| |
| :<math>
| |
| dS = \frac {dq_\mathrm{rev}}{T}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(8)</math>
| |
| | |
| where the subscript indicates a reversible process. The change of this state function around any cycle is zero, as is necessary for any state function. This function corresponds to the entropy of the system, which was described previously. Rearranging Equation 6 gives a new definition for temperature in terms of entropy and heat:
| |
| :<math>
| |
| T = \frac{dq_\mathrm{rev}}{dS}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(9)</math>
| |
| | |
| For a system, where entropy ''S''(''E'') is a function of its energy ''E'', the temperature ''T'' is given by:
| |
| :<math>
| |
| {T}^{-1} = \frac{d}{dE} S(E)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(10)</math>,
| |
| | |
| i.e. the reciprocal of the temperature is the rate of increase of entropy with respect to energy.
| |
| | |
| ===Definition from statistical mechanics===
| |
| | |
| [[Statistical mechanics]] defines temperature based on a system's fundamental degrees of freedom. Eq.(8) is the defining relation of temperature. Eq. (7) can be derived from the principles underlying the [[fundamental thermodynamic relation]].
| |
| | |
| ===Generalized temperature from single particle statistics===
| |
| It is possible to extend the definition of temperature even to systems of few particles, like in a [[quantum dot]]. The generalized temperature is obtained by considering time ensembles instead of configuration space ensembles given in statistical mechanics in the case of thermal and particle exchange between a small system of fermions (N even less than 10) with a single/double occupancy system. The finite quantum [[grand canonical ensemble]],<ref name="finense">{{cite journal
| |
| |author=Prati, E. |title=The finite quantum grand canonical ensemble and temperature from single-electron statistics for a mesoscopic device |journal=J. Stat. Mech. |volume=1 |pages=P01003 |year=2010 |url=http://www.iop.org/EJ/abstract/1742-5468/2010/01/P01003/
| |
| |doi=10.1088/1742-5468/2010/01/P01003|arxiv = 1001.2342 |bibcode = 2010JSMTE..01..003P }} [http://arxiv.org/abs/1001.2342v1 arxiv.org]</ref> obtained under the hypothesis of [[ergodicity]] and [[orthodicity]], allows to express the generalized temperature from the ratio of the average time of occupation <math>\tau</math>''<sub>1</sub>'' and <math>\tau</math>''<sub>2</sub>'' of the single/double occupancy system:<ref name="singlepart">
| |
| {{cite journal |author=Prati, E., ''et al.'' |title=Measuring the temperature of a mesoscopic electron system by means of single electron statistics |journal=Applied Physics Letters |volume=96 |issue= 11|page=113109 |year=2010 |doi=10.1063/1.3365204 |url=http://link.aip.org/link/?APL/96/113109|bibcode = 2010ApPhL..96k3109P |arxiv = 1002.0037 }} [http://arxiv.org/abs/1002.0037v2 arxiv.org]</ref>
| |
| :<math>
| |
| T = k^{-1} \ln 2\frac{\tau_\mathrm{2}}{\tau_\mathrm{1}} \left(E - E_{F} \left(1+\frac{3}{2N}\right) \right),
| |
| </math>
| |
| where ''E<sub>F</sub>'' is the [[Fermi energy]] which tends to the ordinary temperature when N goes to infinity.
| |
| | |
| ===Negative temperature===
| |
| {{main|Negative temperature}}
| |
| On the empirical temperature scales, which are not referenced to absolute zero, a negative temperature is one below the zero-point of the scale used. For example, [[dry ice]] has a sublimation temperature of {{gaps|−78.5|°C}} which is equivalent to {{gaps|−109.3|°F}}. On the absolute Kelvin scale, however, this temperature is 194.6 K. On the absolute scale of thermodynamic temperature no material can exhibit a temperature smaller than or equal to 0 K, both of which are forbidden by the [[third law of thermodynamics]].
| |
| | |
| In the quantum mechanical description of electron and nuclear spin systems that have a limited number of possible states, and therefore a discrete upper limit of energy they can attain, it is possible to obtain a [[negative temperature]], which is numerically indeed less than absolute zero. However, this is not the macroscopic temperature of the material, but instead the temperature of only very specific degrees of freedom, that are isolated from others and do not exchange energy by virtue of the [[equipartition theorem]].
| |
| | |
| A negative temperature is experimentally achieved with suitable radio frequency techniques that cause a [[population inversion]] of spin states from the ground state. As the energy in the system increases upon population of the upper states, the entropy increases as well, as the system becomes less ordered, but attains a maximum value when the spins are evenly distributed among ground and excited states, after which it begins to decrease, once again achieving a state of higher order as the upper states begin to fill exclusively. At the point of maximum entropy, the temperature function shows the behavior of a [[Mathematical singularity|singularity]], because the slope of the entropy function decreases to zero at first and then turns negative. Since temperature is the inverse of the derivative of the entropy, the temperature formally goes to infinity at this point, and switches to negative infinity as the slope turns negative. At energies higher than this point, the spin degree of freedom therefore exhibits formally a negative thermodynamic temperature. As the energy increases further by continued population of the excited state, the negative temperature approaches zero asymptotically.<ref>{{cite book
| |
| |title=Thermal Physics
| |
| |last=Kittel |first=Charles
| |
| |authorlink=Charles Kittel
| |
| |coauthors=[[Herbert Kroemer|Kroemer, Herbert]]
| |
| |year=1980
| |
| |edition=2nd
| |
| |publisher=W. H. Freeman Company
| |
| |isbn=0-7167-1088-9
| |
| |pages=Appendix E
| |
| }}</ref> As the energy of the system increases in the population inversion, a system with a negative temperature is not colder than absolute zero, but rather it has a higher energy than at positive temperature, and may be said to be in fact hotter at negative temperatures. When brought into contact with a system at a positive temperature, energy will be transferred from the negative temperature regime to the positive temperature region.
| |
| | |
| ==Examples of temperature==
| |
| {{main|Orders of magnitude (temperature)}}
| |
| {| class="wikitable" style="text-align:center"
| |
| |-
| |
| ! rowspan=2 |
| |
| ! colspan=2|Temperature
| |
| ! rowspan=2|Peak emittance [[wavelength]]<ref>The cited emission wavelengths are for black bodies in equilibrium. CODATA 2006 recommended value of {{val|2.8977685|(51)|e=-3|u=m K}} used for Wien displacement law constant ''b''.</ref><br /> of [[Wien's displacement law|black-body radiation]]
| |
| |-
| |
| ! [[Kelvin#Usage conventions|Kelvin]]
| |
| ! Degrees Celsius
| |
| |-
| |
| | style="background:#d9d9d3"|[[Absolute zero]]<br />(precisely by definition)
| |
| | 0 K
| |
| | −273.15 °C
| |
| | cannot be defined
| |
| |-
| |
| | style="background:#d9d9d3"|Coldest temperature<br>achieved<ref name="ltl">{{cite web|url = http://ltl.tkk.fi/wiki/LTL/World_record_in_low_temperatures | title = World record in low temperatures|accessdate = 2009-05-05}}</ref>
| |
| | 100 pK
| |
| | {{gaps|−273.149|999|999|900}} °C
| |
| | 29,000 km
| |
| |-
| |
| | style="background:#d9d9d3"|Coldest Bose–Einstein<br />condensate<ref name="recordcold">A temperature of 450 ±80 pK in a Bose–Einstein condensate (BEC) of sodium atoms was achieved in 2003 by researchers at [[Massachusetts Institute of Technology|MIT]]. Citation: ''Cooling Bose–Einstein Condensates Below 500 Picokelvin'', A. E. Leanhardt ''et al''., Science '''301''', 12 Sept. 2003, p. 1515. It's noteworthy that this record's peak emittance black-body wavelength of 6,400 kilometers is roughly the radius of Earth.</ref>
| |
| | 450 pK
| |
| | {{gaps|−273.149|999|999|55}} °C
| |
| | 6,400 [[Terametre|km]]
| |
| |-
| |
| | style="background:#d9d9d3"|One millikelvin<br />(precisely by definition)
| |
| | 0.001 K
| |
| | −273.149 °C
| |
| | {{gaps|2.897|77}} m<br />(radio, [[FM broadcasting|FM band]])<ref>The peak emittance wavelength of {{gaps|2.897|77}} m is a frequency of 103.456 MHz</ref>
| |
| |-
| |
| | style="background:#d9d9d3"|[[Vienna Standard Mean Ocean Water|Water]]'s [[triple point]]<br />(precisely by definition)
| |
| | 273.16 K
| |
| | 0.01 °C
| |
| | 10,608.3 nm<br />(long wavelength [[Infrared|I.R.]])
| |
| |-
| |
| | style="background:#d9d9d3"|Water's [[boiling point]]{{ref label|water|A|A}}
| |
| | 373.1339 K
| |
| | 99.9839 °C
| |
| | 7,766.03 nm<br />(mid wavelength I.R.)
| |
| |-
| |
| | style="background:#d9d9d3" |[[incandescent light bulb|Incandescent lamp]]{{ref label|incadescent|B|B}}
| |
| | 2500 K
| |
| | ≈2,200 °C
| |
| | 1,160 nm<br />(near [[infrared]]){{ref label|tungsten|C|C}}
| |
| |-
| |
| | style="background:#d9d9d3"|[[Sun|Sun's]] visible surface{{ref label|sun|D|D}}<ref>Measurement was made in 2002 and has an uncertainty of ±3 kelvin. A [http://www.kis.uni-freiburg.de/~hw/astroandsolartitles.html 1989 measurement] produced a value of 5,777.0±2.5 K. Citation: [http://theory.physics.helsinki.fi/~sol_phys/Sol0601.pdf ''Overview of the Sun''] (Chapter 1 lecture notes on Solar Physics by Division of Theoretical Physics, Dept. of Physical Sciences, University of Helsinki).</ref>
| |
| | 5,778 K
| |
| | 5,505 °C
| |
| | 501.5 nm<br />([[color#Spectral colors|green-blue light]])
| |
| |-
| |
| | style="background:#d9d9d3" |[[lightning|Lightning bolt's]]<br />channel{{ref label|celsiuskelvin|E|E}}
| |
| | 28 kK
| |
| | 28,000 °C
| |
| | 100 nm<br />(far [[ultraviolet]] light)
| |
| |-
| |
| | style="background:#d9d9d3"|[[Sun#Core|Sun's core]]{{ref label|celsiuskelvin|E|E}}
| |
| | 16 MK
| |
| | 16 million °C
| |
| | 0.18 nm ([[X-ray]]s)
| |
| |-
| |
| | style="background:#d9d9d3"|[[Nuclear weapon|Thermonuclear weapon]]<br />(peak temperature){{ref label|celsiuskelvin|E|E}}<ref>The 350 MK value is the maximum peak fusion fuel temperature in a thermonuclear weapon of the Teller–Ulam configuration (commonly known as a ''hydrogen bomb''). Peak temperatures in Gadget-style fission bomb cores (commonly known as an ''atomic bomb'') are in the range of 50 to 100 MK. Citation: ''Nuclear Weapons Frequently Asked Questions, 3.2.5 Matter At High Temperatures.'' [http://nuclearweaponarchive.org/Nwfaq/Nfaq3.html#nfaq3.2 Link to relevant Web page.] All referenced data was compiled from publicly available sources.</ref>
| |
| | 350 MK
| |
| | 350 million °C
| |
| | 8.3×10<sup>−3</sup> nm<br />([[gamma ray]]s)
| |
| |-
| |
| | style="background:#d9d9d3"|Sandia National Labs'<br />[[Z machine]]{{ref label|celsiuskelvin|E|E}}<ref>Peak temperature for a bulk quantity of matter was achieved by a pulsed-power machine used in fusion physics experiments. The term ''bulk quantity'' draws a distinction from collisions in particle accelerators wherein high ''temperature'' applies only to the debris from two subatomic particles or nuclei at any given instant. The >2 GK temperature was achieved over a period of about ten nanoseconds during ''shot Z1137''. In fact, the iron and manganese ions in the plasma averaged 3.58±0.41 GK (309±35 keV) for 3 ns (ns 112 through 115). [http://prl.aps.org/abstract/PRL/v96/i7/e075003 ''Ion Viscous Heating in a Magnetohydrodynamically Unstable Z Pinch at Over {{val|2|e=9}} Kelvin''], M. G. Haines ''et al.'', Physical Review Letters '''96''' (2006) 075003. [http://sandia.gov/news-center/news-releases/2006/physics-astron/hottest-z-output.html Link to Sandia's news release.]</ref>
| |
| | 2 GK
| |
| | 2 billion °C
| |
| | 1.4×10<sup>−3</sup> nm<br />(gamma rays){{ref label|zmachine|F|F}}
| |
| |-
| |
| | style="background:#d9d9d3"|Core of a [[silicon burning process|high-mass<br />star on its last day]]{{ref label|celsiuskelvin|E|E}}<ref>Core temperature of a high–mass (>8–11 solar masses) star after it leaves the ''main sequence'' on the [[Hertzsprung-Russell diagram|Hertzsprung–Russell diagram]] and begins the ''[[Alpha reactions|alpha process]]'' (which lasts one day) of [[silicon burning process|fusing silicon–28]] into heavier elements in the following steps: sulfur–32 → argon–36 → calcium–40 → titanium–44 → chromium–48 → iron–52 → nickel–56. Within minutes of finishing the sequence, the star explodes as a Type II [[supernova]]. Citation: ''Stellar Evolution: The Life and Death of Our Luminous Neighbors'' (by Arthur Holland and Mark Williams of the University of Michigan). [http://umich.edu/~gs265/star.htm Link to Web site]. More informative links can be found here [http://schools.qps.org/hermanga/images/Astronomy/chapter_21___stellar_explosions.htm], and here [http://cosserv3.fau.edu/~cis/AST2002/Lectures/C13/Trans/Trans.html], and a concise treatise on stars by NASA is here [http://nasa.gov/worldbook/star_worldbook.html].
| |
| {{dead link|date=May 2012}}</ref>
| |
| | 3 GK
| |
| | 3 billion °C
| |
| | 1×10<sup>−3</sup> nm<br />(gamma rays)
| |
| |-
| |
| | style="background:#d9d9d3"|Merging binary [[neutron star|neutron<br />star]] system{{ref label|celsiuskelvin|E|E}}<ref>Based on a computer model that predicted a peak internal temperature of 30 MeV (350 GK) during the merger of a binary neutron star system (which produces a gamma–ray burst). The neutron stars in the model were 1.2 and 1.6 solar masses respectively, were roughly 20 km in diameter, and were orbiting around their barycenter (common center of mass) at about 390 Hz during the last several milliseconds before they completely merged. The 350 GK portion was a small volume located at the pair's developing common core and varied from roughly 1 to 7 km across over a time span of around 5 ms. Imagine two city-sized objects of unimaginable density orbiting each other at the same frequency as the G4 musical note (the 28th white key on a piano). It's also noteworthy that at 350 GK, the average neutron has a vibrational speed of 30% the speed of light and a relativistic mass (''m'') 5% greater than its rest mass (''m''<sub>0</sub>). [http://arxiv.org/pdf/astro-ph/0507099.pdf ''Torus Formation in Neutron Star Mergers and Well-Localized Short Gamma-Ray Bursts''], R. Oechslin ''et al''. of [http://www.mpa-garching.mpg.de/ Max Planck Institute for Astrophysics.], arXiv:astro-ph/0507099 v2, 22 Feb. 2006. [http://www.mpa-garching.mpg.de/mpa/research/current_research/hl2005-10/hl2005-10-en.html An html summary].</ref>
| |
| | 350 GK
| |
| | 350 billion °C
| |
| | 8×10<sup>−6</sup> nm<br />(gamma rays)
| |
| |-
| |
| | style="background:#d9d9d3"|[[Relativistic Heavy Ion Collider|Relativistic Heavy<br />Ion Collider]]{{ref label|celciuskelvin|E|E}}<ref>Results of research by Stefan Bathe using the [http://www.phenix.bnl.gov/ PHENIX] detector on the [http://www.bnl.gov/rhic/ Relativistic Heavy Ion Collider] at [http://www.bnl.gov/world/ Brookhaven National Laboratory] in Upton, New York, U.S.A. Bathe has studied gold-gold, deuteron-gold, and proton-proton collisions to test the theory of quantum chromodynamics, the theory of the strong force that holds atomic nuclei together. [http://bnl.gov/bnlweb/pubaf/pr/PR_display.asp?prID=06-56 Link to news release.]</ref>
| |
| | 1 TK
| |
| | 1 trillion °C
| |
| | 3×10<sup>−6</sup> nm<br />(gamma rays)
| |
| |-
| |
| | style="background:#d9d9d3" |[[CERN|CERN's]] proton vs<br /> nucleus collisions{{ref label|celsiuskelvin|E|E}}<ref>[http://public.web.cern.ch/public/Content/Chapters/AboutCERN/HowStudyPrtcles/HowSeePrtcles/HowSeePrtcles-en.html How do physicists study particles?] by [http://public.web.cern.ch/public/Welcome.html CERN].</ref>
| |
| | 10 TK
| |
| | 10 trillion °C
| |
| | 3×10<sup>−7</sup> nm<br />(gamma rays)
| |
| |-
| |
| | style="background:#d9d9d3"|Universe [[Planck time|5.391×10<sup>−44</sup> s]]<br />after the [[Big Bang]]{{ref label|celsiuskelvin|E|E}}
| |
| | [[Planck temperature|1.417×10<sup>32</sup> K]]
| |
| | 1.417×10<sup>32</sup> °C
| |
| | [[Planck length|1.616×10<sup>−27</sup> nm]]<br />(Planck Length)<ref>The Planck frequency equals {{val|1.85487|(14)|e=43|u=Hz}} (which is the reciprocal of one Planck time). Photons at the Planck frequency have a wavelength of one Planck length. The Planck temperature of {{val|1.41679|(11)|e=32|u=K}} equates to a calculated ''b ''/''T'' = λ<sub>''max''</sub> wavelength of {{val|2.04531|(16)|e=-26|u=nm}}. However, the actual peak emittance wavelength quantizes to the Planck length of {{val|1.61624|(12)|e=-26|u=nm}}.</ref>
| |
| |}
| |
| | |
| <ul style="list-style-type: none;">
| |
| <li>{{note label|water|A|A}} For [[Vienna Standard Mean Ocean Water]] at one standard atmosphere (101.325 kPa) when calibrated strictly per the two-point definition of thermodynamic temperature.</li>
| |
| <li>{{note label|incandescent|B|B}} The 2500 K value is approximate. The 273.15 K difference between K and °C is rounded to 300 K to avoid [[false precision]] in the Celsius value.</li>
| |
| <li>{{note label|tungesten|C|C}} For a true black-body (which tungsten filaments are not). Tungsten filaments' emissivity is greater at shorter wavelengths, which makes them appear whiter.</li>
| |
| <li>{{note label|sun|D|D}} Effective photosphere temperature. The 273.15 K difference between K and °C is rounded to 273 K to avoid false precision in the Celsius value.</li>
| |
| <li>{{note label|celsiuskelvin|E|E}} The 273.15 K difference between K and °C is without the precision of these values.</li>
| |
| <li>{{note label|zmachine|F|F}} For a true black-body (which the plasma was not). The Z machine's dominant emission originated from 40 MK electrons (soft x–ray emissions) within the plasma.</li>
| |
| </ul>
| |
| | |
| ==See also==
| |
| {{Columns-list|2|
| |
| * [[Scale of temperature]]
| |
| * [[Atmospheric temperature]]
| |
| * [[Color temperature]]
| |
| * [[Dry-bulb temperature]]
| |
| * [[Heat conduction]]
| |
| * [[Heat convection]]
| |
| * [[ISO 1]]
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| * [[Instrumental temperature record]]
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| * [[International Temperature Scale of 1990|ITS-90]]
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| * [[Maxwell's demon]]
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| * [[Orders of magnitude (temperature)]]
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| * [[Outside air temperature]]
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| * [[Planck temperature]]
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| * [[Rankine scale]]
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| * [[Relativistic heat conduction]]
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| * [[Satellite temperature measurements]]
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| * [[Stagnation temperature]]
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| * [[Sea Surface Temperature]]
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| * [[Thermal radiation]]
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| * [[Thermoception]]
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| * [[Thermodynamic temperature|Thermodynamic (absolute) temperature]]
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| * [[Thermography]]
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| * [[Thermometer]]
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| * [[Thermoregulation|Body temperature]] (thermoregulation)
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| * [[Virtual temperature]]
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| * [[Wet Bulb Globe Temperature]]
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| * [[Wet-bulb temperature]]
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| }}
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| | |
| == Notes and references==
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| {{Reflist|2}}
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| | |
| ===Bibliography of cited references===
| |
| *Middleton, W.E.K. (1966). ''A History of the Thermometer and its Use in Metrology'', Johns Hopkins Press, Baltimore MD.
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| *Miller, J. (2013). [http://www.physicstoday.org/resource/1/phtoad/v66/i1/p12_s1 Cooling molecules the optoelectric way], ''Physics Today'', '''66'''(1): 12–14.
| |
| *[[J. R. Partington|Partington, J.R.]] (1949). ''An Advanced Treatise on Physical Chemistry'', volume 1, ''Fundamental Principles. The Properties of Gases'', Longmans, Green & Co., London, pp. 175–177.
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| *Quinn, T.J. (1983). ''Temperature'', Academic Press, London, ISBN 0-12-569680-9.
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| *Schooley, J.F. (1986). ''Thermometry'', CRC Press, Boca Raton, ISBN 0-8493-5833-7.
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| *[[William Thomson, 1st Baron Kelvin|Thomson, W. (Lord Kelvin)]] (1848). On an absolute thermometric scale founded on Carnot's theory of the motive power of heat, and calculated from Regnault's observations, ''Proc. Cambridge Phil. Soc.'' (1843/1863) '''1''', No. 5: 66–71.
| |
| *{{cite journal|last=Thomson|first=W. (Lord Kelvin)|author-link=William Thomson, 1st Baron Kelvin|title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule’s equivalent of a Thermal Unit, and M. Regnault’s Observations on Steam|journal=Transactions of the Royal Society of Edinburgh|date=March 1851|volume=XX|issue=part II|pages=261–268; 289–298}}
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| *Truesdell, C.A. (1980). ''The Tragicomical History of Thermodynamics, 1822-1854'', Springer, New York, ISBN 0-387-90403-4.
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| *Zeppenfeld, M., Englert, B.G.U., Glöckner, R., Prehn, A., Mielenz, M., Sommer, C., van Buuren, L.D., Motsch, M., Rempe, G. (2012). [http://www.nature.com/nature/journal/v491/n7425/full/nature11595.html Sysiphus cooling of electrically trapped polyatomic molecules], ''Nature'', '''491''': 570–573.
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| ==Further reading==
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| *Chang, Hasok (2004). ''Inventing Temperature: Measurement and Scientific Progress''. Oxford: Oxford University Press. ISBN 978-0-19-517127-3.
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| *Zemansky, Mark Waldo (1964). ''Temperatures Very Low and Very High''. Princeton, N.J.: Van Nostrand.
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| ==External links==
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| {{Commons category}}
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| {{wiktionary}}
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| *[http://eo.ucar.edu/skymath/SECT1WEB.PDF An elementary introduction to temperature aimed at a middle school audience]
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| *[http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm from Oklahoma State University]
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| *[http://lebanese-economy-forum.com/wdi-gdf-advanced-data-display/show/EN-CLC-AVRT-C/ Average yearly temperature by country] A tabular list of countries and Thermal Map displaying the average yearly temperature by country
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| {{Meteorological variables}}
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| {{Scales of temperature}}
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| {{Portal bar|Energy}}
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| [[Category:Temperature| ]]
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| [[Category:Concepts in physics]]
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| [[Category:Physical quantities]]
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| [[Category:Thermodynamics]]
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| [[Category:Heat transfer]]
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| [[Category:State functions]]
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