Editing Thermodynamic temperature (section)

=== Diffusion of thermal energy: entropy, phonons, and mobile conduction electrons ===
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[[Image:1D normal modes (280 kB).gif|thumb|upright=1.2|'''Figure 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 average inter-molecule separations (''a'').]]

''[[Heat conduction]]'' is the diffusion of thermal energy from hot parts of a system to cold parts. 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 thermal 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 ''[[#Relationship of temperature, motions, conduction, and thermal energy|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 move forward into new territory, bringing their kinetic energy with them. Consequently, temperature differences equalize throughout gases very quickly—especially for light atoms or molecules; [[Convection (heat transfer)|convection]] speeds this process even more.<ref>The ''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 passing per area) through gases is comparatively low. This is why the dead-air spaces in [[insulated glazing|multi-pane windows]] have insulating qualities.</ref>

Translational motion in ''solids'', however, takes the form of ''[[phonon]]s'' (see ''Fig.&nbsp;4'' at right). Phonons are constrained, quantized wave packets that travel at the speed of sound of 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]] is a notable exception. Highly quantized modes of phonon vibration occur in its rigid crystal lattice. Therefore, 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 not restricted to only phonon-based heat conduction. Thermal energy conducts through metals extraordinarily quickly because instead of direct molecule-to-molecule collisions, the vast majority of thermal 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 is 752&nbsp;(W⋅m<sup>−1</sup>⋅K<sup>−1</sup>)/(MS⋅cm), {{mvar|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. Data from ''CRC Handbook of Chemistry and Physics'', 1st Student Edition.</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}} that of a [[proton]]. This is about the same ratio as a [[.22 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|third law of motion]],

{{Quote|Law #3: All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction.}}

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, thermal energy is readily borne by mobile conduction electrons. Additionally, because they are delocalized and ''very'' fast, kinetic thermal energy conducts extremely quickly through metals with abundant conduction electrons.