Editing Thermodynamic temperature (section)

==== Internal motions of molecules and internal energy ====
[[Image:Thermally Agitated Molecule.gif|thumb|upright=1.1|'''Figure 3''' Molecules have internal structures 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]]'', or internal energy, allowing it to contain more internal energy at the same temperature.]]
As mentioned above, there are other ways molecules can jiggle besides the three translational degrees of freedom that imbue substances with their kinetic temperature. 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 (the X, Y, and Z axis). Kinetic energy is stored in molecules' internal degrees of freedom, which gives them an ''internal temperature''. 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 internal energy 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 kinetic energy stored internally in molecules causes substances to contain more heat energy at any given temperature and to absorb additional internal energy for a given temperature increase. This is because any kinetic energy that is, at a given instant, bound in internal motions, is not contributing to the molecules' translational motions at that same instant.<ref>The 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 internal capacity than monatomic gases (where additional internal energy must be added to achieve a given temperature rise).</ref> This extra kinetic energy simply increases the amount of internal energy that substance absorbs for a given temperature rise. This property is known as a substance's [[specific heat capacity]].

Different molecules absorb different amounts of internal 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 measured at constant-volume since different amounts of work must be performed if measured at constant-pressure. Nitrogen's {{math|''C<sub>v</sub>H''}} (100&nbsp;kPa, 20&nbsp;°C) equals {{val|20.8|u=J⋅mol<sup>–1</sup>⋅K<sup>–1</sup>}} vs. the monatomic gases, which equal 12.4717&nbsp;J&nbsp;mol<sup>–1</sup>&nbsp;K<sup>–1</sup>. {{cite book |first=W. H. |last=Freeman |title=Physical Chemistry |url=http://www.whfreeman.com/college/pdfs/pchem8e/PC8eC21.pdf |chapter=Part 3: Change|archive-url=https://wayback.archive-it.org/all/20070927061428/http://www.whfreeman.com/college/pdfs/pchem8e/PC8eC21.pdf |archive-date=2007-09-27 |at=Exercise 21.20b, p.&nbsp;787}} See also {{cite web |first=R. |last=Nave |publisher=Georgia State University |url=http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/shegas.html |title=Molar Specific Heats of Gases |website=HyperPhysics}}</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.