Editing Thermodynamic temperature (section)

== Absolute zero of temperature ==
{{Main|Absolute zero}}

Temperature scales are numerical. The numerical zero of a temperature scale is not bound to the absolute zero of temperature. Nevertheless, some temperature scales have their numerical zero coincident with the absolute zero of temperature. Examples are the International SI temperature scale, the [[Rankine scale|Rankine temperature scale]], and the thermodynamic temperature scale. Other temperature scales have their numerical zero far from the absolute zero of temperature. Examples are the Fahrenheit scale and the Celsius scale.

At the zero point of thermodynamic temperature, [[absolute zero]], the particle constituents of matter have minimal motion and can become no colder.<ref>Rankine, W. J. M., "A manual of the steam engine and other prime movers", Richard Griffin and Co., London (1859), p. 306–307.</ref><ref>[[William Thomson, 1st Baron Kelvin]], "Heat", Adam and Charles Black, Edinburgh (1880), p. 39.</ref> Absolute zero, which is a temperature of zero kelvins (0&nbsp;K), precisely corresponds to −273.15&nbsp;°C and −459.67&nbsp;°F. Matter at absolute zero has no remaining transferable average kinetic energy and the only remaining particle motion is due to an ever-pervasive [[quantum mechanics|quantum mechanical]] phenomenon called ZPE ([[zero-point energy]]).<ref name="T0">[[Image:Zero-point energy v.s. motion.jpg|thumb|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 thermal energy from matter, [[quantum mechanics|quantum mechanical]] ''[[zero-point energy]]'' (ZPE) causes particle motion that can never be eliminated. Encyclopædia 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]''. See also ''[http://www.phys.ualberta.ca/~therman/lowtemp/projects1.htm Solid Helium] {{Webarchive|url=https://web.archive.org/web/20080212140020/http://www.phys.ualberta.ca/~therman/lowtemp/projects1.htm |date=2008-02-12 }}'' by the University of Alberta's Department of Physics to learn more about ZPE's effect on [[Bose–Einstein condensate]]s of helium.

Although absolute zero ({{nowrap|1=''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. {{Anchor|thought experiment}}To understand how atoms can have zero kinetic velocity and simultaneously be vibrating due to ZPE, consider the following thought experiment: two {{nowrap|1=''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 is 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;yoctokelvins (1&nbsp;yK = {{val|1|e=-24|u=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 [[Barycentric coordinates (astronomy)|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 {{nowrap|1=''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 {{nowrap|1=''T'' = 0}}, no [[kinetic energy]] is available for transfer to other systems.

Note 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 thermal 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 thermal 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. Because of ZPE, however, ''virtual'' photons are still emitted at {{nowrap|1=''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 {{nowrap|1=''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 {{nowrap|1=''T'' = 0}}, heat will flow inward, and if the surrounding environment is at '{{nowrap|1=''T'' = 0}}, there will be an equal flux of ZP radiation both inward and outward. A similar ''Q ''equilibrium exists at {{nowrap|1=''T'' = 0}} with the ZPE-induced [[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''. [http://pra.aps.org/abstract/PRA/v42/i4/p1847_1 ''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, '''42''' (1990) 1847.</ref> Though the atoms in, for instance, a container of liquid [[helium]] that was ''precisely'' at absolute zero would still jostle slightly due to zero-point energy, a [[Carnot cycle|theoretically perfect heat engine]] with such helium as one of its [[working fluid]]s could never transfer any net kinetic energy ([[Heat|heat energy]]) to the other working fluid and no [[Work (thermodynamics)|thermodynamic work]] could occur.

Temperature is generally expressed in absolute terms when scientifically examining temperature's interrelationships with certain other physical properties of matter such as its [[Volume (thermodynamics)|volume]] or [[pressure]] (see [[Gay-Lussac's law]]), or the wavelength of its emitted [[black-body radiation]]. Absolute temperature is also useful when calculating chemical reaction rates (see [[Arrhenius equation]]). Furthermore, absolute temperature is typically used in [[cryogenics]] and related phenomena like [[superconductivity]], as per the following example usage:
"Conveniently, tantalum's transition temperature (''T''{{sub|c}}) of 4.4924 kelvin is slightly above the 4.2221&nbsp;K boiling point of helium."