Thermodynamic temperature 41789 225398264 2008-07-13T13:52:05Z 222.164.75.183 '''Thermodynamic temperature''' is the absolute measure of [[temperature]] and is one of the principal parameters of [[thermodynamics]]. Thermodynamic temperature is an “absolute” scale because it is the measure of the fundamental property underlying temperature: its ''null'' or zero point, [[absolute zero]], is the temperature at which the particle constituents of matter have minimal motion and can be no colder.<sub>&nbsp;</sub><!-- NOTE TO EDITORS: Absolute zero is not the temperature at which a substance contains “zero heat energy” and is not always the point at which it contains “minimal heat energy.” Nor is T=0 the point at which particles are stationary. This article explains these nuances in the sub-section titled “Heat energy at absolute zero” as well as in Note #1. Editors are asked to be mindful that Wikipedia policy (see [[Wikipedia:Lead section]]) is that articles on technical subjects, and in particular their lead sections, should be as generally accessible as possible for the subject matter. --><br>[[Image:Z-machine480.jpg|thumb|right|440px|The [[Z machine]] at [[Sandia National Laboratories]] in Albuquerque, New Mexico, U.S.A., set a record man-made temperature for a bulk quantity of matter of greater than two billion kelvin. Courtesy, Sandia National Laboratories.]] <h2>Overview</h2><!--NOTE TO EDITORS: This section is internally linked from elsewhere within the article. Do not rename without correcting referencing links.--> [[Image:Translational motion.gif|thumb|right|300px|'''Fig. 1''' The ''translational motion'' of fundamental particles of nature such as atoms and molecules gives a substance its temperature. Here, the size of [[helium]] atoms relative to their spacing is shown to scale under 1950 [[atmosphere (unit)|atmospheres]] of pressure. These room-temperature atoms have a certain, average speed (slowed down here two trillion fold). At any given instant however, a particular helium atom may be moving much faster than average while another may be nearly motionless. Five atoms are colored red to facilitate following their motions.]]<!-- -->Temperature<sup>&nbsp;</sup>arises from the random submicroscopic vibrations of the particle constituents of [[matter]]. These motions comprise the [[Kinetic energy|kinetic]] [[energy]] in a substance. More specifically, the thermodynamic temperature of any bulk quantity of matter is the measure of the average kinetic energy of a certain kind of vibrational motion of its constituent particles called ''translational motions.'' Translational motions are ordinary, whole-body movements in [[three-dimensional space]] whereby particles move about and exchange energy in collisions. ''Fig.&nbsp;1 ''at right shows translational motion in gases; ''[[#The diffusion of heat energy: Entropy, phonons, and mobile conduction electrons|Fig.&nbsp;4]] ''below shows translational motion in solids. Thermodynamic temperature’s [[null (mathematics)|null]] point, absolute zero, is the temperature at which the particle constituents of matter are as close as possible to complete rest; that is, they have [[wikt:minimal#Adjective|minimal]] motion, retaining only [[quantum mechanics|quantum mechanical]] motion.<!-- --><ref name="T0">[[Image:Zero-point energy v.s. motion.jpg|thumb|right|300px|Absolute zero’s relationship to zero-point energy]]<!-- -->While scientists are achieving temperatures ever closer to [[absolute zero]], they can not fully achieve a state of ''“zero”'' temperature. However, even if scientists could remove ''all'' kinetic heat energy from matter, [[quantum mechanics|quantum mechanical]] ''[[zero-point energy]]'' (ZPE) causes particle motion that can never be eliminated. Encyclopedia Britannica Online [http://britannica.com/eb/article-9078341 defines zero-point] energy as the “''vibrational energy that molecules retain even at the absolute zero of temperature.''” ZPE is the result of all-pervasive energy fields in the vacuum between the fundamental particles of nature; it is responsible for the [[Casimir effect]] and other phenomena. See ''[http://calphysics.org/zpe.html Zero Point Energy and Zero Point Field]'', which is an excellent explanation of ZPE by Calphysics Institute. See also ''[http://www.phys.ualberta.ca/~therman/lowtemp/projects1.htm Solid Helium]'' by the University of Alberta’s Department of Physics to learn more about ZPE’s effect on [[Bose–Einstein condensate]]s of helium.<p><!-- -->Although<sup>&nbsp;</sup>absolute zero (''T''=0) is not a state of zero molecular motion, it ''is&nbsp;''the point of zero temperature and, in accordance with the Boltzmann constant, is also the point of zero particle kinetic energy and zero kinetic velocity. To understand how atoms can have zero kinetic velocity and simultaneously be vibrating due to ZPE, consider the following thought experiment: two ''T''=0 helium atoms in zero gravity are carefully positioned and observed to have an average separation of 620&nbsp;[[picometer|pm]] between them (a gap of ten atomic diameters). It’s an “average” separation because ZPE causes them to jostle about their fixed positions. Then one atom is given a kinetic kick of precisely 83&nbsp;yoctokelvin (1&nbsp;yK = 1&nbsp;×&nbsp;10<sup>–24</sup>&nbsp;K). This is done in a way that directs this atom’s velocity vector at the other atom. With 83&nbsp;yK of kinetic energy between them, the 620-pm gap through their common [[barycenter]] would close at a rate of 719&nbsp;pm/s and they would collide after 0.862 second. This is the same speed as shown in the ''[[#Overview|Fig.&nbsp;1]] ''animation above. Before being given the kinetic kick, both ''T''=0 atoms had zero kinetic energy and zero kinetic velocity because they could persist indefinitely in that state and relative orientation even though both were being jostled by ZPE. At ''T''=0, no kinetic energy is available for transfer to other systems. The Boltzmann constant and its related formulas describe the realm of particle kinetics and velocity vectors whereas ZPE is an energy field that jostles particles in ways described by the mathematics of quantum mechanics. In atomic and molecular collisions in gases, ZPE introduces a degree of ''[[Chaos theory|chaos]]'', i.e., unpredictability, to rebound kinetics; it is as likely that there will be ''less'' ZPE-induced particle motion after a given collision as ''more.'' This random nature of ZPE is why it has no net effect upon either the pressure or volume of any ''bulk quantity'' (a statistically significant quantity of particles) of ''T''>0&nbsp;K gases. However, in ''T''=0 [[condensed matter physics|condensed matter]]; e.g., solids and liquids, ZPE causes inter-atomic jostling where atoms would otherwise be perfectly stationary. Inasmuch as the real-world effects that ZPE has on substances can vary as one alters a thermodynamic system (for example, due to ZPE, helium won’t freeze unless under a pressure of at least 25&nbsp;[[bar (unit)|bar]]), ZPE is very much a form of heat energy and may properly be included when tallying a substance’s internal energy.<p><!-- -->Note<sup>&nbsp;</sup>too that absolute zero serves as the baseline atop which [[thermodynamics]] and its [[thermodynamic equations|equations]] are founded because they deal with the exchange of heat energy between ''“systems”'' (a plurality of particles and fields modeled as an average). Accordingly, one may examine ZPE-induced particle motion ''within'' a system that is at absolute zero but there can never be a net outflow of heat energy from such a system. Also, the peak emittance wavelength of black-body radiation shifts to infinity at absolute zero; indeed, a peak no longer exists and black-body photons can no longer escape. Due to the influence of ZPE however, ''virtual'' photons are still emitted at ''T''=0. Such photons are called “virtual” because they can’t be intercepted and observed. Furthermore, this ''zero-point radiation'' has a unique ''zero-point spectrum.'' However, even though a ''T''=0 system emits zero-point radiation, no net heat flow ''Q'' out of such a system can occur because if the surrounding environment is at a temperature greater than ''T''=0, heat will flow inward, and if the surrounding environment is at ''T''=0, there will be an equal flux of ZP radiation both inward and outward. A similar ''Q ''equilibrium exists at ''T''=0 with the ZPE-induced [[spontaneous emission|“spontaneous” emission]] of photons (which is more properly called a ''stimulated'' emission in this context). The graph at upper right illustrates the relationship of absolute zero to zero-point energy. The graph also helps in the understanding of how zero-point energy got its name: it is the vibrational energy matter retains at the ''“zero kelvin point.”'' Citation: ''Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces'', Daniel C. Cole, Physical Review A, Third Series '''42''', Number 4, 15 August 1990, Pg. 1847–1862.</ref> Zero kinetic energy remains in a substance at absolute zero (see ''[[Thermodynamic temperature#Heat energy at absolute zero|Heat energy at absolute zero]]'', below). Throughout<sup>&nbsp;</sup>the scientific world where measurements are made in [[International System of Units|SI]] units, thermodynamic temperature is measured in [[kelvin]]s (symbol:&nbsp;K). Many engineering fields in the [[United States|U.S.]] however, measure thermodynamic temperature using the [[Rankine scale]]. By [http://www1.bipm.org/en/si/si_brochure/chapter2/2-1/2-1-1/kelvin.html international agreement,] the<sup>&nbsp;</sup>unit “kelvin” and its scale are defined by two points: absolute zero, and the [[triple point]] of [[Vienna Standard Mean Ocean Water]] (water with a specified blend of hydrogen and oxygen isotopes). Absolute zero—the coldest possible temperature—is defined as being precisely 0&nbsp;K ''and'' −273.15&nbsp;[[Celsius|°C]]. The triple point of water is defined as being precisely 273.16&nbsp;K ''and'' 0.01&nbsp;°C. This definition does three things: #It fixes the magnitude of the kelvin unit as being precisely 1 part in 273.16 parts the difference between absolute zero and the triple point of water; #It establishes that one kelvin has precisely the same magnitude as a one-degree increment on the [[Celsius]] scale; and #It establishes the difference between the two scales’ null points as being precisely 273.15 kelvins (0&nbsp;K = −273.15&nbsp;°C and 273.16&nbsp;K = 0.01&nbsp;°C). Temperatures<sup>&nbsp;</sup>expressed in kelvins are converted to degrees Rankine simply by multiplying by 1.8 as follows: ''T''<sub>K</sub>&nbsp;×&nbsp;1.8&nbsp;=&nbsp;''T''<sub>°R</sub>, where ''T''<sub>K</sub> and ''T''<sub>°R</sub> are temperatures in kelvins and degrees Rankine respectively. Temperatures expressed in Rankine are converted to kelvins by ''dividing'' by 1.8 as follows: ''T''<sub>°R</sub>&nbsp;÷&nbsp;1.8&nbsp;=&nbsp;''T''<sub>K</sub>. <h2>Table of thermodynamic temperatures</h2><!-- NOTE TO EDITORS: This section is internally linked from elsewhere within the article. --> The full range of the thermodynamic temperature scale and some notable points along it are shown in the table below. {| border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f5f5f5; border: 2px #525252 solid; border-collapse: collapse; font-size: 95%;" |- |style="background:#d9d9d3" align="center"|'' '' |style="background:#d9d9d3" align="center"|'''kelvin''' |style="background:#d9d9d3" align="center"|'''Celsius''' |style="background:#d9d9d3" align="center"|'''Peak emittance<br>[[wavelength]] <ref>The<sup>&nbsp;</sup>cited emission wavelengths are for true black bodies in equilibrium. In this table, only the sun so qualifies. CODATA 2006 recommended value of 2.897&nbsp;7685(51)&nbsp;×&nbsp;10<sup>−3</sup>&nbsp;m&nbsp;K used for Wien displacement law constant ''b''.</ref> of<br>[[Wien's displacement law|black-body photons]]''' |- |style="background:#d9d9d3" align="right"|[[Absolute zero]]<br> (precisely by definition) |align="center"|0 K |align="center"|−273.15 °C |align="center"|&nbsp;&nbsp;<FONT SIZE="+1">[[Infinity|∞]]</FONT><small>&nbsp;</small><ref name="T0"/> |- |style="background:#d9d9d3" align="right"|Coldest measured<br>temperature<sup><small>&nbsp;</small></sup><ref name="recordcold">A<sup>&nbsp;</sup>record cold temperature of 450&nbsp;±80&nbsp;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, Pg. 1515. It’s noteworthy that this record’s peak emittance black-body wavelength of 6,400 kilometers is roughly the radius of Earth.</ref> |align="center"|450 [[Kelvin#SI prefixes|pK]] |align="center"|–273.149<span style="margin-left:0.3em">999<span style="margin-left:0.3em">999<span style="margin-left:0.3em">55&nbsp;°C |align="center"|6,400 [[kilometre|kilometers]] |- |style="background:#d9d9d3" align="right"|One [[Kelvin#SI prefixes|millikelvin]]<br> (precisely by definition) |align="center"|0.001 K |align="center"|−273.149 °C |align="center"|2.897&nbsp;77 [[metre|meters]]<br> (Radio, [[FM broadcasting|FM band]]) <ref>The<sup>&nbsp;</sup>peak emittance wavelength of 2.897&nbsp;77&nbsp;m is a frequency of 103.456&nbsp;MHz</ref> |- |style="background:#d9d9d3" align="right"|[[Vienna Standard Mean Ocean Water|Water]]’s [[triple point]]<br> (precisely by definition) |align="center"|273.16 K |align="center"|0.01 °C |align="center"|10,608.3 [[metre#SI prefixed forms of metre|nm]]<br>(Long wavelength [[Infrared|I.R.]]) |- |style="background:#d9d9d3" align="right"|Water’s [[boiling point]]<sup> A</sup> |align="center"| 373.1339 K |align="center"|99.9839 °C |align="center"|7766.03 nm<br>(Mid wavelength I.R.) |- |style="background:#d9d9d3" align="right"|[[incandescent light bulb|Incandescent lamp]]<sup>B</sup> |align="center"|2500 K |align="center"|≈2200 °C |align="center"|1160 nm<br>(Near [[infrared]])<sup>C</sup> |- |style="background:#d9d9d3" align="right"|[[Sun|Sun’s]] visible surface<sup>D</sup> <ref>Measurement<sup>&nbsp;</sup>was made in 2002 and has an uncertainty of ±3 kelvins. A [http://www.kis.uni-freiburg.de/~hw/astroandsolartitles.html 1989 measurement] produced a value of 5777 ±2.5&nbsp;K. Citation: ''Overview of the Sun'' (Chapter 1 lecture notes on Solar Physics by Division of Theoretical Physics, Dept. of Physical Sciences, University of Helsinki). [http://theory.physics.helsinki.fi/~sol_phys/Sol0601.pdf Download paper (252&nbsp;kB PDF])</ref> |align="center"|5778 K |align="center"|5505 °C |align="center"|501.5 nm<br>([[color#Spectral colors|Green-Blue light]]) |- |style="background:#d9d9d3" align="right"|[[lightning|Lightning bolt’s]]<br>channel<sup> E</sup> |align="center"|28,000 K |align="center"|28,000 °C |align="center"|100 nm<br>(Far [[Ultraviolet]] light) |- |style="background:#d9d9d3" align="right"|[[Sun#Core|Sun’s core]]<sup> E</sup> |align="center"|16 [[Kelvin#SI prefixes|MK]] |align="center"|16 million °C |align="center"|0.18 nm ([[X-ray]]s) |- |style="background:#d9d9d3" align="right"|[[Nuclear weapon|Thermonuclear weapon]]<br>(peak temperature)<sup>E</sup> <ref>The<sup>&nbsp;</sup>350&nbsp;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&nbsp;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> |align="center"|350 MK |align="center"|350 million °C |align="center"|8.3 × 10<sup>−3</sup> nm<br>([[Gamma ray]]s) |- |style="background:#d9d9d3" align="right"|Sandia National Labs’<br>[[Z machine]]<sup> E</sup> <ref>Peak<sup>&nbsp;</sup>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&nbsp;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&nbsp;GK (309 ±35&nbsp;keV) for 3&nbsp;ns (ns 112 through 115). Citation: ''Ion Viscous Heating in a Magnetohydrodynamically Unstable Z Pinch at Over 2&nbsp;×&nbsp;10<sup>9</sup> Kelvin'', M. G. Haines ''et al.'', Physical Review Letters '''96''', Issue 7, id. 075003. [http://sandia.gov/news-center/news-releases/2006/physics-astron/hottest-z-output.html Link to Sandia’s news release.]</ref> |align="center"|2 [[Kelvin#SI prefixes|GK]] |align="center"|2 billion °C |align="center"|1.4 × 10<sup>−3</sup> nm<br>(Gamma rays)<sup>F</sup> |- |style="background:#d9d9d3" align="right"|Core of a [[silicon burning process|high–mass<br>star on its last day]]<sup> E</sup> <ref>Core<sup>&nbsp;</sup>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&nbsp;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 [http://schools.qps.org/hermanga/images/Astronomy/chapter_21___stellar_explosions.htm here,] and [http://cosserv3.fau.edu/~cis/AST2002/Lectures/C13/Trans/Trans.html here,] and a concise treatise on stars by NASA is&nbsp;[http://nasa.gov/worldbook/star_worldbook.html here].</ref> |align="center"|3 GK |align="center"|3 billion °C |align="center"|1 × 10<sup>−3</sup> nm<br>(Gamma rays) |- |style="background:#d9d9d3" align="right"|Merging binary [[neutron star|neutron<br>star]] system<small> </small><sup>E</sup> <ref>Based<sup>&nbsp;</sup>on a computer model that predicted a peak internal temperature of 30 MeV (350&nbsp;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&nbsp;km in diameter, and were orbiting around their barycenter (common center of mass) at about 390&nbsp;Hz during the last several milliseconds before they completely merged. The 350&nbsp;GK portion was a small volume located at the pair’s developing common core and varied from roughly 1 to 7&nbsp;km across over a time span of around 5&nbsp;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>).&nbsp; Citation: ''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.&nbsp; [http://arxiv.org/pdf/astro-ph/0507099.pdf Download paper (725&nbsp;kB PDF]) (from Cornell University Library’s arXiv.org server). To view a browser-based summary of the research, [http://www.mpa-garching.mpg.de/mpa/research/current_research/hl2005-10/hl2005-10-en.html click here].</ref> |align="center"|350 GK |align="center"|350 billion °C |align="center"|8 × 10<sup>−6</sup> nm<br>(Gamma rays) |- |style="background:#d9d9d3" align="right"|[[Relativistic Heavy Ion Collider|Relativistic Heavy<br>Ion Collider]]<sup> E</sup> <ref>Results<sup>&nbsp;</sup>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.&nbsp; 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.&nbsp; [http://bnl.gov/bnlweb/pubaf/pr/PR_display.asp?prID=06-56 Link to news release.]</ref> |align="center"|1 [[Kelvin#SI prefixes|TK]] |align="center"|1 trillion °C |align="center"|3 × 10<sup>−6</sup> nm<br>(Gamma rays) |- |style="background:#d9d9d3" align="right"|[[CERN|CERN’s]] proton vs.<br> nucleus collisions<sup> E</sup> <ref>Citation:<sup>&nbsp;</sup>''[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> |align="center"|10 TK |align="center"|10 trillion °C |align="center"|3 × 10<sup>−7</sup> nm<br>(Gamma rays) |- |style="background:#d9d9d3" align="right"|Universe [[Planck time|5.391 × 10<sup>−44</sup> s]]<br>after the [[Big Bang]]<sup> E</sup> |align="center"|[[Planck temperature|1.417 × 10<sup>32</sup> K]] |align="center"|1.417 × 10<sup>32</sup> °C |align="center"|[[Planck length|1.616&nbsp;× 10<sup>−26</sup> nm]]<br> (Planck frequency) <ref>The<sup>&nbsp;</sup>Planck frequency equals 1.854&nbsp;87(14)&nbsp;×&nbsp;10<sup>43</sup>&nbsp;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 1.416&nbsp;79(11)&nbsp;×&nbsp;10<sup>32</sup>&nbsp;K equates to a calculated ''b&nbsp;''/''T''&nbsp;=&nbsp;λ<sub>''max''</sub> wavelength of 2.045&nbsp;31(16)&nbsp;×&nbsp;10<sup>−26</sup>&nbsp;nm. However, the actual peak emittance wavelength quantizes to the Planck length of 1.616&nbsp;24(12)&nbsp;×&nbsp;10<sup>−26</sup>&nbsp;nm.</ref> |} <small><sup>A</sup> For [[Vienna Standard Mean Ocean Water]] at one standard atmosphere (101.325&nbsp;kPa) when calibrated strictly per the two-point definition of thermodynamic temperature.<br> <sup>B</sup> The 2500&nbsp;K value is approximate. The 273.15&nbsp;K difference between K and °C is rounded to 300&nbsp;K to avoid [[false precision]] in the Celsius value.<br> <sup>C</sup> For a true blackbody (which tungsten filaments are not). Tungsten filaments’ emissivity is greater at shorter wavelengths, which makes them appear whiter.<br> <sup>D</sup> Effective photosphere temperature. The 273.15&nbsp;K difference between K and °C is rounded to 273&nbsp;K to avoid false precision in the Celsius value.<br> <sup>E</sup> The 273.15&nbsp;K difference between K and °C is ignored to avoid false precision in the Celsius value.<br> <sup>F</sup> For a true blackbody (which the plasma was not). The Z machine’s dominant emission originated from 40&nbsp;MK electrons (soft x–ray emissions) within the plasma.</small> ==The relationship of temperature, motions, conduction, and heat energy== ====The nature of kinetic energy, translational motion, and temperature====<!-- NOTE TO EDITORS: This section is internally linked from elsewhere within the article. --> At its simplest, “temperature” arises from the [[kinetic energy]] of the vibrational motions of [[Matter|matter’s]] particle constituents ([[molecule]]s, [[atom]]s, and [[subatomic particle]]s). The full variety of these kinetic motions contribute to the total [[heat]] energy in a substance. The relationship of kinetic energy, mass, and velocity is given by the formula ''E<sub>k</sub>''&nbsp;=&nbsp;{{frac|2}}''m''&nbsp;•&nbsp;''v''<sup>&nbsp;2</sup>.<ref>At<sup>&nbsp;</sup>non-[[Special relativity|relativistic]] temperatures of less than about 30&nbsp;GK, [[classical mechanics]] are sufficient to calculate the velocity of particles. At 30&nbsp;GK, individual neutrons (the constituent of neutron stars and one of the few materials in the universe with temperatures in this range) have a 1.0042 γ (gamma or [[Lorentz factor]]). Thus, the classic Newtonian formula for kinetic energy is in error less than half a percent for temperatures less than 30&nbsp;GK.</ref> Accordingly, particles with one unit of mass moving at one unit of velocity have precisely the same kinetic energy—and precisely the same temperature—as those with four times the mass but half the velocity. [[Image:Maxwell Dist-Inverse Speed.jpg|thumb|right|300px|'''Fig. 2''' The translational motions of helium atoms occurs across a range of speeds. Compare the shape of this curve to that of a Planck curve in ''[[#The diffusion of heat energy: Black-body radiation|Fig.&nbsp;5&nbsp;]]''below.]]The<sup>&nbsp;</sup>thermodynamic temperature of any ''bulk quantity'' of a substance (a statistically significant quantity of particles) is directly proportional to the average—or “mean”—kinetic energy of a specific kind of particle motion known as ''translational motion.'' These simple movements in the three ''x'', ''y'', and ''z''–axis dimensions of space means the particles move in the three spatial ''[[Degrees of freedom (physics and chemistry)|degrees of freedom]].'' This particular form of kinetic energy is sometimes referred to as ''kinetic temperature.'' Translational motion is but one form of heat energy and is what gives gases not only their temperature, but also their pressure and the vast majority of their volume. This relationship between the temperature, pressure, and volume of gases is established by the [[ideal gas law]]’s formula ''pV''&nbsp;=&nbsp;''nRT'' and is embodied in the [[gas laws]]. The extent to which the kinetic energy of translational motion of an individual atom or molecule (particle) in a gas contributes to the pressure and volume of that gas is a proportional function of thermodynamic temperature as established by the [[Boltzmann constant]] (symbol:&nbsp;''k<sub>B</sub>''). The Boltzmann constant also relates the thermodynamic temperature of a gas to the mean kinetic energy of an individual particle’s translational motion as follows: :''E<sub>mean</sub>''&nbsp;=&nbsp;{{frac|3|2}}''k<sub>B</sub>T'' ::where… ::''E<sub>mean</sub>'' is the mean kinetic energy in [[joule]]s (symbol: J) ::''k<sub>B</sub>'' = {{val|1.3806504|(24)|e=-23|u=J/K}} ::''T'' is the thermodynamic temperature in kelvins While the Boltzmann constant is useful for finding the mean kinetic energy of a particle, it’s important to note that even when a substance is isolated and in [[thermodynamic equilibrium]] (all parts are at a uniform temperature and no heat is going into or out of it), the translational motions of individual atoms and molecules occurs across a wide range of speeds (see animation in ''[[#Overview|Fig.&nbsp;1]] ''above). At any one instant, the proportion of particles moving at a given speed within this range is determined by probability as described by the [[Maxwell–Boltzmann distribution]]. The graph shown here in ''Fig.&nbsp;2&nbsp;'' shows the speed distribution of 5500&nbsp;K helium atoms. They have a ''most probable'' speed of 4.780&nbsp;km/s (0.2092&nbsp;s/km). However, a certain proportion of atoms at any given instant are moving faster while others are moving relatively slowly; some are momentarily at a virtual standstill (off the ''x''–axis to the right). This graph uses ''inverse speed'' for its ''x''–axis so the shape of the curve can easily be compared to the curves in ''[[#The diffusion of heat energy: Black-body radiation|Fig.&nbsp;5]]'' below. In both graphs, zero on the ''x''–axis represents infinite temperature. Additionally, the ''x'' and ''y''–axis on both graphs are scaled proportionally. ====The high speeds of translational motion==== Although very specialized laboratory equipment is required to directly detect translational motions, the resultant collisions by atoms or molecules with small particles suspended in a [[fluid]] produces [[Brownian motion]] that can be seen with an ordinary microscope. The translational motions of elementary particles are ''very'' fast<ref>Even<sup>&nbsp;</sup>room–temperature air has an average molecular translational ''speed'' (not vector-isolated velocity) of 1822&nbsp;km/hour. This is relatively fast for something the size of a molecule considering there are roughly 2.42&nbsp;×&nbsp;10<sup>16</sup> of them crowded into a single cubic millimeter. Assumptions: Average molecular weight of wet air = 28.838 g/mol and ''T'' = 296.15&nbsp;K. Assumption’s primary variables: An altitude of 194 meters above mean sea level (the world–wide median altitude of human habitation), an indoor temperature of 23&nbsp;°C, a dewpoint of 9&nbsp;°C (40.85% relative humidity), and 760&nbsp;[[mmHg]] (101.325 kPa) sea level–corrected barometric pressure.</ref> and temperatures close to [[absolute zero]] are required to directly observe them. For instance, when scientists at the [[National Institute of Standards and Technology|NIST]] achieved a record-setting cold temperature of 700&nbsp;nK (billionths of a kelvin) in 1994, they used [[optical lattice]] laser equipment to [[Adiabatic process|adiabatically]] cool [[caesium]] atoms. They then turned off the entrapment lasers and directly measured atom velocities of 7&nbsp;mm per second to in order to calculate their temperature.<ref>Citation:<sup>&nbsp;</sup>''Adiabatic Cooling of Cesium to 700&nbsp;nK in an Optical Lattice'', A. Kastberg ''et al''., Physical Review Letters '''74''', No. 9, 27 Feb. 1995, Pg. 1542. It’s noteworthy that a record cold temperature of 450&nbsp;[[Kelvin#SI prefixes|pK]] in a Bose–Einstein condensate of sodium atoms (achieved by A. E. Leanhardt ''et al''. of [[Massachusetts Institute of Technology|MIT]]) equates to an average vector-isolated atom velocity of 0.4&nbsp;mm/s and an average atom speed of 0.7&nbsp;mm/s.</ref>&nbsp; Formulas for calculating the velocity and speed of translational motion are given in the following footnote.<ref name="Boltzmann">The<sup>&nbsp;</sup>rate of translational motion of atoms and molecules is calculated based on thermodynamic temperature as follows:<br><br> :<math>\tilde{v} = \sqrt{\frac {{k_B\over 2} \cdot T}{{m\over 2}}}</math> ::where… ::<math>\tilde{v}</math> is the vector-isolated mean velocity of translational particle motion in m/s ::''k<sub>B</sub>'' ([[Boltzmann constant]]) = 1.380<FONT SIZE="-1">&nbsp;</FONT>6504(24)&nbsp;×&nbsp;10<sup>−23</sup>&nbsp;J/K ::''T'' is the thermodynamic temperature in kelvins ::''m'' is the<sub>&nbsp;</sub>molecular mass of substance in kg/particle In<sup>&nbsp;</sup>the above formula, molecular mass, ''m'', in kg/particle is the quotient of a substance’s [[molar mass]] (also known as ''atomic weight'', ''[[atomic mass]]'', ''relative atomic mass'', and ''[[Atomic mass unit|unified atomic mass units]]'') in [[Gram|g]]/[[Mole (unit)|mol]] or [[Atomic mass unit|daltons]] divided by 6.022<FONT SIZE="-1">&nbsp;</FONT>141<FONT SIZE="-1">&nbsp;</FONT>79(30)&nbsp;×&nbsp;10<sup>26</sup> (which is the [[Avogadro's number|Avogadro constant]] times one thousand). For [[diatomic]] molecules such as [[hydrogen|H<sub>2</sub>]], [[nitrogen|N<sub>2</sub>]], and [[oxygen|O<sub>2</sub>]], multiply atomic weight by two before plugging it into the above formula.<br><br> The mean ''speed'' (not vector-isolated velocity) of an atom or molecule along any arbitrary path is calculated as follows:<br><br> :<math>\tilde{s} = \tilde{v} \cdot \sqrt{3}</math> ::where… ::<math>\tilde{s}</math> is the<sub>&nbsp;</sub>mean speed of translational particle motion in m/s<br> Note<sup>&nbsp;</sup>that the mean energy of the translational motions of a substance’s constituent particles correlates to their mean ''speed'', not velocity. Thus, substituting <math>\tilde{s}</math> for ''v'' in the classic formula for kinetic energy, ''E<sub>k</sub>''&nbsp;=&nbsp;{{frac|2}}''m''&nbsp;•&nbsp;''v''<sup>&nbsp;2</sup> produces precisely the same value as does ''E<sub>mean</sub>''&nbsp;=&nbsp;3/2''k<sub>B</sub>T'' (as shown in the section titled ''[[#The nature of kinetic energy, translational motion, and temperature|The nature of kinetic energy, translational motion, and temperature]])''.<sub>&nbsp;</sub><br> Note<sup>&nbsp;</sup>too that the Boltzmann constant and its related formulas establish that absolute zero is the point of both zero kinetic energy of particle motion and zero kinetic velocity (see also ''[[#Notes|Note 1]]'' above).</ref> ====The internal motions of molecules and specific heat==== [[Image:Thermally Agitated Molecule.gif|thumb|right|266px|'''Fig. 3''' Molecules have internal structure because they are composed of atoms that have different ways of moving within molecules. Being able to store kinetic energy in these ''internal degrees of freedom'' contributes to a substance’s ''[[specific heat capacity]]'', allowing it to contain more heat energy at the same temperature.]]There are other forms of heat energy besides the kinetic energy of translational motion. As can be seen in the animation at right, [[molecule]]s are complex objects; they are a population of atoms and thermal agitation can strain their internal [[chemical bond]]s in three different ways: via rotation, bond length, and bond angle movements. These are all types of ''internal degrees of freedom''. This makes molecules distinct from ''[[monatomic]]'' substances (consisting of individual atoms) like the [[noble gas]]es [[helium]] and [[argon]], which have only the three translational degrees of freedom. Kinetic energy is stored in molecules’ internal degrees of freedom, which gives them an ''internal temperature.''&nbsp; Even though these motions are called “internal,” the external portions of molecules still move—rather like the jiggling of a stationary [[water balloon]]. This permits the two-way exchange of kinetic energy between internal motions and translational motions with each molecular collision. Accordingly, as heat is removed from molecules, both their kinetic temperature (the kinetic energy of translational motion) and their internal temperature simultaneously diminish in equal proportions. This phenomenon is described by the [[equipartition theorem]], which states that for any bulk quantity of a substance in equilibrium, the kinetic energy of particle motion is evenly distributed among all the active degrees of freedom available to the particles. Since the internal temperature of molecules are usually equal to their kinetic temperature, the distinction is usually of interest only in the detailed study of non-[[local thermodynamic equilibrium]] (LTE) phenomena such as [[combustion]], the [[sublimation (chemistry)|sublimation]] of solids, and the [[diffusion]] of hot gases in a partial vacuum. The<sup>&nbsp;</sup>kinetic energy stored internally in molecules allows a substance to contain more heat energy at a given temperature (and in the case of gases, at a given pressure and volume), and to absorb more of it for a given temperature increase. This is because any kinetic energy that is, at a given instant, bound in internal motions is not at that same instant contributing to the molecules’ translational motions.<ref>The<sup>&nbsp;</sup>internal degrees of freedom of molecules cause their external surfaces to vibrate and can also produce overall spinning motions (what can be likened to the jiggling and spinning of an otherwise stationary water balloon). If one examines a ''single'' molecule as it impacts a containers’ wall, some of the kinetic energy borne in the molecule’s internal degrees of freedom can constructively add to its translational motion during the instant of the collision and extra kinetic energy will be transferred into the container’s wall. This would induce an extra, localized, impulse-like contribution to the average pressure on the container. However, since the internal motions of molecules are random, they have an equal probability of ''destructively'' interfering with translational motion during a collision with a container’s walls or another molecule. Averaged across any bulk quantity of a gas, the internal thermal motions of molecules have zero net effect upon the temperature, pressure, or volume of a gas. Molecules’ internal degrees of freedom simply provide additional locations where kinetic energy is stored. This is precisely why molecular-based gases have greater specific heat capacity than monatomic gases (where additional heat energy must be added to achieve a given temperature rise).</ref> This extra kinetic energy simply increases the amount of heat energy a substance absorbs for a given temperature rise. This property is known as a substance’s [[specific heat capacity]]. Different<sup>&nbsp;</sup>molecules absorb different amounts of heat energy for each incremental increase in temperature; that is, they have different specific heat capacities. High specific heat capacity arises, in part, because certain substances’ molecules possess more internal degrees of freedom than others do. For instance, room-temperature [[nitrogen]], which is a [[diatomic]] molecule, has ''five'' active degrees of freedom: the three comprising translational motion plus two rotational degrees of freedom internally. Not surprisingly, in accordance with the equipartition theorem, nitrogen has five-thirds the specific heat capacity per [[mole (unit)|mole]] (a specific number of molecules) as do the monatomic gases.<ref>When<sup>&nbsp;</sup>measured at constant-volume since different amounts of work must be performed if measured at constant-pressure. Nitrogen’s ''C<sub>v</sub>H'' (100&nbsp;kPa, 20&nbsp;°C) equals 20.8&nbsp;J&nbsp;mol<sup>–1</sup>&nbsp;K<sup>–1</sup> vs. the monatomic gases, which equal 12.4717&nbsp;J&nbsp;mol<sup>–1</sup>&nbsp;K<sup>–1</sup>. Citations: [http://www.whfreeman.com/ W.H. Freeman’s] ''Physical Chemistry'', Part 3: Change ([http://www.whfreeman.com/college/pdfs/pchem8e/PC8eC21.pdf 422&nbsp;kB PDF, here]), Exercise 21.20b, Pg.&nbsp;787. Also [http://www.gsu.edu/ Georgia State University’s] ''[http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/shegas.html Molar Specific Heats of Gases]''.</ref> Another example is [[gasoline]] (see [[Specific heat capacity#Table of specific heat capacities|table]] showing its specific heat capacity). Gasoline can absorb a large amount of heat energy per mole with only a modest temperature change because each molecule comprises an average of 21 atoms and therefore has many internal degrees of freedom. Even larger, more complex molecules can have dozens of internal degrees of freedom. ====The diffusion of heat energy: Entropy, phonons, and mobile conduction electrons====<!-- NOTE TO EDITORS: This section is internally linked from elsewhere within the article. --> [[Image:1D normal modes (280 kB).gif|thumb|right|275px|'''Fig. 4''' The temperature-induced translational motion of particles in solids takes the form of ''[[phonon]]s. ''Shown here are phonons with identical [[amplitude]]s but with [[wavelength]]s ranging from 2 to 12 molecules.]] ''[[Heat conduction]] ''is the diffusion of heat energy from hot parts of a system to cold. A “system” can be either a single bulk entity or a plurality of discrete bulk entities. The term “bulk” in this context means a statistically significant quantity of particles (which can be a microscopic amount). Whenever heat energy diffuses within an isolated system, temperature differences within the system decrease (and [[entropy]] increases). One particular heat conduction mechanism occurs when translational motion—the particle motion underlying temperature—transfers [[momentum]] from particle to particle in collisions. In gases, these translational motions are of the nature shown above in ''[[#Overview|Fig.&nbsp;1]]. ''As can be seen in that animation, not only does momentum (heat) diffuse throughout the volume of the gas through serial collisions, but entire molecules or atoms can advance forward into new territory, bringing their kinetic energy with them. Consequently, temperature differences equalize throughout gases very quickly—especially for light atoms or molecules; [[convective heat transfer|convection]] speeds this process even more.<ref>The<sup>&nbsp;</sup>''speed'' at which thermal energy equalizes throughout the volume of a gas is very rapid. However, since gases have extremely low density relative to solids, the ''heat [[flux]]''—the thermal power conducting through a unit area—through gases is comparatively low. This is why the dead-air spaces in [[Insulated glazing|multi-pane windows]] have insulating qualities.</ref> Translational<sup>&nbsp;</sup>motion in ''solids ''however, takes the form of ''[[phonon]]s ''(see ''Fig.&nbsp;4'' at right). Phonons are constrained, quantized wave packets traveling at the speed of sound for a given substance. The manner in which phonons interact within a solid determines a variety of its properties, including its thermal conductivity. In electrically insulating solids, phonon-based heat conduction is ''usually'' inefficient<ref>[[Diamond]]<sup>&nbsp;</sup>is a notable exception. Due to the highly quantized modes of phonon vibration occurring in its rigid crystal lattice, not only does diamond have exceptionally ''poor'' [[specific heat capacity]], it also has exceptionally ''high'' [[thermal conductivity]].</ref> and such solids are considered ''thermal insulators'' (such as glass, plastic, rubber, ceramic, and rock). This is because in solids, atoms and molecules are locked into place relative to their neighbors and are not free to roam. [[Metal]]s however, are<sup>&nbsp;</sup>not restricted to only phonon-based heat conduction. Heat energy conducts through metals extraordinarily quickly because instead of direct molecule-to-molecule collisions, the vast majority of heat energy is mediated via very light, mobile ''conduction [[electron]]s.'' This is why there is a near-perfect correlation between metals’ [[thermal conductivity]] and their [[electrical conductivity]].<ref>Correlation<sup>&nbsp;</sup>is 752&nbsp;(W m<sup>−1</sup> K<sup>−1</sup>)&nbsp;/ (MS•cm), σ&nbsp;=&nbsp;81, through a 7:1 range in conductivity. Value and standard deviation based on data for Ag, Cu, Au, Al, Ca, Be, Mg, Rh, Ir, Zn, Co, Ni, Os, Fe, Pa, Pt, and Sn. Citation: Data from ''CRC Handbook of Chemistry and Physics'', 1st Student Edition and [http://www.webelements.com/ this link] to Web Elements’ home page.</ref> Conduction electrons imbue metals with their extraordinary conductivity because they are ''[[Delocalized electron|delocalized,]]'' i.e. not tied to a specific atom, and behave rather like a sort of “quantum gas” due to the effects of ''[[zero-point energy]]'' (for more on ZPE, see ''[[#Notes|Note 1]]'' below). Furthermore, electrons are relatively light with a rest mass only {{frac|1836}}<small>th</small> that of a [[proton]]. This is about the same ratio as a [[.22 Short|.22&nbsp;Short]] bullet (29 [[grain (measure)|grains]] or 1.88&nbsp;[[Gram|g]]) compared to the rifle that shoots it. As [[Isaac Newton]] wrote with his [[Newton's laws of motion#Newton's third law: law of reciprocal actions|third law of motion]], :<font color="#5D5D5D" face="palatino, times, times new roman" strong style="font-size: 107%;">'''''“Law #3: All forces occur in pairs, and these two forces'''''</font> :<font color="#5D5D5D" face="palatino, times, times new roman" strong style="font-size: 107%;">'''''&nbsp;are equal in magnitude and opposite in direction.”'''''</font> However, a bullet accelerates faster than a rifle given an equal force. Since kinetic energy increases as the square of velocity, nearly all the kinetic energy goes into the bullet, not the rifle, even though both experience the same force from the expanding propellant gases. In the same manner—because they are much less massive—heat energy is readily borne by mobile conduction electrons. Additionally, because they’re delocalized and ''very'' fast, kinetic heat energy conducts extremely quickly through metals with abundant conduction electrons. ====The diffusion of heat energy: Black-body radiation====<!-- NOTE TO EDITORS: This section is internally linked from elsewhere within the article. --> [[Image:Wiens law.svg|thumb|right|300px|'''Fig. 5''' The spectrum of black-body radiation has the form of a Planck curve. A 5500&nbsp;K black body has a peak emittance wavelength of 527&nbsp;nm. Compare the shape of this curve to that of a Maxwell distribution in ''[[#The nature of kinetic energy, translational motion, and temperature|Fig.&nbsp;2&nbsp;]]''above.]][[Thermal radiation]] is<sup>&nbsp;</sup>a byproduct of the collisions arising from atoms’ various vibrational motions. These collisions cause the atoms’ electrons to emit thermal [[photon]]s (known as [[black-body]] radiation). Photons are emitted anytime an electric charge is accelerated (as happens when two atoms’ electron clouds collide). Even ''individual molecules'' with internal temperatures greater than absolute zero also emit black-body radiation from their atoms. In any bulk quantity of a substance at equilibrium, black-body photons are emitted across a range of [[wavelength]]s in a spectrum that has a bell curve-like shape called a [[Planck's law of black body radiation|Planck curve]] (see graph in ''Fig.&nbsp;5'' at right). The top of a Planck curve—[[Wien's displacement law|the peak emittance wavelength]]—is located in particular part of the [[electromagnetic spectrum]] depending on the temperature of the black body. Substances at extreme [[cryogenics|cryogenic]] temperatures emit at long radio wavelengths whereas extremely hot temperatures produce short [[gamma ray]]s (see ''[[#Table of thermodynamic temperatures|Table of thermodynamic temperatures]]'', above). Black-body radiation diffuses heat energy throughout a substance as the photons are absorbed by neighboring atoms, transferring momentum in the process. Black-body photons also easily escape from a substance and can be absorbed by the ambient environment; kinetic energy is lost in the process. As established by the [[Stefan-Boltzmann law|Stefan–Boltzmann law]], the intensity of black-body radiation increases as the fourth power of absolute temperature. Thus, a black body at 824&nbsp;K (just short of glowing dull red) emits ''60 times'' the radiant [[Power (physics)|power]] as it does at 296&nbsp;K (room temperature). This is why one can so easily feel the radiant heat from hot objects at a distance. At higher temperatures, such as those found in an [[Incandescent light bulb|incandescent lamp]], black-body radiation can be the principal mechanism by which heat energy escapes a system. [[Image:IceBlockNearJoekullsarlon.jpg|thumb|left|341px|'''Fig. 6'''&nbsp; Ice and water: two phases of the same substance]] ====The heat of phase changes==== The kinetic energy of particle motion is just one contributor to the total heat energy in a substance; another is ''[[phase transition]]s'', which are the [[potential energy]] of molecular bonds that can form in a substance as it cools (such as during [[condensation|condensing]] and [[freezing]]). The heat energy required for a phase transition is called ''[[latent heat]].'' This phenomenon may more easily be grasped by considering it in the reverse direction: latent heat is the energy required to ''break'' [[chemical bonds]] (such as during [[evaporation]] and [[melting]]). Most everyone is familiar with the effects of phase transitions; for instance, [[steam]] at 100&nbsp;°C can cause severe burns much faster than the 100&nbsp;°C air from a [[blowdryer|hair dryer]]. This occurs because a large amount of latent heat is liberated as steam condenses into liquid water on the skin. Even<sup>&nbsp;</sup>though heat energy is liberated or absorbed during phase transitions, pure [[chemical element]]s, [[chemical compound|compounds]], and [[eutectic point|eutectic]] [[alloy]]s ''exhibit no temperature change whatsoever'' while they undergo them (see ''Fig.&nbsp;7,'' below right). Consider one particular type of phase transition: melting. When a solid is melting, [[Crystal structure|crystal lattice]] [[chemical bond]]s are being broken apart; the substance is transitioning from what is known as a ''more ordered state'' to a ''less ordered state''. In ''Fig.&nbsp;7, ''the melting of ice is shown within the lower left box heading from blue to green.[[Image:Energy thru phase changes.jpg|thumb|right|480px|'''Fig. 7''' Water’s temperature does not change during phase transitions as heat flows into or out of it. The total heat capacity of a mole of water in its liquid phase (the green line) is 7.5507&nbsp;kJ.]] At<sup>&nbsp;</sup>one specific thermodynamic point, the [[melting point]] (which is 0&nbsp;°C across a wide pressure range in the case of water), all the atoms or molecules are—on average—at the maximum energy threshold their chemical bonds can withstand without breaking away from the lattice. Chemical bonds are [[Quantization (physics)|quantized]] forces: they either hold fast, or break; there is no in-between state. Consequently, when a substance is at its melting point, every [[joule]] of added heat energy only breaks the bonds of a specific quantity of its atoms or molecules,<ref>Water’s<sup>&nbsp;</sup>enthalpy of fusion (0&nbsp;°C, 101.325&nbsp;kPa) equates to 0.062284&nbsp;eV&nbsp;per molecule so adding one joule of heat energy to 0&nbsp;°C water ice causes 1.0021&nbsp;×&nbsp;10<sup>20</sup> water molecules to break away from the crystal lattice and become liquid.</ref> converting them into a liquid of precisely the same temperature; no kinetic energy is added to translational motion (which is what gives substances their temperature). The effect is rather like [[popcorn]]: at a certain temperature, additional heat energy can’t make the kernels any hotter until the transition (popping) is complete. If the process is reversed (as in the freezing of a liquid), heat energy must be removed from a substance. As<sup>&nbsp;</sup>stated above, the heat energy required for a phase transition is called ''latent heat.'' In the specific cases of melting and freezing, it’s called ''[[Standard enthalpy change of fusion|enthalpy of fusion]]'' or ''heat of fusion.'' If the molecular bonds in a crystal lattice are strong, the heat of fusion can be relatively great, typically in the range of 6 to 30&nbsp;kJ per mole for water and most of the metallic elements.<ref>Water’s<sup>&nbsp;</sup>enthalpy of fusion is 6.0095&nbsp;kJ&nbsp;mol<sup>−1</sup> K<sup>−1</sup> (0&nbsp;°C, 101.325&nbsp;kPa). Citation: ''Water Structure and Science, Water Properties, Enthalpy of fusion, (0&nbsp;°C, 101.325&nbsp;kPa)'' (by London South Bank University). [http://www.lsbu.ac.uk/water/data.html Link to Web site.] The only metals with enthalpies of fusion ''not'' in the range of 6–30&nbsp;J&nbsp;mol<sup>−1</sup>&nbsp;K<sup>−1</sup> are (on the high side): Ta, W, and Re; and (on the low side) most of the group 1 (alkaline) metals plus Ga, In, Hg, Tl, Pb, and Np. Citation: [http://www.webelements.com/ This link] to Web Elements’ home page.</ref> If the substance is one of the monatomic gases, (which have little tendency to form molecular bonds) the heat of fusion is more modest, ranging from 0.021 to 2.3&nbsp;kJ per mole.<ref>Xenon<sup>&nbsp;</sup>value citation: [http://www.webelements.com/webelements/elements/text/Xe/heat.html This link] to WebElements’ xenon data (available values range from 2.3 to 3.1&nbsp;kJ mol<sup>−1</sup>). It is also noteworthy that helium’s heat of fusion of only 0.021&nbsp;kJ mol<sup>−1</sup> is so weak of a bonding force that zero-point energy prevents helium from freezing unless it is under a pressure of at least 25 atmospheres.</ref> Relatively speaking, phase transitions can be truly energetic events. To completely melt ice at 0&nbsp;°C into water at 0&nbsp;°C, one must add roughly 80 times the heat energy as is required to increase the temperature of the same mass of liquid water by one degree Celsius. The metals’ ratios are even greater, typically in the range of 400 to 1200 times.<ref>Citation:<sup>&nbsp;</sup>Data from ''CRC Handbook of Chemistry and Physics'', 1st Student Edition and [http://www.webelements.com/ this link] to Web Elements’ home page.</ref> And the phase transition of [[boiling]] is much more energetic than freezing. For instance, the energy required to completely boil or vaporize water (what is known as ''[[standard enthalpy change of vaporization|enthalpy of vaporization]]'') is roughly ''540 times'' that required for a one-degree increase.<ref>H<sub>2</sub>O<sup> </sup>specific heat capacity, ''C<sub>p</sub>''&nbsp;=&nbsp;0.075327&nbsp;kJ mol<sup>−1</sup>&nbsp;K<sup>−1</sup> (25&nbsp;°C); Enthalpy of fusion = 6.0095&nbsp;kJ mol<sup>−1</sup> (0&nbsp;°C, 101.325&nbsp;kPa); Enthalpy of vaporization (liquid) = 40.657&nbsp;kJ mol<sup>−1</sup> (100&nbsp;°C). Citation: ''Water Structure and Science, Water Properties'' (by London South Bank University). [http://www.lsbu.ac.uk/water/data.html Link to Web site.]</ref> Water’s<sup>&nbsp;</sup>sizable enthalpy of vaporization is why one’s skin can be burned so quickly as steam condenses on it (heading from red to green in ''Fig.&nbsp;7&nbsp;''above). In the opposite direction, this is why one’s skin feels cool as liquid water on it evaporates (a process that occurs at a sub-ambient [[wet-bulb temperature]] that is dependent on [[relative humidity]]). Water’s highly energetic enthalpy of vaporization is also an important factor underlying why “solar pool covers” (floating, insulated blankets that cover [[swimming pool]]s when not in use) are so effective at reducing heating costs: they prevent evaporation. For instance, the evaporation of just 20&nbsp;mm of water from a 1.29-meter-deep pool chills its water 8.4 degrees Celsius. ====Internal energy==== The total kinetic energy of all particle motion—including that of conduction electrons—plus the potential energy of phase changes, plus zero-point energy<ref name="T0"/> comprise the ''[[internal energy]]'' of a substance, which is its total heat energy. The term ''internal energy'' mustn’t be confused with ''internal degrees of freedom.'' Whereas the ''internal degrees of freedom of molecules'' refers to one particular place where kinetic energy is bound, the ''internal energy of a substance'' comprises all forms of heat energy. [[Image:Close-packed spheres.jpg|thumb|left|256px|'''Fig. 8''' When many of the chemical elements, such as the [[noble gas]]es and [[platinum group|platinum-group metals]], freeze to a solid — the most ordered state of matter — their [[crystal structures]] have a ''[[close-packing|closest-packed arrangement]]''. This yields the greatest possible packing density and the lowest energy state.]] ====Heat energy at absolute zero====<!--NOTE TO EDITORS: This section is internally linked from elsewhere within the article.--> As a substance cools, different forms of heat energy and their related effects simultaneously decrease in magnitude: the latent heat of available phase transitions are liberated as a substance changes from a less ordered state to a more ordered state; the translational motions of atoms and molecules diminish (their kinetic temperature decreases); the internal motions of molecules diminish (their internal temperature decreases); conduction electrons (if the substance is an electrical conductor) travel ''somewhat'' slower;<ref><small>&nbsp;</small>Mobile conduction<sup>&nbsp;</sup>electrons are ''delocalized,'' i.e. not tied to a specific atom, and behave rather like a sort of “quantum gas” due to the effects of zero-point energy. Consequently, even at absolute zero, conduction electrons still move between atoms at the ''Fermi velocity'' of about 1.6&nbsp;×&nbsp;10<sup>6</sup>&nbsp;m/s. Kinetic heat energy adds to this speed and also causes delocalized electrons to travel farther away from the nuclei.</ref> and black-body radiation’s peak emittance wavelength increases (the photons’ energy decreases). When the particles of a substance are as close as possible to complete rest and retain only ZPE-induced quantum mechanical motion, the substance is at the temperature of absolute zero (''T''=0). Note<sup>&nbsp;</sup>that whereas absolute zero is the point of zero thermodynamic temperature and is also the point at which the particle constituents of matter have minimal motion, absolute zero is not necessarily the point at which a substance contains zero heat energy; one must be very precise with what one means by “heat energy.” Often, all the phase changes that ''can'' occur in a substance, ''will'' have occurred by the time it reaches absolute zero. However, this is not always the case. Notably, ''T''=0 [[helium]] remains liquid at room pressure and must be under a pressure of at least 25&nbsp;[[bar (unit)|bar]] to crystallize. This is because helium’s heat of fusion—the energy required to melt helium ice—is so low (only 21&nbsp;J&nbsp;mol<sup>−1</sup>) that the motion-inducing effect of zero-point energy is sufficient to prevent it from freezing at lower pressures. Only if under at least 25&nbsp;bar of pressure will this latent heat energy be liberated as helium freezes while approaching absolute zero. A further complication is that many solids change their crystal structure to more compact arrangements at extremely high pressures (up to millions of bars). These are known as ''solid-solid phase transitions'' wherein latent heat is liberated as a crystal lattice changes to a more thermodynamically favorable, compact one. The<sup>&nbsp;</sup>above complexities make for rather cumbersome blanket statements regarding the internal energy in ''T''=0 substances. Regardless of pressure though, what ''can'' be said is that at absolute zero, all solids with a lowest-energy crystal lattice such those with a ''[[close-packing|closest-packed arrangement]]'' (see ''Fig.&nbsp;8,'' above left) contain minimal internal energy, retaining only that due to the ever-present background of zero-point energy.<ref name="T0"/><sup><small>&nbsp;</small></sup><ref>No<sup>&nbsp;</sup>other [[crystal structure]] can exceed the 74.048% packing density of a ''closest-packed arrangement.''&nbsp; The two regular crystal lattices found in nature that have this density are ''[[hexagonal crystal system|hexagonal close packed]]'' (HCP) and ''[[cubic crystal system|face-centered cubic]]'' (FCC). These regular lattices are at the lowest possible energy state. [[Diamond]] is a closest-packed structure with an FCC crystal lattice. Note too that suitable crystalline chemical ''compounds'', although usually composed of atoms of different sizes, can be considered as “closest-packed structures” when considered at the molecular level. One such compound is the common [[mineral]] known as ''magnesium aluminum [[spinel]]'' (MgAl<sub>2</sub>O<sub>4</sub>). It has a face-centered cubic crystal lattice and no change in pressure can produce a lattice with a lower energy state.</ref> One can also say that for a given substance at constant pressure, absolute zero is the point of lowest ''[[enthalpy]]'' (a measure of work potential that takes internal energy, pressure, and volume into consideration).<ref>Nearly<sup>&nbsp;</sup>half of the 92 naturally occurring chemical elements that can freeze under a vacuum also have a closest-packed crystal lattice. This set includes [[beryllium]], [[osmium]], [[neon]], and [[iridium]] (but excludes helium), and therefore have zero latent heat of phase transitions to contribute to internal energy (symbol: ''U)''. In the calculation of enthalpy (formula: ''[[Enthalpy|H''<small>&nbsp;</small>=<small>&nbsp;</small>''U''<small>&nbsp;</small>+<small>&nbsp;</small>''pV]])'', internal energy may exclude different sources of heat energy—particularly ZPE—depending on the nature of the analysis. Accordingly, all ''T''=0 closest-packed matter under a perfect vacuum has either minimal or zero enthalpy, depending on the nature of the analysis. Citation: ''Use Of Legendre Transforms In Chemical Thermodynamics'', Robert A. Alberty, Pure Appl.Chem., '''73''', No.8, 2001, 1349–1380 ([http://iupac.org/publications/pac/2001/pdf/7308x1349.pdf 400&nbsp;kB PDF, here]).</ref> Lastly, it is always true to say that all ''T''=0 substances contain zero kinetic heat energy.<ref name="T0"/><sup><small>&nbsp;</small></sup><ref name="Boltzmann"/> <h2>Practical applications for thermodynamic temperature</h2> Thermodynamic temperature is useful not only for scientists, it can also be useful for lay-people in many disciplines involving gases. By expressing variables in absolute terms and applying [[Gay-Lussac's law|Gay–Lussac’s law]] of temperature/pressure proportionality, the solutions to familiar problems are straightforward. For instance, how is the pressure in an automobile tire affected by temperature? If the tire has a “cold” pressure of 200&nbsp;[[pascal (unit)|kPa]]-gage<!--NOTE TO EDITORS: Regarding the spelling of “GAGE” pressure, this is one of two legitimate spellings. Please read the second footnote attached to this paragraph when not in “edit” view. Wikipedia’s official policy ([[Wikipedia:Manual of Style]]) is that the spelling convention used by the first major contributors should be retained. The policy further states (as of 28 August 2007), that “An overriding principle is that style and formatting should be applied consistently throughout an article, unless there is a good reason to do otherwise, except in direct quotations, where the original text is generally preserved.” This article uses American-English spelling and punctuation conventions. -->, then in absolute terms—relative to a vacuum—its pressure is 300&nbsp;kPa-absolute.<ref>Pressure<sup>&nbsp;</sup>also must be in absolute terms. The air still in a tire at 0&nbsp;kPa-gage expands too as it gets hotter. It’s not uncommon for engineers to overlook that one must work in terms of absolute pressure when compensating for temperature. For instance, a dominant manufacturer of aircraft tires published a document on temperature-compensating tire pressure, which used gage pressure in the formula. However, the high gage pressures involved (180&nbsp;psi ≈ 12.4 bar) means the error would be quite small. With low-pressure automobile tires, where gage pressures are typically around 2 bar, failing to adjust to absolute pressure results in a significant error. Referenced document: ''Aircraft Tire Ratings'' ([http://airmichelin.com/pdfs/05%20-%20Aircraft%20Tire%20Ratings.pdf 155&nbsp;kB PDF, here]).</ref><sup><font size="-1">&nbsp;</font></sup><ref>Regarding<sup>&nbsp;</sup>the spelling “gage” vs. “gauge” in the context of pressures measured relative to atmospheric pressure, the preferred spelling varies by country and even by industry. Further, both spellings are often used ''within'' a particular industry or country. Industries in British English-speaking countries typically use the spelling “gauge pressure” to distinguish it from the pressure-measuring instrument, which in the U.K., is spelled “pressure gage.” For the same reason, many of the largest American manufacturers of pressure transducers and instrumentation use the spelling “gage pressure”—the convention used here—in their formal documentation to distinguish it from the instrument, which is spelled “pressure gauge.” (see ''Honeywell-Sensotec’s'' [http://sensotec.com/pressurefaq.shtml FAQ page] and Fluke Corporation’s [http://us.fluke.com/usen/Home/Search.asp?txtSearchBox=%22gage+pressure%22&x=0&y=0 product search page]).</ref><sup><font size="-1">&nbsp;</font></sup><ref>A<sup>&nbsp;</sup>difference of 100&nbsp;kPa is used here instead of the 101.325&nbsp;kPa value of one [[atmosphere (unit)|standard atmosphere]]. In 1982, the [[International Union of Pure and Applied Chemistry]] (IUPAC) recommended that for the purposes of specifying the physical properties of substances, “''the standard pressure''” (atmospheric pressure) should be defined as precisely 100&#160;kPa (≈750.062&#160;Torr). Besides being a round number, this had a very practical effect: relatively few people live and work at precisely sea level; 100&#160;kPa equates to the mean pressure at an altitude of about 112 meters, which is closer to the 194–meter, worldwide median altitude of human habitation. For especially low-pressure or high-accuracy work, true atmospheric pressure must be measured. Citation: IUPAC.org, Gold Book, ''[http://goldbook.iupac.org/S05921.html Standard Pressure]''</ref> Room temperature (“cold” in tire terms) is 296&nbsp;K. What would the tire pressure be if was 20&nbsp;°C hotter? The answer is {{frac|316 K|296 K}}&nbsp;= 6.8% greater thermodynamic temperature ''and'' absolute pressure; that is, a pressure of 320&nbsp;kPa-absolute and 220&nbsp;kPa-gage. <h2>The origin of heat energy on Earth</h2> [[Image:Sun at 304 Angstroms.jpg|right|128px]] [[Earth|Earth’s]] proximity to the [[Sun]] is why most everything near Earth’s surface is warm with a temperature substantially above absolute zero.<ref>The<sup>&nbsp;</sup>deepest ocean depths (3 to 10&nbsp;km) are no colder than about 274.7 – 275.7&nbsp;K (1.5 – 2.5&nbsp;°C). Even the world-record cold surface temperature established on July 21, 1983 at [[Vostok Station]], Antarctica is 184&nbsp;K (a reported value of −89.2&nbsp;°C). The residual heat of gravitational contraction left over from earth’s formation, tidal friction, and the decay of radioisotopes in earth’s core provide insufficient heat to maintain earth’s surface, oceans, and atmosphere “substantially above” absolute zero in this context. Also, the qualification of “most-everything” provides for the exclusion of lava flows, which derive their temperature from these deep-earth sources of heat.</ref> [[Solar radiation]] constantly replenishes heat energy that Earth loses into space and a relatively stable state of equilibrium is achieved. Because of the wide variety of heat diffusion mechanisms (one of which is black-body radiation which occurs at the speed of light), objects on Earth rarely vary too far from the global mean surface and air temperature of 287 to 288&nbsp;K (14 to 15&nbsp;°C). The more an object’s or system’s temperature varies from this average, the more rapidly it tends to come back into equilibrium with the ambient environment. <h2>History of thermodynamic temperature</h2> * '''1702–1703:''' [[Guillaume Amontons]] (1663&nbsp;–&nbsp;1705) published two papers that may be used to credit him as being the first researcher to deduce the existence of a fundamental (thermodynamic) temperature scale featuring an absolute zero. He made the discovery while endeavoring to improve upon the air thermometers in use at the time. His J-tube thermometers comprised a mercury column that was supported by a fixed mass of air entrapped within the sensing portion of the thermometer. In thermodynamic terms, his thermometers relied upon the volume / temperature relationship of gas under constant pressure. His measurements of the boiling point of water and the melting point of ice showed that regardless of the mass of air trapped inside his thermometers or the weight of mercury the air was supporting, the reduction in air volume at the ice point was always the same ratio. This observation led him to posit that a sufficient reduction in temperature would reduce the air volume to zero. In fact, his calculations projected that absolute zero was equivalent to −240 degrees on today’s Celsius scale—only 33.15 degrees short of the true value of −273.15&nbsp;°C. * '''1742:''' [[Image:Anders Celsius.jpg|thumb|right|200x200px|Anders Celsius]][[Anders Celsius]] (1701&nbsp;–&nbsp;1744) created a “backwards” version of the modern Celsius temperature scale whereby zero represented the boiling point of water and 100 represented the melting point of ice. In his paper ''Observations of two persistent degrees on a thermometer,'' he recounted his experiments showing that ice’s melting point was effectively unaffected by pressure. He also determined with remarkable precision how water’s boiling point varied as a function of atmospheric pressure. He proposed that zero on his temperature scale (water’s boiling point) would be calibrated at the mean barometric pressure at mean sea level. * '''1744:''' [[Image:Carolus Linnaeus (cleaned up version).jpg|thumb|left|200x200px|Carolus Linnaeus]]Coincident with the death of Anders Celsius, the famous botanist [[Carolus Linnaeus]] (1707&nbsp;–&nbsp;1778) effectively reversed<sup>&nbsp;</sup><ref>Citations:<sup>&nbsp;</sup>Thermodynamics-information.net, [http://thermodynamics-information.net/ ''A Brief History of Temperature Measurement''] and; Uppsala University (Sweden), [http://www.linnaeus.uu.se/online/life/6_32.html ''Linnaeus’ thermometer'']</ref> Celsius’s scale upon receipt of his first thermometer featuring a scale where zero represented the melting point of ice and 100 represented water’s boiling point. The custom-made “linnaeus-thermometer,” for use in his greenhouses, was made by Daniel Ekström, Sweden’s leading maker of scientific instruments at the time. For the next 204 years, the scientific and thermometry communities world-wide referred to this scale as the “centigrade scale.” Temperatures on the centigrade scale were often reported simply as “degrees” or, when greater specificity was desired, “degrees centigrade.” The symbol for temperature values on this scale was °C (in several formats over the years). Because the term “centigrade” was also the French-language name for a unit of angular measurement (one-hundredth of a right angle) and had a similar connotation in other languages, the term “centesimal degree” was used when very precise, unambiguous language was required by international standards bodies such as the [[International Bureau of Weights and Measures|Bureau international des poids et mesures]] (BIPM). The 9th CGPM ([[General Conference on Weights and Measures|Conférence générale des poids et mesures]]) and the CIPM ([[International Committee for Weights and Measures|Comité international des poids et mesures]]) [http://www.bipm.org/en/committees/cipm/cipm-1948.html formally adopted] “degree Celsius” (symbol: °C) in 1948.<ref name="°CName">According<sup>&nbsp;</sup>to ''The Oxford English Dictionary'' (OED), the term “Celsius’s thermometer” had been used at least as early as 1797. Further, the term “The Celsius or Centigrade thermometer” was again used in reference to a particular type of thermometer at least as early as 1850. The OED also cites this 1928 reporting of a temperature: “My altitude was about 5,800 metres, the temperature was 28° Celsius.” However, dictionaries seek to find the earliest use of a word or term and are not a useful resource as regards the terminology used throughout the history of science. According to several writings of Dr. Terry Quinn CBE FRS, Director of the BIPM (1988&nbsp;–&nbsp;2004), including ''Temperature Scales from the early days of thermometry to the 21st century'' ([http://www.imeko.org/publications/tc12-2004/PTC12-2004-PL-001.pdf 148&nbsp;kB PDF, here]) as well as ''Temperature'' (2nd Edition / 1990 / Academic Press / 0125696817), the term ''Celsius'' in connection with the centigrade scale was not used whatsoever by the scientific or thermometry communities until after the CIPM and CGPM adopted the term in 1948. The BIPM wasn’t even aware that “degree Celsius” was in sporadic, non-scientific use before that time. It’s also noteworthy that the twelve-volume, 1933 edition of OED didn’t even have a listing for the word ''Celsius'' (but did have listings for both ''centigrade'' and ''centesimal'' in the context of temperature measurement). The 1948 adoption of ''Celsius'' accomplished three objectives: :1) All<sup>&nbsp;</sup>common temperature scales would have their units named after someone closely associated with them; namely, Kelvin, Celsius, Fahrenheit, Réaumur and Rankine.<br>2) Notwithstanding<sup>&nbsp;</sup>the important contribution of Linnaeus who gave the Celsius scale its modern form, Celsius’s name was the obvious choice because it began with the letter C. Thus, the symbol °C that for centuries had been used in association with the name ''centigrade'' could continue to be used and would simultaneously inherit an intuitive association with the new name.<br>3) The<sup>&nbsp;</sup>new name eliminated the ambiguity of the term “centigrade,” freeing it to refer exclusively to the French-language name for the unit of angular measurement.</ref> * '''1777:''' In<sup>&nbsp;</sup>his book ''Pyrometrie'' (Berlin: [http://www.spiess-verlage.de/html/haude___spener.html Haude & Spener,] 1779) completed four months before his death, [[Johann Heinrich Lambert]] (1728&nbsp;–&nbsp;1777)—sometimes incorrectly referred to as Joseph Lambert—proposed an absolute temperature scale based on the pressure&nbsp;/ temperature relationship of a fixed volume of gas. This is distinct from the volume&nbsp;/ temperature relationship of gas under constant pressure that Guillaume Amontons discovered 75 years earlier. Lambert stated that absolute zero was the point where a simple straight-line extrapolation reached zero gas pressure and was equal to −270&nbsp;°C. * '''Circa 1787:''' Notwithstanding the work of Guillaume Amontons 85 years earlier, [[Jacques Charles|Jacques Alexandre César Charles]] (1746&nbsp;–&nbsp;1823) is often credited with “discovering”, but not publishing, that the volume of a gas under constant pressure is proportional to its absolute temperature. The formula he created was ''V''<sub>1</sub>/''T''<sub>1</sub>&nbsp;=&nbsp;''V''<sub>2</sub>/''T''<sub>2</sub>. * '''1802:''' [[Joseph Louis Gay-Lussac]] (1778&nbsp;–&nbsp;1850) published work (acknowledging the unpublished lab notes of Jacques Charles fifteen years earlier) describing how the volume of gas under constant pressure changes linearly with its absolute (thermodynamic) temperature. This behavior is called [[Charles's law|Charles’s Law]] and is one of the [[gas laws]]. His are the first known formulas to use the number “273” for the expansion coefficient of gas relative to the melting point of ice (indicating that absolute zero was equivalent to −273&nbsp;°C). * '''1848:''' [[Image:William_Thomson_1st_Baron_Kelvin.jpg|thumb|right|200x200px|Lord Kelvin]][[William Thomson, 1st Baron Kelvin|William Thomson]], (1824&nbsp;–&nbsp;1907) also known as Lord Kelvin, wrote in his paper, ''[http://zapatopi.net/kelvin/papers/on_an_absolute_thermometric_scale.html On an Absolute Thermometric Scale],'' of the need for a scale whereby “infinite cold” (absolute zero) was the scale’s null point, and which used the degree Celsius for its unit increment. Like Gay-Lussac, Thomson calculated that absolute zero was equivalent to −273&nbsp;°C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale. It’s noteworthy that Thomson’s value of “−273” was actually derived from 0.00366, which was the accepted expansion coefficient of gas per degree Celsius relative to the ice point. The inverse of −0.00366 expressed to five significant digits is −273.22&nbsp;°C which is remarkably close to the true value of −273.15&nbsp;°C. * '''1859:''' [[William John Macquorn Rankine]] (1820&nbsp;–&nbsp;1872) proposed a thermodynamic temperature scale similar to William Thomson’s but which used the degree [[Fahrenheit]] for its unit increment. This absolute scale is known today as the [[rankine scale|Rankine]] thermodynamic temperature scale. * '''1877 - 1884:''' [[Image:Boltzmann2.jpg|thumb|left|200x200px|Ludwig Boltzmann]][[Ludwig Boltzmann]] (1844&nbsp;–&nbsp;1906) made major contributions to thermodynamics through an understanding of the role that particle kinetics and black-body radiation played. His name is now attached to several of the formulas used today in thermodynamics. * '''Circa 1930s:''' Gas thermometry experiments carefully calibrated to the melting point of ice and boiling point of water showed that absolute zero was equivalent to −273.15&nbsp;°C. * '''1948:''' [http://www.bipm.fr/en/CGPM/db/9/3/ Resolution 3] of the 9th CGPM (Conférence Générale des Poids et Mesures, also known as the [[General Conference on Weights and Measures]]) fixed the triple point of water at precisely 0.01&nbsp;°C. At this time, the triple point still had no formal definition for its equivalent kelvin value, which the resolution declared “will be fixed at a later date.” The implication is that ''if'' the value of absolute zero measured in the 1930s was truly −273.15&nbsp;°C, then the triple point of water (0.01&nbsp;°C) was equivalent to 273.16&nbsp;K. Additionally, both the CIPM (Comité international des poids et mesures, also known as the International Committee for Weights and Measures) and the CGPM [http://www.bipm.org/en/committees/cipm/cipm-1948.html formally adopted] the name “Celsius” for the “degree Celsius” and the “Celsius temperature scale.”<small>&nbsp;</small><ref name="°CName"/> * '''1954:''' [http://www.bipm.fr/en/CGPM/db/10/3/ Resolution 3] of the 10th CGPM gave the Kelvin scale its modern definition by choosing the triple point of water as its second defining point and assigned it a temperature of precisely 273.16 kelvin (what was actually written 273.16 “degrees Kelvin” at the time). This, in combination with Resolution 3 of the 9th CGPM, had the effect of defining absolute zero as being precisely zero kelvin and −273.15&nbsp;°C. * '''1967/1968:''' [http://www.bipm.fr/en/CGPM/db/13/3/ Resolution 3] of the 13th CGPM renamed the unit increment of thermodynamic temperature “kelvin”, symbol K, replacing “degree absolute”, symbol °K. Further, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also decided in [http://www.bipm.fr/en/CGPM/db/13/4/ Resolution 4] that “The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.” * '''2005:''' The CIPM (Comité International des Poids et Mesures, also known as the [[International Committee for Weights and Measures]]) [http://www.bipm.fr/en/si/si_brochure/chapter2/2-1/kelvin.html affirmed] that for the purposes of delineating the temperature of the triple point of water, the definition of the Kelvin thermodynamic temperature scale would refer to water having an isotopic composition defined as being precisely equal to the nominal specification of [[Vienna Standard Mean Ocean Water]]. <h2>Derivations of thermodynamic temperature</h2> Strictly speaking, the temperature of a system is well-defined only if its particles ([[atom]]s, [[molecule]]s, [[electron]]s, [[photon]]s) are at [[thermodynamic equilibrium|equilibrium]], so that their energies obey a [[Boltzmann distribution]] (or its [[quantum mechanics|quantum mechanical]] counterpart). There are many possible scales of temperature, derived from a variety of observations of physical phenomena. The thermodynamic temperature can be shown to have special properties, and in particular can be seen to be uniquely defined ([[up to]] some constant multiplicative factor) by considering the [[energy conversion efficiency|efficiency]] of idealized [[heat engine]]s. Thus the ''[[ratio]]'' ''T''<sub>2</sub>/''T''<sub>1</sub> of two temperatures ''T''<sub>1</sub> and''T''<sub>2</sub> is the same in all absolute scales. Loosely stated, temperature controls the flow of heat between two systems, and the [[universe]] as a whole, as with any natural system, tends to progress so as to maximize [[entropy]]. This suggests that there should be a relationship between temperature and entropy. To elucidate this, consider first the relationship between heat, [[mechanical work|work]] and temperature. One way to study this is to analyse a heat engine, which is a device for converting heat into mechanical work, such as the [[Carnot heat engine]]. Such a heat engine functions by using a temperature gradient between a high temperature ''T''<sub>H</sub> and a low temperature ''T''<sub>C</sub> to generate work, and the work done (per cycle, say) by the heat engine is equal to the difference between the heat energy ''q''<sub>H</sub> put into the system at the high temperature the heat ''q''<sub>C</sub> ejected at the low temperature (in that cycle). The '''efficiency''' of the engine 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} \qquad (1) </math> where w<sub>cy</sub> is the work done per cycle. Thus 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, the ratio ''q''<sub>C</sub>/''q''<sub>H</sub> should be a function ''f'' of these temperatures: :<math> \frac{q_C}{q_H} = f(T_H,T_C)\qquad (2). </math> [[Carnot heat engine|Carnot’s theorem]] states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between temperatures ''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 another (intermediate) temperature ''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> f(T_1,T_3) = \frac{q_3}{q_1} = \frac{q_2 q_3} {q_1 q_2} = f(T_1,T_2)f(T_2,T_3). </math> Now specialize to the case that <math>T_1</math> is a fixed reference temperature: the temperature of the triple point of water. Then for any ''T''<sub>2</sub> and ''T''<sub>3</sub>, :<math> f(T_2,T_3) = \frac{f(T_1,T_3)}{f(T_1,T_2)} = \frac{273.16 \cdot f(T_1,T_3)}{273.16 \cdot f(T_1,T_2)}. </math> Therefore if thermodynamic temperature is defined by :<math> T = 273.16 \cdot f(T_1,T) \, </math> then the function ''f'', viewed as a function of thermodynamic temperature, is simply :<math> f(T_2,T_3) = \frac{T_3}{T_2}, </math> and the reference temperature ''T''<sub>1</sub> will have the value 273.16. (Of course any reference temperature and any positive numerical value could be used &mdash; the choice here corresponds to the Kelvin scale.) It follows immediately that :<math> \frac{q_C}{q_H} = f(T_H,T_C) = \frac{T_C}{T_H}.\qquad (3). </math> Substituting Equation 3 back into Equation 1 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}\qquad (4). </math> Notice that for ''T''<sub>C</sub>=0 the efficiency is 100% and that efficiency becomes greater than 100% for ''T''<sub>C</sub><0. Since an efficiency greater than 100% violates the [[first law of thermodynamics]], this requires that zero must be the minimum possible temperature. This has an intuitive interpretation: temperature is the motion of particles, so no system can, on average, have less motion than the minimum permitted by quantum physics. In fact, as of June 2006, the coldest man-made temperature was 450&nbsp;[[Kelvin#SI prefixes|pK]].<ref name="recordcold"/> Subtracting the right hand side of Equation 4 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'' (i.e., a function which depends only on the state of the system, not on how it reached that state) defined (up to an additive constant) by :<math> dS = \frac {dq_\mathrm{rev}}{T}\qquad (5), </math> where the subscript indicates heat transfer in a reversible process. The function ''S'' corresponds to the [[entropy]] of the system, mentioned previously, and the change of ''S'' around any cycle is zero (as is necessary for any state function). Equation 5 can be rearranged to get an alternative definition for temperature in terms of entropy and heat: :<math> T = \frac{dq_\mathrm{rev}}{dS}. </math> For a system in which the entropy ''S'' is a function ''S''(''E'') of its energy ''E'', the thermodynamic temperature ''T'' is therefore given by :<math> \frac{1}{T} = \frac{dS}{dE}, </math> so that the reciprocal of the thermodynamic temperature is the rate of increase of entropy with energy. <h2>See also</h2> {{col-begin}} {{col-break}} * [[Absolute zero]] * [[Adiabatic process]] * [[Black body]] * [[Boiling]] * [[Boltzmann constant]] * [[Brownian motion]] * [[Carnot heat engine]] * [[Celsius]] * [[Chemical bond]] * [[Condensation]] * [[Convection]] * [[Degrees of freedom (physics and chemistry)|Degrees of freedom]] * [[Delocalized electron]] * [[Diffusion]] * [[Elastic collision]] * [[Electron]] * [[Energy]] * [[Energy conversion efficiency]] * [[Enthalpy]] * [[Entropy]] * [[Equipartition theorem]] :(recommended reading) * [[Evaporation]] * [[Fahrenheit]] * [[First law of thermodynamics]] {{col-break}} * [[Freezing]] * [[Gas laws]] * [[Heat]] * [[Heat conduction]] * [[Heat engine]] * [[Internal energy]] * [[International Temperature Scale of 1990|ITS-90]] * [[Ideal gas law]] * [[Joule]] * [[Kelvin]] * [[Kinetic energy]] * [[Latent heat]] * [[Laws of thermodynamics]] * [[Maxwell–Boltzmann distribution]] * [[Melting]] * [[Mole (unit)|Mole]] * [[Molecule]] * [[Orders of magnitude (temperature)]] * [[Phase transition]] * [[Phonon]] * [[Planck's law of black body radiation|Planck’s law of black body radiation]] * [[Potential energy]] * Quantum mechanics: ** [[Introduction to quantum mechanics]] ** [[Quantum mechanics|Quantum mechanics (main article)]] {{col-break}} * [[Rankine scale]] * [[Specific heat capacity]] * [[Standard enthalpy change of fusion]] * [[Standard enthalpy change of vaporization]] * [[Stefan-Boltzmann law|Stefan–Boltzmann law]] * [[Sublimation (chemistry)|Sublimation]] * [[Temperature]] * [[Temperature conversion formulas]] * [[Thermal conductivity]] * [[Thermal radiation]] * [[Thermodynamic equations]] * [[Thermodynamic equilibrium]] * [[Thermodynamics]] * [[:Category:Thermodynamics|Thermodynamics Category (list of articles)]] * [[Triple point]] * [[Gas constant|Universal gas constant]] * [[Vienna Standard Mean Ocean Water]] (VSMOW) * [[Wien's displacement law|Wien’s displacement law]] * [[Mechanical work|Work (Mechanical)]] * [[Work (thermodynamics)]] * [[Zero-point energy]] {{col-end}} <h2>Notes</h2><!-- NOTE TO EDITORS: This section is internally linked from elsewhere within the article. --> ''In the following notes, wherever numeric equalities are shown in ‘concise form’—such as'' 1.854<span style="margin-left:0.3em">87(14)</span>&nbsp;×&nbsp;10<sup>43</sup>''—the two digits between the parentheses denotes the [[uncertainty]] at ''1σ'' [[standard deviation]] ''(68%'' confidence level) in the two least significant digits of the [[significand]].'' <references/> <h2>External links</h2> * ''[http://www.chm.davidson.edu/ChemistryApplets/KineticMolecularTheory/index.html Kinetic Molecular Theory of Gases.]'' An excellent explanation (with interactive animations) of the kinetic motion of molecules and how it affects matter. By David N. Blauch, [http://www.chm.davidson.edu/ Department of Chemistry], [http://www2.davidson.edu/index.asp Davidson College]. * ''[http://www.calphysics.org/zpe.html Zero Point Energy and Zero Point Field.]'' A Web site with in-depth explanations of a variety of quantum effects. By Bernard Haisch, of [http://www.calphysics.org/index.html Calphysics Institute]. [[Category:Temperature]] [[Category:Thermodynamics]] [[bn:পরম তাপমাত্রা]] [[be-x-old:Абсалютная тэрмадынамічная тэмпэратура]] [[bg:Термодинамична температура]] [[ca:Temperatura termodinàmica]] [[cs:Termodynamická teplota]] [[de:Absolute Temperatur]] [[et:Absoluutne temperatuur]] [[es:Temperatura absoluta]] [[hi:ऊष्मगतिकीय तापमान]] [[it:Temperatura assoluta]] [[hu:Abszolút hőmérséklet]] [[nl:Absolute temperatuur]] [[ja:熱力学温度]] [[nn:Termodynamisk temperatur]] [[pt:Temperatura termodinâmica]] [[ru:Абсолютная термодинамическая температура]] [[sk:Termodynamická teplota]] [[sl:Absolutna temperatura]] [[uk:Абсолютна температура]]