TheInfoList

Thermodynamic temperature is a quantity defined in
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

as distinct from
kinetic theory of the ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation o ...

or
statistical mechanics In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
. A thermodynamic temperature reading of zero is of particular importance for the
third law of thermodynamics The third law of thermodynamics states as follows, regarding the properties of closed systems in thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics Thermodynamics is a branch of physics that deals wit ...
. By courtesy, it reported on the ''
Kelvin scale The kelvin is the base unit of temperature in the International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonasticall ...

'' of
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

in which the unit of measure is the ''kelvin'' (unit symbol: K). For comparison, a temperature of 295 K is equal to 21.85 °C and 71.33 °F. At the zero point of thermodynamic temperature,
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature Thermodynamic temperature is the measure of ''absolute temperature'' and is one of the principal parameters of thermodynamics. A thermodynamic temperature reading of zero deno ...
, the particle constituents of matter have minimal motion and can become no colder. Absolute zero, which is a temperature of zero kelvins (0 K), is precisely equal to −273.15 °C and −459.67 °F. Matter at absolute zero has no remaining transferable average kinetic energy and the only remaining particle motion is due to an ever-pervasive
quantum mechanical Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...
phenomenon called
zero-point energy Zero point may refer to: *Origin (mathematics), a fixed point of reference for a coordinate system *Zero Point (film), ''Zero Point'' (film), an Estonian film *Zero point (photometry), a calibration mechanism for magnitude in astronomy *Zero Point ...
. While scientists are achieving temperatures ever closer to
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature Thermodynamic temperature is the measure of ''absolute temperature'' and is one of the principal parameters of thermodynamics. A thermodynamic temperature reading of zero deno ...
, they can not fully achieve a state of ''zero'' temperature. However, even if scientists could remove ''all'' kinetic thermal energy from matter,
quantum mechanical Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...
''
zero-point energy Zero point may refer to: *Origin (mathematics), a fixed point of reference for a coordinate system *Zero Point (film), ''Zero Point'' (film), an Estonian film *Zero point (photometry), a calibration mechanism for magnitude in astronomy *Zero Point ...
'' (ZPE) causes particle motion that can never be eliminated. Encyclopædia Britannica Onlin
defines zero-point
energy as the "vibrational energy that molecules retain even at the absolute zero of temperature". ZPE is the result of all-pervasive energy fields in the vacuum between the fundamental particles of nature; it is responsible for the
Casimir effect In quantum field theory, the Casimir effect is a physical force (physics), force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Cas ...
and other phenomena. See
Zero Point Energy and Zero Point Field

'' by the University of Alberta's Department of Physics to learn more about ZPE's effect on
Bose–Einstein condensate In condensed matter physics Condensed matter physics is the field of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science ...
s of helium. Although absolute zero (''T''=0) is not a state of zero molecular motion, it ''is ''the point of zero temperature and, in accordance with the Boltzmann constant, is also the point of zero particle kinetic energy and zero kinetic velocity. To understand how atoms can have zero kinetic velocity and simultaneously be vibrating due to ZPE, consider the following thought experiment: two ''T''=0 helium atoms in zero gravity are carefully positioned and observed to have an average separation of 620  pm between them (a gap of ten atomic diameters). It's an "average" separation because ZPE causes them to jostle about their fixed positions. Then one atom is given a kinetic kick of precisely 83 yoctokelvins (1 yK = ). This is done in a way that directs this atom's velocity vector at the other atom. With 83 yK of kinetic energy between them, the 620 pm gap through their common
barycenter In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses ...
would close at a rate of 719 pm/s and they would collide after 0.862 second. This is the same speed as shown in the '' Fig. 1 ''animation above. Before being given the kinetic kick, both ''T''=0 atoms had zero kinetic energy and zero kinetic velocity because they could persist indefinitely in that state and relative orientation even though both were being jostled by ZPE. At ''T''=0, no
kinetic energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
is available for transfer to other systems. The Boltzmann constant and its related formulas describe the realm of particle kinetics and velocity vectors whereas ZPE is an energy field that jostles particles in ways described by the mathematics of quantum mechanics. In atomic and molecular collisions in gases, ZPE introduces a degree of ''
chaos Chaos or CHAOS may refer to: Arts, entertainment and media Fictional elements * Chaos (Kinnikuman), Chaos (''Kinnikuman'') * Chaos (Sailor Moon), Chaos (''Sailor Moon'') * Chaos (Sesame Park), Chaos (''Sesame Park'') * Chaos (Warhammer), Chaos ('' ...
'', i.e., unpredictability, to rebound kinetics; it is as likely that there will be ''less'' ZPE-induced particle motion after a given collision as ''more.'' This random nature of ZPE is why it has no net effect upon either the pressure or volume of any ''bulk quantity'' (a statistically significant quantity of particles) of ''T''>0 K gases. However, in ''T''=0
condensed matter Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases which arise from electromagnetic forces between atoms. More ge ...
; e.g., solids and liquids, ZPE causes inter-atomic jostling where atoms would otherwise be perfectly stationary. Inasmuch as the real-world effects that ZPE has on substances can vary as one alters a thermodynamic system (for example, due to ZPE, helium won't freeze unless under a pressure of at least 25
bar Bar or BAR may refer to: Food *Bar (establishment) A bar is a long raised narrow table or bench designed for dispensing beer or other alcoholic beverage, alcoholic drinks. They were originally chest high, and a bar, often brass, ran the len ...
or 2.5
MPa MPA or mPa may refer to: Academia Academic degrees * Master of Performing Arts * Master of Professional Accountancy * Master of Public Administration * Master of Public Affairs Schools * Mesa Preparatory Academy * Morgan Park Academy * Mounds ...
), ZPE is very much a form of thermal energy and may properly be included when tallying a substance's internal energy. Note too that absolute zero serves as the baseline atop which
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

and its
equations In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
are founded because they deal with the exchange of thermal energy between ''"systems"'' (a plurality of particles and fields modeled as an average). Accordingly, one may examine ZPE-induced particle motion ''within'' a system that is at absolute zero but there can never be a net outflow of thermal energy from such a system. Also, the peak emittance wavelength of black-body radiation shifts to infinity at absolute zero; indeed, a peak no longer exists and black-body photons can no longer escape. Because of ZPE, however, ''virtual'' photons are still emitted at ''T''=0. Such photons are called "virtual" because they can't be intercepted and observed. Furthermore, this ''zero-point radiation'' has a unique ''zero-point spectrum.'' However, even though a ''T''=0 system emits zero-point radiation, no net heat flow ''Q'' out of such a system can occur because if the surrounding environment is at a temperature greater than ''T''=0, heat will flow inward, and if the surrounding environment is at ''T''=0, there will be an equal flux of ZP radiation both inward and outward. A similar ''Q ''equilibrium exists at ''T''=0 with the ZPE-induced
spontaneous emission Spontaneous emission is the process in which a quantum mechanical system (such as a molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. ...
of photons (which is more properly called a ''stimulated'' emission in this context). The graph at upper right illustrates the relationship of absolute zero to zero-point energy. The graph also helps in the understanding of how zero-point energy got its name: it is the vibrational energy matter retains at the ''zero-kelvin point''
''Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces''
Daniel C. Cole, Physical Review A, 42 (1990) 1847.
Though the atoms in, for instance, a container of liquid
helium Helium (from el, ἥλιος, helios Helios; Homeric Greek: ), Latinized as Helius; Hyperion and Phaethon are also the names of his father and son respectively. often given the epithets Hyperion ("the one above") and Phaethon ("the shining" ...

that was ''precisely'' at absolute zero would still jostle slightly due to zero-point energy, a with such helium as one of its
working fluid For fluid power, a working fluid is a gas or liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external force ...
s could never transfer any net kinetic energy (
heat energy In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is go ...

) to the other working fluid and no
thermodynamic work In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is govern ...
could occur. Temperature is generally expressed in absolute terms when scientifically examining temperature's interrelationships with certain other physical properties of matter such as its
volume Volume is a scalar quantity expressing the amount Quantity or amount is a property that can exist as a multitude Multitude is a term for a group of people who cannot be classed under any other distinct category, except for their shared fact ...
or
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

(see
Gay-Lussac's law Gay-Lussac's law (also referred to as Amonton's law) states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas when the volume is kept constant. Mathematically, it can be written as: \frac = k. It is ...
), or the wavelength of its emitted
black-body radiation Black-body radiation is the within or surrounding a body in with its environment, emitted by a (an idealized opaque, non-reflective body). It has a specific spectrum of wavelengths, inversely related to intensity that depend only on the bod ...
. Absolute temperature is also useful when calculating chemical reaction rates (see
Arrhenius equation In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 ...
). Furthermore, absolute temperature is typically used in
cryogenics In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

and related phenomena like
superconductivity Superconductivity is a set of physical properties observed in certain materials where electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current An electric current is a st ...

, as per the following example usage: “Conveniently, tantalum’s transition temperature (''T'') of 4.4924 kelvin is slightly above the 4.2221 K boiling point of helium.”

# Overview

The
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
(SI) specifies the ''Kelvin scale'' for measuring thermodynamic temperature, and the unit of measure ''
kelvin The kelvin is the base unit of temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal en ...

'' (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 in relation to the ''very physical property'' underlying thermodynamic temperature: the kinetic energy of atomic particle motion. The redefinition fixed the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality, Multiplication, multiplicatively connected to a Constant (mathematics), c ...
at precisely (J/K).
CODATA Value: Boltzmann constant
'' ''The NIST Reference on Constants, Units, and Uncertainty''.
National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is a physical sciences Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, e ...
.
The compound unit of measure for the Boltzmann constant is often also given as J·K−1, which may seem abstract due the multiplication dot (·) and a kelvin symbol that is followed by a superscripted ''negative 1'' exponent, however this is merely another mathematical syntax denoting the same measure: ''
joules The joule ( ; symbol: J) is a derived unit of energy In physics, energy is the physical quantity, quantitative physical property, property that must be #Energy transfer, transferred to a physical body, body or physical system to perform W ...
'' (the SI unit for
energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

, including kinetic energy) ''per kelvin.'' The property that imbues any substances with a temperature can be readily understood by examining the
ideal gas law The ideal gas law, also called the general gas equation, is the equation of state In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the na ...

, which relates, per the Boltzmann constant, how
heat energy In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is go ...

causes precisely defined changes in the
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

and temperature of certain gases. This is because
monatomic gas In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Spa ...
es like
helium Helium (from el, ἥλιος, helios Helios; Homeric Greek: ), Latinized as Helius; Hyperion and Phaethon are also the names of his father and son respectively. often given the epithets Hyperion ("the one above") and Phaethon ("the shining" ...

and
argon Argon is a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behav ...

behave kinetically like perfectly elastic and spherical billiard balls that move only in a specific subset of the possible vibrational motions that can occur in matter: that comprising the ''three translational''
degrees of freedom Degrees of Freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or other physical ...
. The translational degrees of freedom are the familiar billiard ball-like movements in the X, Y, and Z axis of 3D space (see ''Fig. 1'', below). This is why the noble gases all have the same specific heat capacity per atom and why that value is lowest of all the gases.
Molecule A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon ...

s (two or more chemically bound atoms), however, have ''internal structure'' and therefore have additional ''internal'' degrees of freedom, (see ''Fig. 3'', below), which makes molecules absorb more heat energy for any given amount of temperature rise than do the monoatomic gases. Heat energy is born in all available degrees of freedom; this is in accordance with the
equipartition theorem In , the equipartition theorem relates the of a system to its average . The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in , e ...
, 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 Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

, 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 atoms’ and molecules’ three translational degrees of freedom. Fixing the Boltzmann constant at specific value, along with other rule making, had the effect of precisely establishing the magnitude of the unit interval of thermodynamic 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.

# The Rankine scale

Though there have been many other temperature scales throughout history, there have been only two scales for measuring thermodynamic temperature where absolute zero is their null point (0): The
Kelvin scale The kelvin is the base unit of temperature in the International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonasticall ...
and the
Rankine scale __NOTOC__ The Rankine scale () is an absolute scale An absolute scale is a system of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or ...
. Throughout the scientific world where modern measurements are nearly always made using the International System of Units, thermodynamic temperature is measured using the Kelvin scale. The Rankine scale is part of
English engineering units Some fields of engineering in the United States use a system of measurement of physical quantities known as the English Engineering Units. Despite its name, the system is based on United States customary units of measure; it is not used in England ...
in the United States and finds use in certain engineering fields, particularly in legacy reference works. The Rankine scale uses the ''degree Rankine'' (symbol: °R) as its unit, which is the same magnitude as the
degree Fahrenheit The Fahrenheit scale ( or ) is a temperature scale Scale of temperature is a methodology of calibrating the physical quantity temperature in metrology. Empirical scales measure temperature in relation to convenient and stable parameters, such a ...

(symbol: °F). A unit increment of one degree Rankine is precisely 1.8 times smaller in magnitude than one kelvin; thus, to convert a specific temperature on the Kelvin scale to the Rankine scale, and to convert from a temperature on the Rankine scale to the Kelvin scale, Consequently, absolute zero is “0” for both scales, but the melting point of water ice (0 °C and 273.15 K) is 491.67 °R. To convert temperature ''intervals'' (a span or difference between two temperatures), one uses the same formulas from the preceding paragraph; for instance, a range of 5 kelvins is precisely equal to a range of 9 degrees Rankine.

# Modern redefinition of the kelvin

For 65 years, between 1954 and the
2019 redefinition of the SI base units Effective 20 May 2019, the 144th anniversary of the Metre Convention The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty A treaty is a formal, legally bi ...
, a temperature interval of one kelvin was defined as the difference between the
triple point In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quan ...
of water and absolute zero. The 1954 resolution by the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation An intergovernmental organization (IGO) is an organization composed primarily of sovereign state ...
(known by the French-language acronym BIPM), plus later resolutions and publications, defined the triple point of water as precisely 273.16 K and acknowledged that it was “common practice” to accept that due to previous conventions (namely, that 0 °C had long been defined as the melting point of water and that the triple point of water had long been experimentally determined to be indistinguishably close to 0.01 °C), the difference between the Celsius scale and Kelvin scale is accepted as 273.15 kelvins; which is to say, 0 °C equals 273.15 kelvins. The net effect of this as well as later resolutions was twofold: 1) they defined absolute zero as precisely 0 K, and 2) they defined that the triple point of special isotopically controlled water called
Vienna Standard Mean Ocean Water Vienna Standard Mean Ocean Water (VSMOW) is an isotopic standard for water. Despite the name, VSMOW is pure water with no salt or other chemicals found in the oceans. The VSMOW standard was promulgated by the International Atomic Energy Agency ...
was precisely 273.16 kelvins and 0.01 °C. One effect of the aforementioned resolutions was that the melting point of water, while ''very'' close to 273.15 kelvin and 0 °C, was not a defining value and was subject to refinement with more precise measurements. The 1954 BIPM standard did a good job of establishing—within the uncertainties due to isotopic variations between water samples—temperatures around the freezing and triple points of water, but required that ''intermediate values'' between the triple point and absolute zero, as well as extrapolated values from room temperature and beyond, to be experimentally determined via apparatus and procedures in individual labs. This shortcoming was addressed by the
International Temperature Scale of 1990 The International Temperature Scale of 1990 (ITS-90) is an equipment calibration standard specified by the CIPM, International Committee of Weights and Measures (CIPM) for making measurements on the Kelvin and Degree Celsius, Celsius temperature sca ...
, or ITS90, which defined 13 additional points, from 13.8033 K, to 1,357.77 K. While definitional, ITS90 had—and still has—some challenges, partly because eight of its extrapolated values depend upon the melting or freezing points of metal samples, which must remain exceedingly pure lest their melting or freezing points be affected—usually depressed. The 2019 redefinition of the SI base units was primarily for the purpose of decoupling much of the SI system's definitional underpinnings from the
kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of " ...
, which was the last physical artifact defining an
SI base unit The SI base units are the standard units of measurement A unit of measurement is a definite magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mat ...

(a platinum/iridium cylinder stored under three nested bell jars in a safe located in France) and which had highly questionable stability. The solution required that four physical constants, including the Boltzmann constant, be definitionally fixed. Assigning the Boltzmann constant a precisely defined value had no practical effect on modern thermometry except for the most exquisitely precise measurements. Before the redefinition, the triple point of water was exactly 273.16 K and 0.01 °C and the Boltzmann constant was experimentally determined to be , where the “(51)” denotes the uncertainty in the two least significant digits (the 03) and equals a of 0.37 ppm. Afterwards, by defining the Boltzmann constant as exactly , the 0.37 ppm uncertainty was transferred to the triple point of water, which became an experimentally determined value of 273.1600 ±0.0001 K (0.0100 ±0.0001 °C). That the triple point of water ended up being exceedingly close to 273.16 K after the SI redefinition was no accident; the final value of the Boltzmann constant was determined, in part, through clever experiments with
argon Argon is a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behav ...

and helium that used the triple point of water for their key reference temperature.  Notwithstanding the 2019 redefinition, water triple-point cells continue to serve in modern thermometry as exceedingly precise calibration references at 273.16 K and 0.01 °C. Moreover, the triple point of water remains one of the 14 calibration points comprising ITS90, which spans from the triple point of hydrogen (13.8033 K) to the freezing point of copper (1,357.77 K), which is a nearly hundredfold range of thermodynamic temperature.

# The relationship of temperature, motions, conduction, and thermal energy

## The nature of kinetic energy, translational motion, and temperature

The thermodynamic temperature of any ''bulk quantity'' of a substance (a statistically significant quantity of particles) is directly proportional to the mean average kinetic energy of a specific kind of particle motion known as ''translational motion.'' These simple movements in the three X, Y, and Z–axis dimensions of space means the particles move in the three spatial ''
degrees of freedom Degrees of Freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or other physical ...
.'' This particular form of kinetic energy is sometimes referred to as ''kinetic temperature.'' Translational motion is but one form of heat energy and is what gives gases not only their temperature, but also their pressure and the vast majority of their volume. This relationship between the temperature, pressure, and volume of gases is established by the
ideal gas law The ideal gas law, also called the general gas equation, is the equation of state In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the na ...

's formula and is embodied in the
gas laws The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the ...
. Though the kinetic energy borne exclusively in the three translational degrees of freedom comprise the thermodynamic temperature of a substance, molecules, as can be seen in ''Fig. 3'', can have other degrees of freedom, all of which fall under three categories: bond length, bond angle, and rotational. All three additional categories are not necessarily available to all molecules, and even for molecules that ''can'' experience all three, some can be “frozen out” below a certain temperature. Nonetheless, all those degrees of freedom that are available to the molecules under a particular set of conditions contribute to the
specific heat capacity In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qua ...
of a substance; which is to say, they increase the amount of heat (kinetic energy) required to raise a given amount of the substance by one kelvin or one degree Celsius. The relationship of kinetic energy, mass, and velocity is given by the formula ''Ek'' = ''mv''. Accordingly, particles with one unit of mass moving at one unit of velocity have precisely the same kinetic energy, and precisely the same temperature, as those with four times the mass but half the velocity. The extent to which the kinetic energy of translational motion in a statistically significant collection of atoms or molecules in a gas contributes to the pressure and volume of that gas is a proportional function of thermodynamic temperature as established by the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality, Multiplication, multiplicatively connected to a Constant (mathematics), c ...
(symbol: ''k''B). The Boltzmann constant also relates the thermodynamic temperature of a gas to the mean kinetic energy of an ''individual'' particles’ translational motion as follows: $\tilde \, = \, \frac k_\text T$ where: * $\tilde$ is the mean kinetic energy for any individual particle, in
joule The joule ( ; symbol: J) is a derived unit of energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates ...

s (J) * ''k''B = * ''T'' is the thermodynamic temperature of the bulk quantity of the substance, in kelvins (K) While the Boltzmann constant is useful for finding the mean kinetic energy in a sample of particles, it's important to note that even when a substance is isolated and in
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic An axiom, postulate or assumption is a statement that is taken to be true True most commonly refers to truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Onlin ...
(all parts are at a uniform temperature and no heat is going into or out of it), the translational motions of individual atoms and molecules occurs across a wide range of speeds (see animation in '' Fig. 1 ''above). At any one instant, the proportion of particles moving at a given speed within this range is determined by probability as described by the
Maxwell–Boltzmann distribution In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
. The graph shown here in ''Fig. 2 '' shows the speed distribution of 5500 K helium atoms. They have a ''most probable'' speed of 4.780 km/s (0.2092 s/km). However, a certain proportion of atoms at any given instant are moving faster while others are moving relatively slowly; some are momentarily at a virtual standstill (off the ''x''–axis to the right). This graph uses ''inverse speed'' for its ''x''–axis so the shape of the curve can easily be compared to the curves in '' Fig. 5'' below. In both graphs, zero on the ''x''–axis represents infinite temperature. Additionally, the ''x'' and ''y''–axis on both graphs are scaled proportionally.

### The high speeds of translational motion

Although very specialized laboratory equipment is required to directly detect translational motions, the resultant collisions by atoms or molecules with small particles suspended in a
fluid In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
produces
Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physica ...

that can be seen with an ordinary microscope. The translational motions of elementary particles are ''very'' fast and temperatures close to
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature Thermodynamic temperature is the measure of ''absolute temperature'' and is one of the principal parameters of thermodynamics. A thermodynamic temperature reading of zero deno ...
are required to directly observe them. For instance, when scientists at the
NIST The National Institute of Standards and Technology (NIST) is a physical sciences Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, e ...
achieved a record-setting cold temperature of 700 nK (billionths of a kelvin) in 1994, they used
optical lattice An optical lattice is formed by the interference of counter-propagating laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The term "laser" ...
laser equipment to cool
cesium Caesium (IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering OrganizationsNational Adhering Organizations in chemistry are the organizations that work as the authoritative ...

atoms. They then turned off the entrapment lasers and directly measured atom velocities of 7 mm per second to in order to calculate their temperature.  Formulas for calculating the velocity and speed of translational motion are given in the following footnote.The rate of translational motion of atoms and molecules is calculated based on thermodynamic temperature as follows: $\tilde = \sqrt$ where… *$\tilde$ is the vector-isolated mean velocity of translational particle motion in m/s *''k''B (
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality, Multiplication, multiplicatively connected to a Constant (mathematics), c ...
) = *''T'' is the thermodynamic temperature in kelvins *''m'' is the molecular mass of substance in kg/particle In the above formula, molecular mass, ''m'', in kg/particle is the quotient of a substance’s
molar mass In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in t ...
(also known as ''atomic weight'', '' atomic mass'', ''relative atomic mass'', and '' unified atomic mass units'') in g/ mol or daltons divided by (which is the
Avogadro constant The Avogadro constant (''N''A or ''L'') is the proportionality factor In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality, Multiplication, multiplicatively connected to a Constant (mathem ...
times one thousand). For
diatomic Diatomic molecules are molecule A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position I ...
molecules such as , , and , multiply atomic weight by two before plugging it into the above formula. The mean ''speed'' (not vector-isolated velocity) of an atom or molecule along any arbitrary path is calculated as follows: $\tilde = \tilde \cdot \sqrt$ where $\tilde$ is the mean speed of translational particle motion in m/s. Note that the mean energy of the translational motions of a substance’s constituent particles correlates to their mean ''speed'', not velocity. Thus, substituting $\tilde$ for ''v'' in the classic formula for kinetic energy, produces precisely the same value as does (as shown in the section titled '' The nature of kinetic energy, translational motion, and temperature)''.  Note too that the Boltzmann constant and its related formulas establish that absolute zero is the point of both zero kinetic energy of particle motion and zero kinetic velocity (see also ''
Note 1 The Samsung Galaxy Note is an Android Android may refer to: Science and technology * Android (robot), a humanoid robot or synthetic organism designed to imitate a human * Android (operating system), Google's mobile operating system ** Android ...
'' above).
It is neither difficult to imagine atomic motions due to kinetic temperature, nor distinguish between such motions and those due to zero-point energy. Consider the following hypothetical thought experiment, as illustrated in ''Fig. 2.5'' at left, with an atom that is exceedingly close to absolute zero. Imagine peering through a common optical microscope set to 400 power, which is about the maximum practical magnification for optical microscopes. Such microscopes generally provide fields of view a bit over 0.4 mm in diameter. At the center of the field of view is a single levitated argon atom (argon comprises about 0.93% of air) that is illuminated and glowing against a dark backdrop. If this argon atom was at a beyond-record-setting ''one-trillionth'' of a kelvin above absolute zero, and was moving perpendicular to the field of view towards the right, it would require 13.9 seconds to move from the center of the image to the 200-micron tick mark; this travel distance is about the same as the width of the period at the end of this sentence on modern computer monitors. As the argon atom slowly moved, the positional jitter due to zero-point energy would be much less than the 200-nanometer (0.0002 mm) resolution of an optical microscope. Importantly, the atom's translational velocity of 14.43 microns per second constitutes all its retained kinetic energy due to not being precisely at absolute zero. Were the atom ''precisely'' at absolute zero, imperceptible jostling due to zero-point energy would cause it to very slightly wander, but the atom would perpetually be located, on average, at the same spot within the field of view. This is analogous to a boat that has had its motor turned off and is now bobbing slightly in relatively calm and windless ocean waters; even though the boat randomly drifts to and fro, it stays in the same spot in the long term and makes no headway through the water. Accordingly, an atom that was precisely at absolute zero would not be “motionless,” and yet, a statistically significant collection of such atoms would have zero net kinetic energy available to transfer to any other collection of atoms. This is because regardless of the kinetic temperature of the second collection of atoms, they too experience the effects of zero-point energy. Such are the consequences of
statistical mechanics In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
and the nature of thermodynamics.

### The internal motions of molecules and internal energy

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 A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon ...

s are complex objects; they are a population of atoms and thermal agitation can strain their internal
chemical bond A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyda ...
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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...
'' substances (consisting of individual atoms) like the
noble gas The noble gases (historically also the inert gases; sometimes referred to as aerogens) make up a class of chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that m ...
es
helium Helium (from el, ἥλιος, helios Helios; Homeric Greek: ), Latinized as Helius; Hyperion and Phaethon are also the names of his father and son respectively. often given the epithets Hyperion ("the one above") and Phaethon ("the shining" ...

and
argon Argon is a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behav ...

, 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 In , the equipartition theorem relates the of a system to its average . The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in , e ...
, 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 Thermodynamic equilibrium is an axiomatic concept of thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of ma ...
(LTE) phenomena such as
combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion ...
, the sublimation of solids, and the
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration In chemistry Chemistry is the study of the properties and behavior of . It is a that covers ...

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 at that same instant contributing to the molecules’ translational motions. This extra kinetic energy simply increases the amount of internal energy a substance absorbs for a given temperature rise. This property is known as a substance's
specific heat capacity In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qua ...
. 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 Nitrogen is the chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science ...

, which is a
diatomic Diatomic molecules are molecule A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position I ...
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 Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpidae ...
(a specific number of molecules) as do the monatomic gases. Another example is
gasoline Gasoline () or petrol () (see the etymology Etymology ()The New Oxford Dictionary of English ''The'' () is a grammatical article Article often refers to: * Article (grammar) An article is any member of a class of dedicated word ...

(see
table Table may refer to: * Table (information) A table is an arrangement of data Data are units of information Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus define ...
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.

## The diffusion of thermal energy: Entropy, phonons, and mobile conduction electrons

''
Heat conduction Thermal conduction is the transfer of internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes u ...

'' 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 Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

increases). One particular heat conduction mechanism occurs when translational motion, the particle motion underlying temperature, transfers
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...

from particle to particle in collisions. In gases, these translational motions are of the nature shown above in '' Fig. 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 Convection is single or multiphase fluid flow that occurs Spontaneous process, spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When t ...
speeds this process even more. Translational motion in ''solids'', however, takes the form of ''
phonon In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
s'' (see ''Fig. 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 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 A metal (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ...

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 The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

s.'' This is why there is a near-perfect correlation between metals'
thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...

and their
electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current An electric current is a stream of charged particle In p ...
. Conduction electrons imbue metals with their extraordinary conductivity because they 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 Zero point may refer to: *Origin (mathematics), a fixed point of reference for a coordinate system *Zero Point (film), ''Zero Point'' (film), an Estonian film *Zero point (photometry), a calibration mechanism for magnitude in astronomy *Zero Point ...
'' (for more on ZPE, see ''
Note 1 The Samsung Galaxy Note is an Android Android may refer to: Science and technology * Android (robot), a humanoid robot or synthetic organism designed to imitate a human * Android (operating system), Google's mobile operating system ** Android ...
'' below). Furthermore, electrons are relatively light with a rest mass only that of a
proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collecti ...

. This is about the same ratio as a
.22 Short .22 Short is a variety of .22 caliber (5.6 mm) rimfire ammunition Rimfire ammunition is a type of firearm metallic cartridge whose primer (firearm), primer is located within a hollow circumferential rim (firearms), rim protruding from t ...
bullet (29
grains A grain is a small, hard, dry seed A seed is an embryonic ''Embryonic'' is the twelfth studio album by experimental rock band the Flaming Lips released on October 13, 2009, on Warner Bros. Records, Warner Bros. The band's first double albu ...
or 1.88  g) compared to the rifle that shoots it. As
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

wrote with his , 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're delocalized and ''very'' fast, kinetic thermal energy conducts extremely quickly through metals with abundant conduction electrons.

## The diffusion of thermal energy: Black-body radiation

Thermal radiation Thermal radiation is electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space an ...
is a byproduct of the collisions arising from various vibrational motions of atoms. These collisions cause the electrons of the atoms to emit thermal
photon The photon ( el, φῶς, phōs, light) is a type of elementary particle In , an elementary particle or fundamental particle is a that is not composed of other particles. Particles currently thought to be elementary include the fundamental s ...

s (known as
black-body radiation Black-body radiation is the within or surrounding a body in with its environment, emitted by a (an idealized opaque, non-reflective body). It has a specific spectrum of wavelengths, inversely related to intensity that depend only on the bod ...
). Photons are emitted anytime an electric charge is accelerated (as happens when electron clouds of two atoms collide). Even ''individual molecules'' with internal temperatures greater than absolute zero also emit black-body radiation from their atoms. In any bulk quantity of a substance at equilibrium, black-body photons are emitted across a range of
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

s in a spectrum that has a bell curve-like shape called a Planck curve (see graph in ''Fig. 5'' at right). The top of a Planck curve ( the peak emittance wavelength) is located in a particular part of the
electromagnetic spectrum The electromagnetic spectrum is the range of frequency, frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energy, photon energies. The electromagnetic spectrum covers electromagnetic waves with f ...

depending on the temperature of the black-body. Substances at extreme
cryogenic In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and fo ...

temperatures emit at long radio wavelengths whereas extremely hot temperatures produce short
gamma ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, it ...
s (see '' Table of common temperatures''). Black-body radiation diffuses thermal energy throughout a substance as the photons are absorbed by neighboring atoms, transferring momentum in the process. Black-body photons also easily escape from a substance and can be absorbed by the ambient environment; kinetic energy is lost in the process. As established by the
Stefan–Boltzmann law The Stefan–Boltzmann law describes the power radiated from a black body A black body or blackbody is an idealized physical object, physical body that absorption (electromagnetic radiation), absorbs all incident electromagnetic radiation, r ...
, the intensity of black-body radiation increases as the fourth power of absolute temperature. Thus, a black-body at 824 K (just short of glowing dull red) emits ''60 times'' the radiant
power Power most often refers to: * Power (physics) In physics, power is the amount of energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, bu ...
as it does at 296 K (room temperature). This is why one can so easily feel the radiant heat from hot objects at a distance. At higher temperatures, such as those found in an
incandescent lamp An incandescent light bulb, incandescent lamp or incandescent light globe is an electric light An electric light is a device that produces visible light Light or visible light is electromagnetic radiation within the portion of the ...

, black-body radiation can be the principal mechanism by which thermal energy escapes a system.

### Table of thermodynamic temperatures

The full range of the thermodynamic temperature scale, from absolute zero to absolute hot, and some notable points between them are shown in the table below.

## The heat of phase changes

The kinetic energy of particle motion is just one contributor to the total thermal energy in a substance; another is ''
phase transition In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in ...
s'', which are the
potential energy In physics, potential energy is the energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measure ...

of molecular bonds that can form in a substance as it cools (such as during and
freezing Freezing is a phase transition In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as fa ...

). The thermal energy required for a phase transition is called ''
latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any su ...
.'' This phenomenon may more easily be grasped by considering it in the reverse direction: latent heat is the energy required to ''break''
chemical bonds A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyd ...
(such as during
evaporation Evaporation is a type of vaporization Vaporization (or vaporisation) of an element or compound is a phase transition from the liquid phase to vapor. There are two types of vaporization: evaporation and boiling. Evaporation is a surface phe ...

and
melting Melting, or fusion, is a physical process that results in the phase transition In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiari ...

). Almost everyone is familiar with the effects of phase transitions; for instance,
steam Steam is water Water (chemical formula H2O) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fl ...

at 100 °C can cause severe burns much faster than the 100 °C air from a
hair dryer A hair dryer, hairdryer or blow dryer is an electromechanical In engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, ro ...
. This occurs because a large amount of latent heat is liberated as steam condenses into liquid water on the skin. Even though thermal energy is liberated or absorbed during phase transitions, pure
chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo du ...
s,
compounds Compound may refer to: Architecture and built environments * Compound (enclosure), a cluster of buildings having a shared purpose, usually inside a fence or wall ** Compound (fortification), a version of the above fortified with defensive structu ...
, and eutectic
alloy An alloy is an admixture of metal A metal (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in ...
s ''exhibit no temperature change whatsoever'' while they undergo them (see ''Fig. 7,'' below right). Consider one particular type of phase transition: melting. When a solid is melting,
crystal lattice In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of f ...

chemical bond A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyda ...
s are being broken apart; the substance is transitioning from what is known as a ''more ordered state'' to a ''less ordered state''. In ''Fig. 7, ''the melting of ice is shown within the lower left box heading from blue to green. At one specific thermodynamic point, the
melting point The melting point (or, rarely, liquefaction point) of a substance is the temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can b ...

(which is 0 °C across a wide pressure range in the case of water), all the atoms or molecules are, on average, at the maximum energy threshold their chemical bonds can withstand without breaking away from the lattice. Chemical bonds are all-or-nothing forces: they either hold fast, or break; there is no in-between state. Consequently, when a substance is at its melting point, every
joule The joule ( ; symbol: J) is a derived unit of energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates ...

of added thermal energy only breaks the bonds of a specific quantity of its atoms or molecules, converting them into a liquid of precisely the same temperature; no kinetic energy is added to translational motion (which is what gives substances their temperature). The effect is rather like
popcorn Popcorn (popped corn, popcorns or pop-corn) is a variety of corn Maize ( ; ''Zea mays'' subsp. ''mays'', from es, maíz after tnq, mahiz), also known as corn (North American North America is a continent entirely within the N ...

: at a certain temperature, additional thermal energy can't make the kernels any hotter until the transition (popping) is complete. If the process is reversed (as in the freezing of a liquid), thermal energy must be removed from a substance. As stated above, the thermal energy required for a phase transition is called ''latent heat.'' In the specific cases of melting and freezing, it's called ''
enthalpy of fusion The enthalpy of fusion of a substance, also known as (latent) heat of fusion is the change in its enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. ...
'' or ''heat of fusion.'' If the molecular bonds in a crystal lattice are strong, the heat of fusion can be relatively great, typically in the range of 6 to 30 kJ per mole for water and most of the metallic elements. If the substance is one of the monatomic gases, (which have little tendency to form molecular bonds) the heat of fusion is more modest, ranging from 0.021 to 2.3 kJ per mole. Relatively speaking, phase transitions can be truly energetic events. To completely melt ice at 0 °C into water at 0 °C, one must add roughly 80 times the thermal energy as is required to increase the temperature of the same mass of liquid water by one degree Celsius. The metals' ratios are even greater, typically in the range of 400 to 1200 times. And the phase transition of
boiling Boiling is the rapid vaporization of a liquid, which occurs when a liquid is heated to its boiling point, the temperature at which the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere. Ther ...
is much more energetic than freezing. For instance, the energy required to completely boil or vaporize water (what is known as ''
enthalpy of vaporization The enthalpy of vaporization (symbol ), also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy an ...
'') is roughly ''540 times'' that required for a one-degree increase. Water's sizable enthalpy of vaporization is why one's skin can be burned so quickly as steam condenses on it (heading from red to green in ''Fig. 7 ''above). In the opposite direction, this is why one's skin feels cool as liquid water on it evaporates (a process that occurs at a sub-ambient
wet-bulb temperature The wet-bulb temperature (WBT) is the temperature Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of ene ...
that is dependent on
relative humidity Humidity is the concentration of water vapour (99.9839 °C) , - , Boiling point , , - , specific gas constant , 461.5 J/( kg·K) , - , Heat of vaporization , 2.27 MJ/kg , - , Heat capacity , 1.864 kJ/(kg·K) Water vap ...

). Water's highly energetic enthalpy of vaporization is also an important factor underlying why ''solar pool covers'' (floating, insulated blankets that cover
swimming pool A swimming pool, swimming bath, wading pool, paddling pool, or simply pool, is a structure designed to hold water to enable Human swimming, swimming or other leisure activities. Pools can be built into the ground (in-ground pools) or built ...

s when not in use) are so effective at reducing heating costs: they prevent evaporation. For instance, the evaporation of just 20 mm of water from a 1.29-meter-deep pool chills its water 8.4 degrees Celsius (15.1 °F).

## Internal energy

The total energy of all particle motion translational and internal, including that of conduction electrons, plus the potential energy of phase changes, plus
zero-point energy Zero point may refer to: *Origin (mathematics), a fixed point of reference for a coordinate system *Zero Point (film), ''Zero Point'' (film), an Estonian film *Zero point (photometry), a calibration mechanism for magnitude in astronomy *Zero Point ...
comprise the ''
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that ca ...
'' of a substance.

## Internal energy at absolute zero

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 temperature decreases); the internal motions of molecules diminish (their internal temperature decreases); conduction electrons (if the substance is an electrical conductor) travel ''somewhat'' slower;  and black-body radiation's peak emittance wavelength increases (the photons' energy decreases). When the particles of a substance are as close as possible to complete rest and retain only ZPE-induced quantum mechanical motion, the substance is at the temperature of absolute zero (''T'' = 0). Note that 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, ''T'' = 0
helium Helium (from el, ἥλιος, helios Helios; Homeric Greek: ), Latinized as Helius; Hyperion and Phaethon are also the names of his father and son respectively. often given the epithets Hyperion ("the one above") and Phaethon ("the shining" ...

remains liquid at room pressure (''Fig. 9'' at right) and must be under a pressure of at least to crystallize. This is because helium's heat of fusion (the energy required to melt helium ice) is so low (only 21 joules per 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 ''T'' = 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 '' closest-packed arrangement'' (see ''Fig. 8,'' above left) contain minimal internal energy, retaining only that due to the ever-present background of zero-point energy.  One can also say that for a given substance at constant pressure, absolute zero is the point of lowest ''
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant p ...

'' (a measure of work potential that takes internal energy, pressure, and volume into consideration). Lastly, it is always true to say that all ''T'' = 0 substances contain zero kinetic thermal energy.

# Practical applications for thermodynamic temperature

Thermodynamic temperature is useful not only for scientists, it can also be useful for lay-people in many disciplines involving gases. By expressing variables in absolute terms and applying Gay–Lussac's law of temperature/pressure proportionality, solutions to everyday problems are straightforward; for instance, calculating how a temperature change affects the pressure inside an automobile tire. If the tire has a cold of 200
kPa The pascal (symbol: Pa) is the SI derived unit SI derived units are units of measurement derived from the seven SI base unit, base units specified by the International System of Units (SI). They are either dimensionless quantity, dimensionles ...
, then its
absolute pressure Pressure measurement is the analysis of an applied force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. m ...
is 300 kPa. Room temperature ("cold" in tire terms) is 296 K. If the tire temperature is 20 °C hotter (20 kelvins), the solution is calculated as  = 6.8% greater thermodynamic temperature ''and'' absolute pressure; that is, an absolute pressure of 320 kPa, which is a of 220 kPa.

# Relationship to ideal gas law

The thermodynamic temperature is closely linked to the
ideal gas law The ideal gas law, also called the general gas equation, is the equation of state In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the na ...

and its consequences. It can be linked also to the second law of thermodynamics. The thermodynamic temperature can be shown to have special properties, and in particular can be seen to be uniquely defined (up to some constant multiplicative factor) by considering the
efficiency Efficiency is the (often measurable) ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and withou ...
of idealized
heat engine In thermodynamics and engineering, a heat engine is a system that converts heat to mechanical energy, which can then be used to do work (physics), mechanical work. It does this by bringing a working substance from a higher state temperature to ...

s. Thus the ''
ratio In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to ...

'' ''T''2/''T''1 of two temperatures ''T''1 and ''T''2 is the same in all absolute scales. Strictly speaking, the temperature of a system is well-defined only if it is at
thermal equilibrium Two physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment (systems), environment. The enviro ...

. From a microscopic viewpoint, a material is at thermal equilibrium if the quantity of heat between its individual particles cancel out. There are many possible scales of temperature, derived from a variety of observations of physical phenomena. Loosely stated, temperature differences dictate the direction of heat between two systems such that their combined energy is maximally distributed among their lowest possible states. We call this distribution "
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

". To better understand the relationship between temperature and entropy, consider the relationship between heat,
work Work may refer to: * Work (human activity) Work or labor is intentional activity people perform to support themselves, others, or the needs and wants of a wider community. Alternatively, work can be viewed as the human activity that cont ...
and temperature illustrated in the
Carnot heat engine A Carnot heat engine is a theoretical engine that operates on the Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded by Benoît Paul Émile Clapeyr ...

. The engine converts heat into work by directing a temperature gradient between a higher temperature heat source, ''T''H, and a lower temperature heat sink, ''T''C, through a gas filled piston. The work done per cycle is equal to the difference between the heat supplied to the engine by ''T''H, ''q''H, and the heat supplied to ''T''C by the engine, ''q''C. The efficiency of the engine is the work divided by the heat put into the system or where $w_\text$ is the work done per cycle. Thus the efficiency depends only on ''q''C/''q''H. Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, any reversible heat engine operating between temperatures ''T''1 and ''T''2 must have the same efficiency, that is to say, the efficiency is the function of only temperatures In addition, a reversible heat engine operating between temperatures ''T''1 and ''T''3 must have the same efficiency as one consisting of two cycles, one between ''T''1 and another (intermediate) temperature ''T''2, and the second between ''T''2 and''T''3. If this were not the case, then energy (in the form of ''Q'') will be wasted or gained, resulting in different overall efficiencies every time a cycle is split into component cycles; clearly a cycle can be composed of any number of smaller cycles. With this understanding of ''Q''1, ''Q''2 and ''Q''3, mathematically, $f(T_1,T_3) = \frac = \frac = f(T_1,T_2)f(T_2,T_3).$ But the first function is ''NOT'' a function of ''T''2, therefore the product of the final two functions ''MUST'' result in the removal of ''T''2 as a variable. The only way is therefore to define the function as follows: $f(T_1,T_2) = \frac.$ and $f(T_2,T_3) = \frac.$ so that $f(T_1,T_3) = \frac = \frac.$ i.e. The ratio of heat exchanged is a function of the respective temperatures at which they occur. We can choose any monotonic function for our $g\left(T\right)$; it is a matter of convenience and convention that we choose $g\left(T\right) = T$. Choosing then ''one'' fixed reference temperature (i.e. triple point of water), we establish the thermodynamic temperature scale. Such a definition coincides with that of the ideal gas derivation; also it is this ''definition'' of the thermodynamic temperature that enables us to represent the Carnot efficiency in terms of ''T''H and ''T''C, and hence derive that the (complete) Carnot cycle is isentropic: Substituting this back into our first formula for efficiency yields a relationship in terms of temperature: Notice that for the efficiency is 100% and that efficiency becomes greater than 100% for , which cases are unrealistic. Subtracting the right hand side of Equation 4 from the middle portion and rearranging gives $\frac - \frac = 0,$ where the negative sign indicates heat ejected from the system. The generalization of this equation is
Clausius theorem The Clausius theorem (1855) states that for a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All every ...
, which suggests the existence of a state function $S$ (i.e., a function which depends only on the state of the system, not on how it reached that state) defined (up to an additive constant) by where the subscript indicates heat transfer in a reversible process. The function $S$ corresponds to the
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

of the system, mentioned previously, and the change of $S$ around any cycle is zero (as is necessary for any state function). Equation 5 can be rearranged to get an alternative definition for temperature in terms of entropy and heat (to avoid logic loop, we should first define statistical entropy, entropy through statistical mechanics): $T = \frac.$ For a system in which the entropy $S$ is a function $S\left(E\right)$ of its energy $E$, the thermodynamic temperature $T$ is therefore given by $\frac = \frac,$ so that the reciprocal of the thermodynamic temperature is the rate of increase of entropy with energy.

# History

1702–1703: Guillaume Amontons (1663–1705) published two papers that may be used to credit him as being the first researcher to deduce the existence of a fundamental (thermodynamic) temperature scale featuring an absolute zero. He made the discovery while endeavoring to improve upon the air thermometers in use at the time. His J-tube thermometers comprised a mercury column that was supported by a fixed mass of air entrapped within the sensing portion of the thermometer. In thermodynamic terms, his thermometers relied upon the volume / temperature relationship of gas under constant pressure. His measurements of the boiling point of water and the melting point of ice showed that regardless of the mass of air trapped inside his thermometers or the weight of mercury the air was supporting, the reduction in air volume at the ice point was always the same ratio. This observation led him to posit that a sufficient reduction in temperature would reduce the air volume to zero. In fact, his calculations projected that absolute zero was equivalent to −240 °C—only 33.15 degrees short of the true value of −273.15 °C. Amonton's discovery of a one-to-one relationship between absolute temperature and absolute pressure was rediscovered a century later and popularized within the scientific community by Joseph Louis Gay-Lussac. Today, this principle of thermodynamics is commonly known as ''
Gay-Lussac's law Gay-Lussac's law (also referred to as Amonton's law) states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas when the volume is kept constant. Mathematically, it can be written as: \frac = k. It is ...
'' but is also known as ''Amonton's law''. 1742: Anders Celsius (1701–1744) created a “backwards” version of the modern Celsius temperature scale. In Celsius's original scale, zero represented the boiling point of water and 100 represented the melting point of ice. In his paper ''Observations of two persistent degrees on a thermometer,'' he recounted his experiments showing that ice's melting point was effectively unaffected by pressure. He also determined with remarkable precision how water's boiling point varied as a function of atmospheric pressure. He proposed that zero on his temperature scale (water's boiling point) would be calibrated at the mean barometric pressure at mean sea level. 1744: Coincident with the death of Anders Celsius, the famous botanist Carl Linnaeus (1707–1778) effectively reversed Celsius's scale upon receipt of his first thermometer featuring a scale where zero represented the melting point of ice and 100 represented water's boiling point. The custom-made ''linnaeus-thermometer'', for use in his greenhouses, was made by Daniel Ekström, Sweden's leading maker of scientific instruments at the time. For the next 204 years, the scientific and thermometry communities worldwide referred to this scale as the ''centigrade scale''. Temperatures on the centigrade scale were often reported simply as ''degrees'' or, when greater specificity was desired, ''degrees centigrade''. The symbol for temperature values on this scale was °C (in several formats over the years). Because the term ''centigrade'' was also the French-language name for a unit of angular measurement (one-hundredth of a right angle) and had a similar connotation in other languages, the term "centesimal degree" was used when very precise, unambiguous language was required by international standards bodies such as the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation An intergovernmental organization (IGO) is an organization composed primarily of sovereign state ...
(''Bureau international des poids et mesures'') (BIPM). The 9th CGPM (General Conference on Weights and Measures (''Conférence générale des poids et mesures'') and the CIPM (International Committee for Weights and Measures (''Comité international des poids et mesures'') formally adoptedbipm.org
/ref> ''degree Celsius'' (symbol: °C) in 1948.According to ''The Oxford English Dictionary'' (OED), the term "Celsius's thermometer" had been used at least as early as 1797. Further, the term "The Celsius or Centigrade thermometer" was again used in reference to a particular type of thermometer at least as early as 1850. The OED also cites this 1928 reporting of a temperature: "My altitude was about 5,800 metres, the temperature was 28° Celsius". However, dictionaries seek to find the earliest use of a word or term and are not a useful resource as regards the terminology used throughout the history of science. According to several writings of Dr. Terry Quinn CBE FRS, Director of the BIPM (1988–2004), including ''Temperature Scales from the early days of thermometry to the 21st century''
150 kB PDF, here
as well as ''Temperature'' (2nd Edition / 1990 / Academic Press / 0125696817), the term ''Celsius'' in connection with the centigrade scale was not used whatsoever by the scientific or thermometry communities until after the CIPM and CGPM adopted the term in 1948. The BIPM wasn't even aware that ''degree Celsius'' was in sporadic, non-scientific use before that time. It's also noteworthy that the twelve-volume, 1933 edition of OED did not even have a listing for the word ''Celsius'' (but did have listings for both ''centigrade'' and ''centesimal'' in the context of temperature measurement). The 1948 adoption of ''Celsius'' accomplished three objectives: # All common temperature scales would have their units named after someone closely associated with them; namely, Kelvin, Celsius, Fahrenheit, Réaumur and Rankine. # Notwithstanding the important contribution of Linnaeus who gave the Celsius scale its modern form, Celsius's name was the obvious choice because it began with the letter C. Thus, the symbol °C that for centuries had been used in association with the name ''centigrade'' could continue to be used and would simultaneously inherit an intuitive association with the new name. # The new name eliminated the ambiguity of the term ''centigrade'', freeing it to refer exclusively to the French-language name for the unit of angular measurement.
1777: In his book ''Pyrometrie'' (Berlin

1779) completed four months before his death, Johann Heinrich Lambert (1728–1777), sometimes incorrectly referred to as Joseph Lambert, proposed an absolute temperature scale based on the pressure/temperature relationship of a fixed volume of gas. This is distinct from the volume/temperature relationship of gas under constant pressure that Guillaume Amontons discovered 75 years earlier. Lambert stated that absolute zero was the point where a simple straight-line extrapolation reached zero gas pressure and was equal to −270 °C. Circa 1787: Notwithstanding the work of Guillaume Amontons 85 years earlier, Jacques Charles, Jacques Alexandre César Charles (1746–1823) is often credited with discovering, but not publishing, that the volume of a gas under constant pressure is proportional to its absolute temperature. The formula he created was . 1802: Joseph Louis Gay-Lussac (1778–1850) published work (acknowledging the unpublished lab notes of Jacques Charles fifteen years earlier) describing how the volume of gas under constant pressure changes linearly with its absolute (thermodynamic) temperature. This behavior is called Charles's law, Charles's Law and is one of the
gas laws The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the ...
. His are the first known formulas to use the number ''273'' for the expansion coefficient of gas relative to the melting point of ice (indicating that absolute zero was equivalent to −273 °C). 1848: William Thomson, 1st Baron Kelvin, William Thomson, (1824–1907) also known as Lord Kelvin, wrote in his paper,
On an Absolute Thermometric Scale
'' of the need for a scale whereby ''infinite cold'' (absolute zero) was the scale's zero point, and which used the degree Celsius for its unit increment. Like Gay-Lussac, Thomson calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. This absolute scale is known today as the kelvin thermodynamic temperature scale. It's noteworthy that Thomson's value of ''−273'' was actually derived from 0.00366, which was the accepted expansion coefficient of gas per degree Celsius relative to the ice point. The inverse of −0.00366 expressed to five significant digits is −273.22 °C which is remarkably close to the true value of −273.15 °C. 1859: Macquorn Rankine (1820–1872) proposed a thermodynamic temperature scale similar to William Thomson's but which used the degree Fahrenheit for its unit increment. This absolute scale is known today as the rankine scale, Rankine thermodynamic temperature scale. 1877–1884: Ludwig Boltzmann (1844–1906) made major contributions to thermodynamics through an understanding of the role that particle kinetics and black body radiation played. His name is now attached to several of the formulas used today in thermodynamics. Circa 1930s: Gas thermometry experiments carefully calibrated to the melting point of ice and boiling point of water showed that absolute zero was equivalent to −273.15 °C. 1948:''
Resolution 3
of the 9th CGPM (Conférence Générale des Poids et Mesures, also known as the General Conference on Weights and Measures) fixed the triple point of water at precisely 0.01 °C. At this time, the triple point still had no formal definition for its equivalent kelvin value, which the resolution declared "will be fixed at a later date". The implication is that ''if'' the value of absolute zero measured in the 1930s was truly −273.15 °C, then the triple point of water (0.01 °C) was equivalent to 273.16 K. Additionally, both the CIPM (Comité international des poids et mesures, also known as the International Committee for Weights and Measures) and the CGP
the name ''Celsius'' for the ''degree Celsius'' and the ''Celsius temperature scale''.  1954:''
Resolution 3
of the 10th CGPM gave the kelvin scale its modern definition by choosing the triple point of water as its upper defining point (with no change to absolute zero being the null point) and assigning it a temperature of precisely 273.16 kelvins (what was actually written 273.16 ''degrees Kelvin'' at the time). This, in combination with Resolution 3 of the 9th CGPM, had the effect of defining absolute zero as being precisely zero kelvins and −273.15 °C. 1967/1968:''
Resolution 3
of the 13th CGPM renamed the unit increment of thermodynamic temperature ''kelvin'', symbol K, replacing ''degree absolute'', symbol °K. Further, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also decided i
Resolution 4
that "The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water". 2005: The CIPM (Comité International des Poids et Mesures, also known as the International Committee for Weights and Measures
affirmed
that for the purposes of delineating the temperature of the triple point of water, the definition of the kelvin thermodynamic temperature scale would refer to water having an isotopic composition defined as being precisely equal to the nominal specification of
Vienna Standard Mean Ocean Water Vienna Standard Mean Ocean Water (VSMOW) is an isotopic standard for water. Despite the name, VSMOW is pure water with no salt or other chemicals found in the oceans. The VSMOW standard was promulgated by the International Atomic Energy Agency ...
. 2019: In November 2018, the 26th General Conference on Weights and Measures (CGPM) changed the definition of the Kelvin by fixing the Boltzmann constant to when expressed in the unit J/K. 2019 redefinition of the SI base units, This change (and other changes in the definition of SI units) was made effective on the 144th anniversary of the Metre Convention, 20 May 2019.

* Absolute zero * Hagedorn temperature * Adiabatic process *
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality, Multiplication, multiplicatively connected to a Constant (mathematics), c ...
* Carnot heat engine * Energy conversion efficiency * Enthalpy * Entropy * Equipartition theorem * Fahrenheit * First law of thermodynamics * Freezing * Gas laws * International System of Quantities * International Temperature Scale of 1990, ITS-90 * Ideal gas law * Kelvin * Laws of thermodynamics *
Maxwell–Boltzmann distribution In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
* Orders of magnitude (temperature) * Phase transition * Planck's law of black body radiation, Planck's law of black-body radiation *
Rankine scale __NOTOC__ The Rankine scale () is an absolute scale An absolute scale is a system of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or ...
* Specific heat capacity * Standard enthalpy change of fusion * Standard enthalpy change of vaporization * Temperature * Temperature conversion formulas *
Thermal radiation Thermal radiation is electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space an ...
* Thermodynamic beta * Thermodynamic equations * Thermodynamic equilibrium * Thermodynamics * :Thermodynamics, Thermodynamics Category (list of articles) * Timeline of heat engine technology * Timeline of temperature and pressure measurement technology * Triple point

# Notes

: ''In the following notes, wherever numeric equalities are shown in ''concise form'', such as , the two digits between the parentheses denotes the uncertainty at 1-σ (1 standard deviation, 68% confidence level) in the two least significant digits of the significand.''