Editing Thermodynamic temperature (section)

=== Internal energy at absolute zero ===
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As a substance cools, different forms of internal energy and their related effects simultaneously decrease in magnitude: the latent heat of available phase transitions is 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 energy or temperature decreases); the internal motions of molecules diminish (their internal energy or temperature decreases); conduction electrons (if the substance is an electrical conductor) travel ''somewhat'' slower;<ref>Mobile conduction 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 {{val|1.6|e=6|u=m/s}}. Kinetic thermal 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 particles of a substance are as close as possible to complete rest and retain only ZPE (zero-point energy)-induced quantum mechanical motion, the substance is at the temperature of absolute zero ({{mvar|T}}&nbsp;=&nbsp;0).

[[Image:Liquid helium superfluid phase.jpg|thumb|right|upright=1.1|'''Figure 9''' Due to the effects of zero-point energy, helium at ambient pressure remains a [[superfluid]] even when exceedingly close to absolute zero; it will not freeze unless under 25 bar of pressure (c.&nbsp;25 atmospheres).]]
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 internal energy; one must be very precise with what one means by ''internal 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, {{mvar|T}}&nbsp;=&nbsp;0 [[helium]] remains liquid at room pressure (''Fig.&nbsp;9'' at right) and must be under a pressure of at least {{convert|25|bar|MPa|abbr=on|lk=on}} to crystallize. This is because helium's heat of fusion (the energy required to melt helium ice) is so low (only 21&nbsp;joules&nbsp;per&nbsp;mole) that the motion-inducing effect of zero-point energy is sufficient to prevent it from freezing at lower pressures.

A further complication is that many solids change their crystal structure to more compact arrangements at extremely high pressures (up to millions of bars, or hundreds of gigapascals). 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 above complexities make for rather cumbersome blanket statements regarding the internal energy in {{mvar|T}}&nbsp;=&nbsp;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"/><ref>No other [[crystal structure]] can exceed the 74.048% packing density of a ''closest-packed arrangement''. 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 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: {{math|''H''{{=}}''U''&nbsp;+&nbsp;''pV''}}), internal energy may exclude different sources of thermal energy (particularly ZPE) depending on the nature of the analysis. Accordingly, all {{mvar|T}}&nbsp;=&nbsp;0 closest-packed matter under a perfect vacuum has either minimal or zero enthalpy, depending on the nature of the analysis. {{cite journal |url=http://iupac.org/publications/pac/2001/pdf/7308x1349.pdf |title=Use of Legendre Transforms In Chemical Thermodynamics |first=Robert A. |last=Alberty |journal=Pure and Applied Chemistry |volume=73 |issue=8 |year=2001 |page=1349|doi=10.1351/pac200173081349 }}</ref> Lastly, all {{mvar|T}}&nbsp;=&nbsp;0 substances contain zero kinetic thermal energy.<ref name="T0"/><ref name="Boltzmann"/>
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