          # Thermodynamic temperature

• this article needs to be updated. in particular: it needs to reflect the 2019 redefinition of the si base units, which came into effect on may 20, 2019. please update this article to reflect recent events or newly available information. (january 2020)

thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics.

thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. at this point, absolute zero, the particle constituents of matter have minimal motion and can become no colder. in the quantum-mechanical description, matter at absolute zero is in its ground state, which is its state of lowest energy. thermodynamic temperature is often also called absolute temperature, for two reasons: the first, proposed by kelvin, that it does not depend on the properties of a particular material; the second, that it refers to an absolute zero according to the properties of the ideal gas.

the international system of units specifies a particular scale for thermodynamic temperature. it uses the kelvin scale for measurement and selects the triple point of water at 273.16 k as the fundamental fixing point. other scales have been in use historically. the rankine scale, using the degree fahrenheit as its unit interval, is still in use as part of the english engineering units in the united states in some engineering fields. its-90 gives a practical means of estimating the thermodynamic temperature to a very high degree of accuracy.

roughly, the temperature of a body at rest is a measure of the mean of the energy of the translational, vibrational and rotational motions of matter's particle constituents, such as molecules, atoms, and subatomic particles. the full variety of these kinetic motions, along with potential energies of particles, and also occasionally certain other types of particle energy in equilibrium with these, make up the total internal energy of a substance. internal energy is loosely called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings, or by the substance upon the surroundings. internal energy may be stored in a number of ways within a substance, each way constituting a "degree of freedom". at equilibrium, each degree of freedom will have on average the same energy: where is the boltzmann constant, unless that degree of freedom is in the quantum regime. the internal degrees of freedom (rotation, vibration, etc.) may be in the quantum regime at room temperature, but the translational degrees of freedom will be in the classical regime except at extremely low temperatures (fractions of kelvins) and it may be said that, for most situations, the thermodynamic temperature is specified by the average translational kinetic energy of the particles.

• overview
• the relationship of temperature, motions, conduction, and thermal energy
• practical applications for thermodynamic temperature
• definition of thermodynamic temperature
• history
## Thermodynamics The classical Carnot heat engine Branches Classical Statistical Chemical Quantum thermodynamics Equilibrium / Non-equilibrium Laws Zeroth First Second Third Systems State Equation of state Ideal gas Real gas State of matter Equilibrium Control volume Instruments Processes Isobaric Isochoric Isothermal Adiabatic Isentropic Isenthalpic Quasistatic Polytropic Free expansion Reversibility Irreversibility Endoreversibility Cycles Heat engines Heat pumps Thermal efficiency System propertiesNote: Conjugate variables in italics Property diagrams Intensive and extensive properties Process functions Work Heat Functions of state Temperature / Entropy (introduction) Pressure / Volume Chemical potential / Particle number Vapor quality Reduced properties Material properties Property databases Specific heat capacity  $c=$ $T$ $\partial S$ $N$ $\partial T$ Compressibility  $\beta =-$ $1$ $\partial V$ $V$ $\partial p$ Thermal expansion  $\alpha =$ $1$ $\partial V$ $V$ $\partial T$ Equations Carnot's theorem Clausius theorem Fundamental relation Ideal gas law Maxwell relations Onsager reciprocal relations Bridgman's equations Table of thermodynamic equations Potentials Free energy Free entropy Internal energy$U(S,V)$ Enthalpy$H(S,p)=U+pV$ Helmholtz free energy$A(T,V)=U-TS$ Gibbs free energy$G(T,p)=H-TS$ HistoryCulture History General Entropy Gas laws "Perpetual motion" machines Philosophy Entropy and time Entropy and life Brownian ratchet Maxwell's demon Heat death paradox Loschmidt's paradox Synergetics Theories Caloric theory Theory of heat ("living force") Mechanical equivalent of heat Motive power Key publications "An Experimental EnquiryConcerning ... Heat" "On the Equilibrium ofHeterogeneous Substances" "Reflections on theMotive Power of Fire" Timelines Thermodynamics Heat engines ArtEducation Maxwell's thermodynamic surface Entropy as energy dispersal Scientists Bernoulli Boltzmann Carnot Clapeyron Clausius Carathéodory Duhem Gibbs von Helmholtz Joule Maxwell von Mayer Onsager Rankine Smeaton Stahl Thompson Thomson van der Waals Waterston Book Categoryvt This article needs to be updated. In particular: it needs to reflect the 2019 redefinition of the SI base units, which came into effect on May 20, 2019. Please update this article to reflect recent events or newly available information. (January 2020) Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, absolute zero, the particle constituents of matter have minimal motion and can become no colder. In the quantum-mechanical description, matter at absolute zero is in its ground state, which is its state of lowest energy. Thermodynamic temperature is often also called absolute temperature, for two reasons: the first, proposed by Kelvin, that it does not depend on the properties of a particular material; the second, that it refers to an absolute zero according to the properties of the ideal gas. The International System of Units specifies a particular scale for thermodynamic temperature. It uses the kelvin scale for measurement and selects the triple point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically. The Rankine scale, using the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United States in some engineering fields. ITS-90 gives a practical means of estimating the thermodynamic temperature to a very high degree of accuracy. Roughly, the temperature of a body at rest is a measure of the mean of the energy of the translational, vibrational and rotational motions of matter's particle constituents, such as molecules, atoms, and subatomic particles. The full variety of these kinetic motions, along with potential energies of particles, and also occasionally certain other types of particle energy in equilibrium with these, make up the total internal energy of a substance. Internal energy is loosely called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings, or by the substance upon the surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a "degree of freedom". At equilibrium, each degree of freedom will have on average the same energy: $k_{\text{B}}T/2$ where $k_{\text{B}}$ is the Boltzmann constant, unless that degree of freedom is in the quantum regime. The internal degrees of freedom (rotation, vibration, etc.) may be in the quantum regime at room temperature, but the translational degrees of freedom will be in the classical regime except at extremely low temperatures (fractions of kelvins) and it may be said that, for most situations, the thermodynamic temperature is specified by the average translational kinetic energy of the particles. Contents 1 Overview 1.1 Practical realization 2 The relationship of temperature, motions, conduction, and thermal energy 2.1 The nature of kinetic energy, translational motion, and temperature 2.2 The high speeds of translational motion 2.3 The diffusion of thermal energy: Entropy, phonons, and mobile conduction electrons 2.4 The diffusion of thermal energy: Black-body radiation 2.4.1 Table of thermodynamic temperatures 2.4.2 The heat of phase changes 2.4.3 Internal energy 2.4.4 Internal energy at absolute zero 3 Practical applications for thermodynamic temperature 4 Definition of thermodynamic temperature 5 History 6 See also 7 Notes 8 External links  