Editing Thermodynamic temperature (section)

== Overview ==
Thermodynamic temperature, as distinct from SI temperature, is defined in terms of a macroscopic [[Carnot cycle]]. Thermodynamic temperature is of importance in thermodynamics because it is defined in purely thermodynamic terms. SI temperature is conceptually far different from thermodynamic temperature. Thermodynamic temperature was rigorously defined historically long before there was a fair knowledge of microscopic particles such as atoms, molecules, and electrons.

The [[International System of Units]] (SI) specifies the international absolute scale for measuring temperature, and the unit of measure ''[[kelvin]]'' (unit symbol: K) for specific values along the scale. The kelvin is also used for denoting temperature ''intervals'' (a span or difference between two temperatures) as per the following example usage: "A 60/40 tin/lead solder is non-eutectic and is plastic through a range of 5 kelvins as it solidifies." A temperature interval of one degree Celsius is the same magnitude as one kelvin.

The magnitude of the kelvin was [[2019 revision of the SI#Kelvin|redefined in 2019]] in relation to the ''physical property'' underlying thermodynamic temperature: the kinetic energy of atomic free particle motion. The revision fixed the [[Boltzmann constant]] at exactly {{val|1.380649|e=-23|u=joules per kelvin}} (J/K).<ref name="Accessible_k">''[https://physics.nist.gov/cgi-bin/cuu/Value?k CODATA Value: Boltzmann constant]''. ''The NIST Reference on Constants, Units, and Uncertainty''. [[National Institute of Standards and Technology]].</ref> 

The microscopic property that imbues material substances with a temperature can be readily understood by examining the [[ideal gas law]], which relates, per the Boltzmann constant, how [[heat|heat energy]] causes precisely defined changes in the [[pressure]] and temperature of certain gases. This is because [[monatomic gas]]es like [[helium]] and [[argon]] behave kinetically like freely moving perfectly elastic and spherical billiard balls that move only in a specific subset of the possible motions that can occur in matter: that comprising the ''three translational'' [[Degrees of freedom (physics and chemistry)|degrees of freedom]]. The translational degrees of freedom are the familiar billiard ball-like movements along the X, Y, and Z axes of 3D space (see [[#Nature of kinetic energy, translational motion, and temperature|''Fig.&nbsp;1'']], below). This is why the noble gases all have the [[Table of specific heat capacities|same specific heat capacity per atom]] and why that value is lowest of all the gases.

[[Molecule]]s (two or more chemically bound atoms), however, have ''internal structure'' and therefore have additional ''internal'' degrees of freedom (see [[#Internal_motions_of_molecules_and_internal_energy|''Fig. 3'']], below), which makes molecules absorb more heat energy for any given amount of temperature rise than do the monatomic gases. Heat energy is born in all available degrees of freedom; this is in accordance with the [[equipartition theorem]], so all available internal degrees of freedom have the same temperature as their three external degrees of freedom. However, the property that gives all gases their [[pressure]], which is the net force per unit area on a container arising from gas particles recoiling off it, is a function of the kinetic energy borne in the freely moving atoms' and molecules' three translational degrees of freedom.<ref>Georgia State University, HyperPhysics Project, "[http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/eqpar.html Equipartition of Energy]"</ref>

Fixing the Boltzmann constant at a specific value, along with other rule making, had the effect of precisely establishing the magnitude of the unit interval of SI temperature, the kelvin, in terms of the average kinetic behavior of the noble gases. Moreover, the ''starting point'' of the thermodynamic temperature scale, absolute zero, was reaffirmed as the point at which ''zero average kinetic energy'' remains in a sample; the only remaining particle motion being that comprising random vibrations due to zero-point energy.