(for information in Kelvin) (for information in degrees Celsius)
The temperature is a state variable of central importance in the macroscopic description of physical and chemical states and processes in science , technology and the environment . Temperature is an objective measure of how warm or cold an object is. It is measured with a thermometer . Your SI unit is the Kelvin with the unit symbol K. In Germany, Austria and Switzerland the unit degree Celsius (° C) is also permitted. The measured temperature can sometimes differ significantly from the perceived temperature .
If you bring two bodies with different temperatures into thermal contact, heat transfer takes place. As a result, the temperature difference decreases until the two temperatures have equalized. The heat always flows from the hotter to the colder body. When the temperatures are the same, there is thermal equilibrium in which there is no longer any heat exchange.
The microscopic interpretation of temperature results from statistical physics , which assumes that every material substance is composed of many particles (mostly atoms or molecules ) that are in constant disorderly motion and have an energy that is kinetic , potential and possibly also internal excitation energy . An increase in temperature causes an increase in the average energy of the particles. In the state of thermal equilibrium, the energy values of the individual particles are statistically distributed according to a frequency distribution, the shape of which is determined by the temperature (see - depending on the type of particle - Boltzmann statistics , Fermi-Dirac statistics , Bose-Einstein statistics ). This picture can also be used when it is not a question of a system of material particles, but of photons (see thermal radiation ).
In the ideal gas the entire energy of each particle is given by its kinetic energy alone . Their mean value has been taken since 2019 through an agreement in the International System of Units for the quantitative definition of absolute temperature . Since then, the temperature unit Kelvin has been linked to the energy unit Joule and is no longer defined by a certain property of the substance water as it was until 2019.
The temperature is an intense state variable . This means that it retains its value when one shares the body under consideration. On the other hand, the internal energy as an extensive quantity has the properties of a quantity that can be divided.
All solid substances , liquids and gases consist of very small particles, the atoms and molecules. These are in constant disorderly movement and forces act between them. In this context, “disordered” means that z. B. the velocity vectors of the particles of a body, based on the velocity of its center of mass , are evenly distributed over all directions and also differ in their amounts . The mean value of the velocities depends on the type of substance, the physical state and, above all, the temperature. The following applies to solid, liquid and gaseous bodies: the higher the temperature of a body, the greater the average speed of its particles. In general, this also applies to all other forms in which the particles can have energy in a disordered manner, e.g. B. rotational movements, vibrations (this also includes lattice vibrations around their rest position in the crystal lattice of the solid body). This clear connection already suggests that there is a lowest possible temperature, the absolute zero point , at which the smallest particles no longer move. Due to the uncertainty relation , however, complete immobility is not possible ( zero point energy ).
A certain temperature, which applies uniformly throughout the system, only exists when the system is in a state of thermal equilibrium . Systems that are not in equilibrium often consist of sub-systems, each with its own temperature, e.g. B. tap water and ice cubes in a glass, or the electrons and ions in a non-equilibrium plasma , or the degrees of freedom for translation, rotation or vibration in an expanding molecular beam. If there is thermal contact between the sub-systems, then the overall system naturally tends to achieve thermal equilibrium through heat exchange between the parts.
From a theoretical point of view, the temperature is introduced as a fundamental term by the fact that any two systems that are in thermal equilibrium with a third system are then also in thermal equilibrium with one another. This fact is also called the zeroth law of thermodynamics. Equality of temperatures means thermal equilibrium, i.e. That is, there is no heat exchange even with thermal contact. The fact that a single state variable such as temperature is sufficient to decide whether equilibrium exists can be derived from the zeroth law.
The sum of all energies of the disordered movements of the particles of a system and their internal potential and kinetic energies represents a certain energy content, which is called the internal energy of the system. The internal energy can partly be converted into an orderly movement by means of a heat engine and then work when a second system with a lower temperature is available. Because only part of the internal energy can be used for conversion into work, while the rest has to be given off as waste heat to the second system. According to the second law of thermodynamics, there is a lower limit for this waste heat which is independent of the substances and types of processes used and which is only determined by the ratio of the two temperatures. This was noticed by Lord Kelvin in 1848 and used to define thermodynamic temperature since 1924 . The same result can be obtained if the state variable entropy is derived from the internal energy.
Almost all physical and chemical properties of substances are (at least slightly) dependent on temperature. Examples are the thermal expansion of substances, the electrical resistance , the solubility of substances in solvents, the speed of sound or the pressure and density of gases. In contrast, sudden changes in material properties occur even with the smallest changes in temperature, when the state of aggregation changes or another phase transition occurs.
The temperature also influences the reaction speed of chemical processes, as it typically doubles for every 10 ° C increase in temperature ( van-'t-Hoff rule ). This also applies to the metabolic processes of living things.
The ideal gas is a model gas that is well suited to developing the fundamentals of thermodynamics and properties of temperature. According to the model, the particles of the gas are point-like, but can still collide elastically against each other and against the vessel wall. Otherwise there is no interaction between the particles. The ideal gas reproduces the behavior of the monatomic noble gases very well, but also applies to a good approximation for normal air, although polyatomic molecules can rotate or vibrate and therefore cannot always be simplified as point-like objects without internal degrees of freedom.
For the ideal gas, the temperature is proportional to the mean kinetic energy of the particles
where is the Boltzmann constant . In this case, the macroscopic variable temperature is linked in a very simple way to microscopic particle properties. Multiplied by the number of particles , you get the total energy of the gas. In addition, the thermal equation of state applies to the ideal gas , which links the macroscopic quantities temperature, volume and pressure ,
This equation was made in 2019 in the International System of Units for the definition of temperature, because with the simultaneous numerical determination of the value of the Boltzmann constant, apart from T, it only contains measurable quantities. The measurement specification takes into account that this equation is only approximately fulfilled for a real gas , but it applies exactly in borderline cases .
Since the quantities cannot become negative, one can see from these equations that there must be an absolute temperature zero at which the gas particles would no longer move and the pressure or volume of the gas would be zero. Absolute zero of the temperature really does exist, although this derivation is not reliable because there is no substance that remains until it is gaseous. At least helium is an almost ideal gas under atmospheric pressure even at temperatures of a few K.
Temperature, heat and thermal energy
Sometimes the variables temperature, heat and thermal energy are confused with one another. However, they are different sizes. The temperature and the thermal energy describe the state of a system, the temperature being an intensive quantity, but the thermal energy (which can have different meanings) often an extensive quantity. With ideal gases, the temperature is a direct measure of the mean value of the kinetic energy of the particles. The thermal energy in its macroscopic meaning is equal to the internal energy , i.e. the sum of all kinetic, potential and excitation energies of the particles.
Heat, on the other hand, as a physical term does not characterize a single system state, but a process that leads from one system state to another. Heat is the resulting change in internal energy minus any work that may have been done (see first law of thermodynamics ). Conversely, assuming a certain amount of heat emitted or absorbed, the process can lead to different end states with different temperatures depending on the process control (e.g. isobaric , isochoric or isothermal ).
If two systems with different temperatures are in a connection that enables heat transfer ( thermal contact or diabatic connection ), then heat flows from the hotter to the colder system and both temperatures approach the same equilibrium temperature . If there are no phase transitions or chemical reactions , it is between the initial temperatures. is then a weighted mean of and , with the heat capacities of the two systems (provided that they are sufficiently constant) act as weighting factors. The same end result occurs when two liquids or two gases are mixed together ( mixing temperature ), e.g. B. hot and cold water. If phase transitions occur, the equilibrium temperature can also be one of the two initial temperatures, e.g. B. 0 ° C when cooling a warm drink with unnecessarily many ice cubes of 0 ° C. In the case of chemical reactions, the final temperature can also be outside the range , e.g. B. with cold mixtures below, with combustion above.
Temperature in relativity
A thermodynamic equilibrium initially applies in the common rest system of both bodies. In terms of the special theory of relativity, a system in thermodynamic equilibrium is characterized not only by temperature but also by a system of rest. Thermodynamic equations are not invariant under Lorentz transformations. A specific question would be: B. what temperature is measured by a moving observer. The redshift of the thermal radiation, for example, shifts the frequencies in Planck's law of radiation in proportion and thus makes a radiating body appear colder if you move away from it at speed . In principle, the same problem occurs when hot water flows through an initially cold pipe.
The temperature is represented as a time-like four-vector. The three position coordinates are in the system of rest and the time coordinate is the usual temperature. For a moving system one has to convert using the Lorentz transformation. In the context of the equations of state, however, it is more favorable and therefore more common to represent the inverse temperature, more precisely , as a time-like four-vector vector.
To justify this, consider the 1st law, the one for reversible processes in the form
and note that the energy of a moving system is greater by the kinetic energy than its internal energy , i.e. approximately
where is the three-dimensional velocity. thats why
in 4-dimensional notation the same
if (with the spatial momentum vector ) is the quad momentum and the inverse quad temperature.
In general relativity, spacetime is curved, so that in general the thermodynamic limit is not well defined. If the space-time metric is independent of time, i.e. static, a global temperature term can be defined. In the general case of a time-dependent metric, such as that which is the basis of the description of the expanding universe, state variables such as temperature can only be defined locally. A common criterion for a system to be at least locally thermal is that the phase space density satisfies the Boltzmann equation without scattering.
Temperature in quantum physics
In the field of quantum physics, the temperature can only be described with a disordered particle movement, in which all possible forms of energy occur, if it is “sufficiently high”. “Sufficiently high” means that the energy is large compared to the typical distances between the energy levels of the individual particles in the given system. For example, the temperature must be well above 1000 K so that the molecular vibrations are also excited in diatomic gases such as N 2 , O 2 . In the case of H 2 molecules, the excitation of the rotation also requires temperatures above a few 100 K. Degrees of freedom that do not participate in the heat movement at lower temperatures are referred to as frozen . That expresses itself z. B. clearly in the temperature dependence of the specific heat .
The theoretical treatment of thermodynamics in quantum physics takes place exclusively with the methods of statistical physics (see quantum statistics , many-body theory ). Here, the temperature appears in the exponent of the Boltzmann distribution, just like in classical statistical physics, and thus determines the form of the frequency distribution with which the particles assume the various energy states.
Temperature sensation and heat transfer
There are two bodies of different temperature in thermal contact, so, after the zeroth law of thermodynamics as long as energy transferred from the warmer to the colder body until both have the same temperature assumed, and thus in thermal equilibrium are. There may initially be temperature jumps between the two sides of the interface . There are three ways of heat transfer :
Humans can only feel temperatures in the range between about 5 ° C and 40 ° C with their skin. Strictly speaking, it is not the temperature of a touched object that is perceived, but the temperature at the location of the thermoreceptors in the skin , which varies depending on the strength of the heat flow through the skin surface ( perceived temperature ). This has several consequences for the temperature perception:
- Temperatures above the surface temperature of the skin feel warm, while those below we perceive as cold
- Materials with high thermal conductivity , such as metals, lead to higher heat flows and therefore feel warmer or colder than materials with lower thermal conductivity, such as wood or polystyrene
- The perceived air temperature is lower when there is wind than when there is no wind (vice versa in extremely hot weather). The effect is described by the wind chill at temperatures <10 ° C and by the heat index at higher temperatures .
- A slightly heated, tiled floor can be perceived as pleasantly warm with bare feet, but touched with the hands as cool. This is the case when the skin temperature on the hands is higher than that on the feet and the temperature of the floor is in between.
- The sensation of the skin can not distinguish between air temperature and superimposed thermal radiation . The same is generally true of thermometers; therefore z. B. Air temperatures are always measured in the shade
- Lukewarm water is perceived as different by the two hands if you have held them in hot or cold water for a while.
Strictly speaking, this does not only apply to human feelings. Also in many technical contexts, it is not the temperature that is decisive, but the heat flow. For example, in an area above 1000 km, the earth's atmosphere has temperatures of more than 1000 ° C; Nevertheless, no satellites burn up there, because the energy transfer is minimal due to the low particle density.
Definitions of temperature
When the ideal gas z. B. the gas temperature defined by the equation of state fulfills this condition.
According to Boltzmann, the statistical interpretation of entropy is :
and therefore that of temperature:
- the entropy
- the inner energy
- the smoothed, averaged curve over , which indicates how many possibilities the energy U can be distributed in the system; broken down into the smallest possible energy packages (see Quant ).
- the Boltzmann constant
The same physical quantity results when the most probable distribution of the particles of a (classical) system is determined over the various possible energies of all possible states of an individual particle. The states for a given energy have a probability W which is proportional to the Boltzmann factor .
From this Boltzmann distribution it follows u. a. the Maxwell-Boltzmann distribution of the molecular velocities in a gas as well as the uniform distribution law of the energy over all degrees of freedom of the particles.
The term temperature can be expanded so that negative temperatures can also be defined.
A system that appears macroscopically in thermal equilibrium, i.e. has a uniform temperature, consists microscopically of particles that do not all have the same energy. In fact, these particles constantly exchange energy with each other through collisions, so that they are distributed to states with different energies ( Boltzmann statistics ) and z. B. sets a Maxwell speed distribution . As already described at the beginning, the temperature measures the energy averaged over all particles. This distribution is not uniform, but accumulates (at positive temperatures) at low energies, while only a few particles have a lot of energy. As the energies increase, there is an exponential decrease in frequency. If the temperature is increased, the different frequencies become more and more similar; in the hypothetical limit case of infinite temperature, the same number of particles would be in every energy state.
The extension of the concept of temperature now assumes that the energy distribution of the particles is changed in such a way that the higher energy classes can be more heavily occupied than the lower ones (population reversal, inversion). This would be formally expressed as negative temperature in the equation of the Boltzmann statistics.
In the meantime it has been possible to produce corresponding gases with negative temperatures under laboratory conditions. The population inversion in the active medium of a laser can also be understood as a state of negative temperature.
However, the state of negative temperature is unstable. The energy from such a system would flow off on contact with a body of any positive temperature. In this respect one has to say that a body with a negative temperature is hotter than any body with a positive temperature.
Measurement by thermal contact
The temperature is measured with the help of thermometers or temperature sensors . Establishing thermal contact requires sufficient heat conduction , convection or a radiation equilibrium between the measurement object (solid, liquid, gas) and the sensor. The measurement accuracy can e.g. B. be affected by unbalanced thermal radiation balance, air movements or heat dissipation along the sensor. Theoretically, the measurement accuracy is limited by the random Brownian molecular motion .
Temperature detection through thermal contact can be divided into four methods:
- mechanical detection by using the different thermal expansion coefficients of materials by means of
- Measuring electrical quantities
- Use of temperature-dependent electrical resistance of conductors and semiconductors : PTC (PTC) and thermistor (NTC), see also RTD
- Thermocouples supply voltages that depend on temperature differences.
- Special semiconductor circuits use the band gap to generate a voltage proportional to the absolute temperature, see band gap reference .
- Time or frequency measurement
- The temperature-dependent difference frequency of differently cut quartz crystals is long-term stable and can be measured with high resolution.
- The temperature-dependent decay rate of the fluorescence of a phosphor can be measured via an optical fiber.
- The fiber optic temperature measurement uses the Raman effect in fiber optics for spatially resolved measurement of the absolute temperature over the entire length of the fiber.
- indirect measurement via temperature-dependent changes in the state of materials
Measurement based on thermal radiation
The temperature of a surface can be determined without contact by measuring the thermal radiation , provided that the emissivity is known with sufficient accuracy. The measurement takes place z. B. with a pyrometer or with a thermography camera.
Depending on the temperature, different wavelength ranges come into question (see Stefan-Boltzmann's law or Wien's law of displacement ). At low temperatures, bolometers , microbolometers or cooled semiconductor detectors can be used; at high temperatures, uncooled photodiodes or a visual comparison of the intensity and color of the glow are used ( tungsten filament pyrometer , glow colors ).
A thermography can be seen on the right; a false color representation of the radiation emission in the middle infrared (approx. 5 ... 10 µm wavelength) is generated, which can be linked to the temperature scale by calibration in the form of a color scale. The reflection of the radiation from the hot mug can be seen on the left in the picture.
As with pyrometers, measurement errors result from this
- different or unknown emissivities of the measuring objects
- Reflections of extraneous radiation on smooth surfaces
- Radiation of the air between the object and the sensor
If all disturbing influences are minimized, measuring accuracies and contrasts down to temperature differences of 0.01 K are possible.
The non-contact temperature measurement based on thermal radiation is also used for remote sensing and to determine the surface temperature of stars , provided that the natural radiation of the air envelope is low enough. IR telescopes are therefore only useful on high mountains.
Temperature scales and their units
An empirical temperature scale is an arbitrary determination of the magnitude of the temperature and allows the temperature to be specified in relation to a reference value.
There are two methods of defining a scale:
According to the first method, two fixed points are established. These fixed points are appropriately naturally occurring values that can be reproduced through experiments. The distance between the fixed points is then evenly divided based on a temperature-dependent material or process property. A. Celsius , for example, chose the melting point and the boiling point of water as fixed points for his scale and divided the change in volume of mercury between these points into 100 equal parts. DG Fahrenheit , on the other hand, chose the temperature of a cold mixture and the human body temperature as fixed points. An example of a process property is e.g. B. the change in angle of the pointer in a bimetal thermometer .
With the second method, a fixed point is sufficient, which, as before, is defined by a material property (e.g. melting point of the ice) and an additional temperature-dependent material property. One could e.g. B. define a certain relative change in volume of mercury as "one degree" and then, starting from the fixed point, mark scale mark by scale mark.
Rudolf Plank had an idea for a scale based on the second method . It is based on the change in volume of gases at constant pressure. The melting point of water is again used as the fixed point; the unit is the temperature difference, which corresponds to a change in volume by the factor (1 + 1 / 273.15). Such a logarithmic temperature scale extends from minus infinity to plus infinity. Absolute zero is not required, which by definition cannot be reached.
The most popular temperature scales with their various characteristics are shown in the table below. The temperature scale valid today is the "International Temperature Scale of 1990" ( ITS-90 ). The definition of the units via certain specific measuring points was lifted in May 2019, see table.
Scales with SI units
The thermodynamic definition of temperature with the help of the 2nd law has been in effect since 1924 , which determines the ratio of two temperatures from the ratio of two energies. The existence of such an absolute and substance-independent temperature scale follows from the efficiency of the Carnot process . The following applies to the efficiency of any heat engine that works between two heat reservoirs with the temperatures and periodically and reversibly:
The zero point of the scale is at absolute zero , but the temperature unit ( ) is still open. Their size was initially determined by choosing a numerical value (273.16) for the temperature of a well-defined state of water ( triple point ). Since May 2019, the temperature unit, now again with recourse to the equation of state of the ideal gas, has been connected to the joule energy unit through the numerical definition of the Boltzmann constant : 1 K is the temperature change that increases the energy by 1 .380 649e-23 Jincreased.
After that, the triple point of water no longer has a defining meaning, but is a measured value to be determined.
The Celsius temperature (symbol or ) are by their modern definition no longer the empirical temperature of the historic Celsius scale, but rather is the thermodynamic temperature of the Kelvin scale shifted by 273.15 K:
The unit degree Celsius (° C) is a derived SI unit . For temperature differences, the degree Celsius is identical to the Kelvin. Temperature differences should generally be given in K, whereby the difference between two Celsius temperatures can also be given in ° C. The numerical value is the same in both cases.
Scales without SI unit
In the USA the Fahrenheit scale with the unit degree Fahrenheit (unit symbol: ° F) is still very common. The absolute temperature based on Fahrenheit is denoted by degrees Rankine (unit symbol: ° Ra). The Rankine scale has the zero point like the Kelvin scale at absolute temperature zero, in contrast to this, however, the scale intervals of the Fahrenheit scale. Today, both scales are defined using a kelvin conversion formula that is exact by definition.
|unit||Unit symbol||lower anchor point F 1||upper anchor point F 2||Unit value||inventor||Year of creation||Distribution area|
Absolute zero point ,
T 0 = 0 K
|Now without a fixed point,
originally later T Tri ( H 2 O ) = 273.16 K
|William Thomson Baron Kelvin||1848||worldwide
( SI unit )
|centigrade||° C||Now 0 ° C = 273.15 K,
previously T Schm (H 2 O) = 0 ° C
|Now coupling to Kelvin,
previously T boiling (H 2 O) = 100 ° C
|Different Celsius||1742||worldwide ( derived SI unit )|
|degrees Fahrenheit||° F||Now 32 ° F = 273.15 K,
originally T cold. = 0 ° F,
later T Schm (H 2 O) = 32 ° F
|Now coupling to Kelvin,
originally T human = 96 ° F,
later T boiling (H 2 O) = 212 ° F
|Daniel Fahrenheit||1714||United States|
|Rankine degree||° Ra, ° R||T 0 = 0 ° Ra||Now coupling to Kelvin||William Rankine||1859||United States|
|Degree Delisle||° De, ° D||T Schm (H 2 O) = 150 ° De||T boiling (H 2 O) = 0 ° De||Joseph-Nicolas Delisle||1732||Russia (19th century)|
|Degree Réaumur||° Ré, ° Re, ° R||T Schm (H 2 O) = 0 ° Ré||T boiling (H 2 O) = 80 ° Ré||René-Antoine Ferchault de Réaumur||1730||Western Europe until the end of the 19th century|
|Degrees Newtons||° N||T Schm (H 2 O) = 0 ° N||T boiling (H 2 O) = 33 ° N||Isaac Newton||≈ 1700||none|
|Degree Rømer||° Rø||T Schm ( Lake ) = 0 ° Rø||T boiling (H 2 O) = 60 ° Rø||Ole Romer||1701||none|
Notes on the table:
|→ from →||
|↓ to ↓|
|T Kelvin||=||T K||T C + 273.15||(T F + 459.67) 5 ⁄ 9||T Ra · 5 / 9|
|T Celsius||=||T K - 273.15||T C||(T F - 32) 5 ⁄ 9||T Ra · 5 / 9 - 273.15|
|T Fahrenheit||=||T K * 1.8 - 459.67||T C * 1.8 + 32||T F||T Ra - 459.67|
|T Rankine||=||T K * 1.8||T C * 1.8 + 491.67||T F + 459.67||T Ra|
|T Réaumur||=||(T K - 273.15) x 0.8||T C x 0.8||(T F - 32) 4 ⁄ 9||T Ra · 4 / 9 - 218.52|
|T Rømer||=||(T K - 273.15) 21 ⁄ 40 + 7.5||T C · 21 / 40 + 7.5||(T F - 32) 7 ⁄ 24 + 7.5||(T Ra - 491.67) 7 ⁄ 24 + 7.5|
|T Delisle||=||(373.15 - T K ) x 1.5||(100 - T C ) x 1.5||(212 - T F ) 5 ⁄ 6||(671.67 - T Ra ) 5 ⁄ 6|
|T Newtons||=||(T K - 273.15) x 0.33||T C x 0.33||(T F - 32) 11 ⁄ 60||(T Ra - 491.67) 11 ⁄ 60|
|→ from →||Degree Réaumur
|↓ to ↓|
|T Kelvin||=||T Ré 1.25 + 273.15||(T Rø - 7.5) 40 ⁄ 21 + 273.15||373.15 - T De · 2 / 3||T N · 100 / 33 + 273.15|
|T Celsius||=||T Ré 1.25||(T Rø - 7.5) 40 ⁄ 21||100 - T De · 2 / 3||T N · 100 / 33|
|T Fahrenheit||=||T Ré · 2.25 + 32||(T Rø - 7.5) 24 ⁄ 7 + 32||212 - T De 1.2||T N · 60 / 11 + 32|
|T Rankine||=||T Ré · 2.25 + 491.67||(T Rø - 7.5) 24 ⁄ 7 + 491.67||671.67 - T De * 1.2||T N · 60 ⁄ 11 + 491.67|
|T Réaumur||=||T Ré||(T Rø - 7.5) 32 ⁄ 21||80 - T De · 8 / 15||T N · 80 / 33|
|T Rømer||=||T Re · 21 / 32 + 7.5||T Rø||60 - T De 0.35||T N · 35 / 22 + 7.5|
|T Delisle||=||(80 - T Ré ) · 1.875||(60 - T Rø ) 20 ⁄ 7||T De||(33 - T N ) 50 ⁄ 11|
|T Newtons||=||T Re · 33 / 80||(T Rø - 7.5) 22 ⁄ 35||33 - T De · 0.22||T N|
|Kelvin||° Celsius||° Fahrenheit||° Rankine||° Réaumur|
|Boiling point of water at normal pressure||373.150K||100,000 ° C||212,000 ° F||671.670 ° Ra||80,000 ° Ré|
|" Human body temperature " according to Fahrenheit||308.70 5 K||35, 555 ° C||96,000 ° F||555.670 ° Ra||28, 444 ° Ré|
|Triple point of water||273.160K||0.010 ° C||32.018 ° F||491.688 ° Ra||0.008 ° Ré|
|Freezing point of water at normal pressure||273.150K||0.000 ° C||32,000 ° F||491.670 ° Ra||0.000 ° Ré|
|Cold mixture of water, ice and NH 4 Cl||255.37 2 K||−17, 777 ° C||0.000 ° F||459.670 ° Ra||−14, 222 ° Ré|
|absolute zero||0 K||−273.150 ° C||−459.670 ° F||0 ° Ra||−218.520 ° Ré|
The fixed points with which the scales were originally defined are highlighted in color and converted exactly into the other scales. Today they have lost their role as fixed points and are only approximate. Only the absolute zero point still has exactly the specified values. For temperature examples see order of magnitude (temperature) .
- Max Born: Critical remarks on the traditional representation of thermodynamics . In: Physikalische Zeitschrift . tape 22 , 1921, pp. 218-224 .
- Bošnjaković, Knoche, "Technical Thermodynamics", 8th edition 1998, Steinkopf-Verlag Darmstadt, ISBN 978-3-642-63818-3 ; Section 9.9 "Extension of the temperature concept".
- Klaus Goeke, "Statistics and Thermodynamics", 1st edition 2010, Vieweg + Teubner Verlag / Springer Fachmedien Wiesbaden GmbH 2010, ISBN 978-3-8348-0942-1 ; Section 2.6.9 “Positive and negative temperatures”.
- S. Brown, JP Ronzheimer, M. Schreiber, SS Hodgman, T. Rome, I. Bloch, U. Schneider: Negative Absolute Temperature for Motional Degrees of Freedom . In: Science . tape 339 , no. 6115 , January 4, 2013, ISSN 0036-8075 , p. 52-55 , doi : 10.1126 / science.1227831 .
- See article in Spektrum der Wissenschaft 3/2013, , "Colder than cold and hotter than infinitely hot" by Olliver Morsch on the results of Bloch / Schneider from the Max Planck Institute for Quantum Optics in Garching and the Ludwig Maximilians -University of Munich.
- Le système international d'unités  . 9e édition, 2019 (the so-called "SI brochure", French and English), pp. 21 and 133.
- DIN 1301-1: 2010 units - unit names, unit symbols
- DIN 1345: 1993 Thermodynamics - Basic Terms .
- NIST , SI Units - Temperature, version dated June 5, 2019.