Temperature is a physical quantity expressing hot and cold. It is measured with a thermometer calibrated in one or more temperature scales. The most commonly used scales are the Celsius scale (formerly called centigrade) (denoted °C), Fahrenheit scale (denoted °F), and Kelvin scale (denoted K). The kelvin (the word is spelled with a lower-case k) is the unit of temperature in the International System of Units (SI), in which temperature is one of the seven fundamental base quantities. The Kelvin scale is widely used in science and technology.

Theoretically, the coldest a system can be is when its temperature is absolute zero, at which point the thermal motion in matter would be zero. However, an actual physical system or object can never attain a temperature of absolute zero. Absolute zero is denoted as 0 K on the Kelvin scale, −273.15 °C on the Celsius scale, and −459.67 °F on the Fahrenheit scale.

For an ideal gas, temperature is proportional to the average kinetic energy of the random microscopic motions of the constituent microscopic particles.

Temperature is important in all fields of natural science, including physics, chemistry, Earth science, medicine, and biology, as well as most aspects of daily life.[1]

Annual Average Temperature Map
Annual mean temperature around the world
Common symbols
SI unitkelvin (K)
Other units
°C, °F, °R
Derivations from
other quantities
Thermally Agitated Molecule
Thermal vibration of a segment of protein alpha helix: The amplitude of the vibrations increases with temperature.
Body Temp Variation
Average daily variation in human body temperature


Many physical processes are affected by temperature, such as


Temperature scales differ in two ways: the point chosen as zero degrees, and the magnitudes of incremental units or degrees on the scale.

The Celsius scale (°C) is used for common temperature measurements in most of the world. It is an empirical scale that was developed by a historical progress, which led to its zero point 0 °C being defined by the freezing point of water, and additional degrees defined so that 100 °C was the boiling point of water, both at sea-level atmospheric pressure. Because of the 100-degree interval, it was called a centigrade scale.[4] Since the standardization of the kelvin in the International System of Units, it has subsequently been redefined in terms of the equivalent fixing points on the Kelvin scale, and so that a temperature increment of one degree Celsius is the same as an increment of one kelvin, though they differ by an additive offset of 273.15.

The United States commonly uses the Fahrenheit scale, on which water freezes at 32 °F and boils at 212 °F at sea-level atmospheric pressure.

Many scientific measurements use the Kelvin temperature scale (unit symbol: K), named in honor of the Scots-Irish physicist who first defined it. It is a thermodynamic or absolute temperature scale. Its zero point, 0 K, is defined to coincide with the coldest physically-possible temperature (called absolute zero). Its degrees are defined through thermodynamics. The temperature of absolute zero occurs at 0 K = −273.15 °C (or −459.67 °F), and the freezing point of water at sea-level atmospheric pressure occurs at 273.15 K = 0 °C.

The International System of Units (SI) defines a scale and unit for the kelvin or thermodynamic temperature by using the reliably reproducible temperature of the triple point of water as a second reference point (the first reference point being 0 K at absolute zero). The triple point is a singular state with its own unique and invariant temperature and pressure, along with, for a fixed mass of water in a vessel of fixed volume, an autonomically and stably self-determining partition into three mutually contacting phases, vapour, liquid, and solid, dynamically depending only on the total internal energy of the mass of water. For historical reasons, the triple point temperature of water is fixed at 273.16 units of the measurement increment.


There is a variety of kinds of temperature scale. It may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in the middle of the nineteenth century.[5][6]


Empirically based temperature scales rely directly on measurements of simple physical properties of materials. For example, the length of a column of mercury, confined in a glass-walled capillary tube, is dependent largely on temperature, and is the basis of the very useful mercury-in-glass thermometer. Such scales are valid only within convenient ranges of temperature. For example, above the boiling point of mercury, a mercury-in-glass thermometer is impracticable. Most materials expand with temperature increase, but some materials, such as water, contract with temperature increase over some specific range, and then they are hardly useful as thermometric materials. A material is of no use as a thermometer near one of its phase-change temperatures, for example its boiling-point.

In spite of these restrictions, most generally used practical thermometers are of the empirically based kind. Especially, it was used for calorimetry, which contributed greatly to the discovery of thermodynamics. Nevertheless, empirical thermometry has serious drawbacks when judged as a basis for theoretical physics. Empirically based thermometers, beyond their base as simple direct measurements of ordinary physical properties of thermometric materials, can be re-calibrated, by use of theoretical physical reasoning, and this can extend their range of adequacy.


Theoretically-based temperature scales are based directly on theoretical arguments, especially those of thermodynamics, kinetic theory and quantum mechanics. They rely on theoretical properties of idealized devices and materials. They are more or less comparable with practically feasible physical devices and materials. Theoretically based temperature scales are used to provide calibrating standards for practical empirically based thermometers.

The accepted fundamental thermodynamic temperature scale is the Kelvin scale, based on an ideal cyclic process envisaged for a Carnot heat engine.

An ideal material on which a temperature scale can be based is the ideal gas. The pressure exerted by a fixed volume and mass of an ideal gas is directly proportional to its temperature. Some natural gases show so nearly ideal properties over suitable temperature ranges that they can be used for thermometry; this was important during the development of thermodynamics and is still of practical importance today.[7][8] The ideal gas thermometer is, however, not theoretically perfect for thermodynamics. This is because the entropy of an ideal gas at its absolute zero of temperature is not a positive semi-definite quantity, which puts the gas in violation of the third law of thermodynamics. The physical reason is that the ideal gas law, exactly read, refers to the limit of infinitely high temperature and zero pressure.[9][10][11]

Measurement of the spectrum of electromagnetic radiation from an ideal three-dimensional black body can provide an accurate temperature measurement because the frequency of maximum spectral radiance of black-body radiation is directly proportional to the temperature of the black body; this is known as Wien's displacement law and has a theoretical explanation in Planck's law and the Bose–Einstein law.

Measurement of the spectrum of noise-power produced by an electrical resistor can also provide an accurate temperature measurement. The resistor has two terminals and is in effect a one-dimensional body. The Bose-Einstein law for this case indicates that the noise-power is directly proportional to the temperature of the resistor and to the value of its resistance and to the noise band-width. In a given frequency band, the noise-power has equal contributions from every frequency and is called Johnson noise. If the value of the resistance is known then the temperature can be found.[12][13]

If molecules, or atoms, or electrons,[14][15] are emitted from a material and their velocities are measured, the spectrum of their velocities often nearly obeys a theoretical law called the Maxwell–Boltzmann distribution, which gives a well-founded measurement of temperatures for which the law holds.[16] There have not yet been successful experiments of this same kind that directly use the Fermi–Dirac distribution for thermometry, but perhaps that will be achieved in future.[17]

Thermodynamic approach

Temperature is one of the principal quantities in the study of thermodynamics.

Kelvin scale and absolute thermodynamic definitions

The Kelvin scale is called absolute for two reasons. One is that its formal character is independent of the properties of particular materials. The other reason is that its zero is in a sense absolute, in that it indicates absence of microscopic classical motion of the constituent particles of matter, so that they have a limiting specific heat of zero for zero temperature, according to the third law of thermodynamics. Nevertheless, a Kelvin temperature does in fact have a definite numerical value that has been arbitrarily chosen by tradition and is dependent on the property of a particular materials; it is simply less arbitrary than relative "degrees" scales such as Celsius and Fahrenheit. Being an absolute scale with one fixed point (zero), there is only one degree of freedom left to arbitrary choice, rather than two as in relative scales. For the Kelvin scale in modern times, this choice of convention is made to be that of setting the gas–liquid–solid triple point of water, a point which can be reliably reproduced as a standard experimental phenomenon, at a numerical value of 273.16 kelvins. The Kelvin scale is also called the thermodynamic scale. However, to demonstrate that its numerical value is indeed arbitrary, it is useful to point out that an alternate, less widely used absolute temperature scale exists called the Rankine scale, made to be aligned with the Fahrenheit scale as Kelvin is with Celsius.

The thermodynamic definition of temperature is due to Kelvin.

It is framed in terms of an idealized device called a Carnot engine, imagined to define a continuous cycle of states of its working body. The cycle is imagined to run so slowly that at each point of the cycle the working body is in a state of thermodynamic equilibrium. There are four limbs in such a Carnot cycle. The engine consists of four bodies. The main one is called the working body. Two of them are called heat reservoirs, so large that their respective non-deformation variables are not changed by transfer of energy as heat through a wall permeable only to heat to the working body. The fourth body is able to exchange energy with the working body only through adiabatic work; it may be called the work reservoir. The substances and states of the two heat reservoirs should be chosen so that they are not in thermal equilibrium with one another. This means that they must be at different fixed temperatures, one, labeled here with the number 1, hotter than the other, labeled here with the number 2. This can be tested by connecting the heat reservoirs successively to an auxiliary empirical thermometric body that starts each time at a convenient fixed intermediate temperature. The thermometric body should be composed of a material that has a strictly monotonic relation between its chosen empirical thermometric variable and the amount of adiabatic isochoric work done on it. In order to settle the structure and sense of operation of the Carnot cycle, it is convenient to use such a material also for the working body; because most materials are of this kind, this is hardly a restriction of the generality of this definition. The Carnot cycle is considered to start from an initial condition of the working body that was reached by the completion of a reversible adiabatic compression. From there, the working body is initially connected by a wall permeable only to heat to the heat reservoir number 1, so that during the first limb of the cycle it expands and does work on the work reservoir. The second limb of the cycle sees the working body expand adiabatically and reversibly, with no energy exchanged as heat, but more energy being transferred as work to the work reservoir. The third limb of the cycle sees the working body connected, through a wall permeable only to heat, to the heat reservoir 2, contracting and accepting energy as work from the work reservoir. The cycle is closed by reversible adiabatic compression of the working body, with no energy transferred as heat, but energy being transferred to it as work from the work reservoir.

With this set-up, the four limbs of the reversible Carnot cycle are characterized by amounts of energy transferred, as work from the working body to the work reservoir, and as heat from the heat reservoirs to the working body. The amounts of energy transferred as heat from the heat reservoirs are measured through the changes in the non-deformation variable of the working body, with reference to the previously known properties of that body, the amounts of work done on the work reservoir, and the first law of thermodynamics. The amounts of energy transferred as heat respectively from reservoir 1 and from reservoir 2 may then be denoted respectively Q1 and Q2. Then the absolute or thermodynamic temperatures, T1 and T2, of the reservoirs are defined so that to be such that


Kelvin's original work postulating absolute temperature was published in 1848. It was based on the work of Carnot, before the formulation of the first law of thermodynamics. Kelvin wrote in his 1848 paper that his scale was absolute in the sense that it was defined "independently of the properties of any particular kind of matter". His definitive publication, which sets out the definition just stated, was printed in 1853, a paper read in 1851.[18][19][20][21]

This definition rests on the physical assumption that there are readily available walls permeable only to heat. In his detailed definition of a wall permeable only to heat, Carathéodory includes several ideas. The non-deformation state variable of a closed system is represented as a real number. A state of thermal equilibrium between two closed systems connected by a wall permeable only to heat means that a certain mathematical relation holds between the state variables, including the respective non-deformation variables, of those two systems (that particular mathematical relation is regarded by Buchdahl as a preferred statement of the zeroth law of thermodynamics).[22] Also, referring to thermal contact equilibrium, "whenever each of the systems S1 and S2 is made to reach equilibrium with a third system S3 under identical conditions, the systems S1 and S2 are in mutual equilibrium."[23] It may be viewed as a re-statement of the principle stated by Maxwell in the words: "All heat is of the same kind."[24] This physical idea is also expressed by Bailyn as a possible version of the zeroth law of thermodynamics: "All diathermal walls are equivalent."[25] Thus the present definition of thermodynamic temperature rests on the zeroth law of thermodynamics. Explicitly, this present definition of thermodynamic temperature also rests on the first law of thermodynamics, for the determination of amounts of energy transferred as heat.

Implicitly for this definition, the second law of thermodynamics provides information that establishes the virtuous character of the temperature so defined. It provides that any working substance that complies with the requirement stated in this definition will lead to the same ratio of thermodynamic temperatures, which in this sense is universal, or absolute. The second law of thermodynamics also provides that the thermodynamic temperature defined in this way is positive, because this definition requires that the heat reservoirs not be in thermal equilibrium with one another, and the cycle can be imagined to operate only in one sense if net work is to be supplied to the work reservoir.

Numerical details are settled by making one of the heat reservoirs a cell at the triple point of water, which is defined to have an absolute temperature of 273.16 K.[26] The zeroth law of thermodynamics allows this definition to be used to measure the absolute or thermodynamic temperature of an arbitrary body of interest, by making the other heat reservoir have the same temperature as the body of interest.

Intensive variability

In thermodynamic terms, temperature is an intensive variable because it is equal to a differential coefficient of one extensive variable with respect to another, for a given body. It thus has the dimensions of a ratio of two extensive variables. In thermodynamics, two bodies are often considered as connected by contact with a common wall, which has some specific permeability properties. Such specific permeability can be referred to a specific intensive variable. An example is a diathermic wall that is permeable only to heat; the intensive variable for this case is temperature. When the two bodies have been in contact for a very long time, and have settled to a permanent steady state, the relevant intensive variables are equal in the two bodies; for a diathermal wall, this statement is sometimes called the zeroth law of thermodynamics.[27][28][29]

In particular, when the body is described by stating its internal energy U, an extensive variable, as a function of its entropy S, also an extensive variable, and other state variables V, N, with U = U (S, V, N), then the temperature is equal to the partial derivative of the internal energy with respect to the entropy:[28][29][30]


Likewise, when the body is described by stating its entropy S as a function of its internal energy U, and other state variables V, N, with S = S (U, V, N), then the reciprocal of the temperature is equal to the partial derivative of the entropy with respect to the internal energy:[28][30][31]


The above definition, equation (1), of the absolute temperature is due to Kelvin. It refers to systems closed to transfer of matter, and has special emphasis on directly experimental procedures. A presentation of thermodynamics by Gibbs starts at a more abstract level and deals with systems open to the transfer of matter; in this development of thermodynamics, the equations (2) and (3) above are actually alternative definitions of temperature.[32]

Local thermodynamic equilibrium

Real world bodies are often not in thermodynamic equilibrium and not homogeneous. For study by methods of classical irreversible thermodynamics, a body is usually spatially and temporally divided conceptually into 'cells' of small size. If classical thermodynamic equilibrium conditions for matter are fulfilled to good approximation in such a 'cell', then it is homogeneous and a temperature exists for it. If this is so for every 'cell' of the body, then local thermodynamic equilibrium is said to prevail throughout the body.[33][34][35][36][37]

It makes good sense, for example, to say of the extensive variable U, or of the extensive variable S, that it has a density per unit volume, or a quantity per unit mass of the system, but it makes no sense to speak of density of temperature per unit volume or quantity of temperature per unit mass of the system. On the other hand, it makes no sense to speak of the internal energy at a point, while when local thermodynamic equilibrium prevails, it makes good sense to speak of the temperature at a point. Consequently, temperature can vary from point to point in a medium that is not in global thermodynamic equilibrium, but in which there is local thermodynamic equilibrium.

Thus, when local thermodynamic equilibrium prevails in a body, temperature can be regarded as a spatially varying local property in that body, and this is because temperature is an intensive variable.

Kinetic theory approach

A more thorough account of this is below at Theoretical foundation.

Kinetic theory provides a microscopic explanation of temperature, based on macroscopic systems' being composed of many microscopic particles, such as molecules and ions of various species, the particles of a species being all alike. It explains macroscopic phenomena through the classical mechanics of the microscopic particles. The equipartition theorem of kinetic theory asserts that each classical degree of freedom of a freely moving particle has an average kinetic energy of kBT/2 where kB denotes Boltzmann's constant. The translational motion of the particle has three degrees of freedom, so that, except at very low temperatures where quantum effects predominate, the average translational kinetic energy of a freely moving particle in a system with temperature T will be 3kBT/2.

It is possible to measure the average kinetic energy of constituent microscopic particles if they are allowed to escape from the bulk of the system. The spectrum of velocities has to be measured, and the average calculated from that. It is not necessarily the case that the particles that escape and are measured have the same velocity distribution as the particles that remain in the bulk of the system, but sometimes a good sample is possible.

Molecules, such as oxygen (O2), have more degrees of freedom than single spherical atoms: they undergo rotational and vibrational motions as well as translations. Heating results in an increase in temperature due to an increase in the average translational kinetic energy of the molecules. Heating will also cause, through equipartitioning, the energy associated with vibrational and rotational modes to increase. Thus a diatomic gas will require more energy input to increase its temperature by a certain amount, i.e. it will have a greater heat capacity than a monatomic gas.

The process of cooling involves removing internal energy from a system. When no more energy can be removed, the system is at absolute zero, though this cannot be achieved experimentally. Absolute zero is the null point of the thermodynamic temperature scale, also called absolute temperature. If it were possible to cool a system to absolute zero, all classical motion of its particles would cease and they would be at complete rest in this classical sense. Microscopically in the description of quantum mechanics, however, matter still has zero-point energy even at absolute zero, because of the uncertainty principle.

Basic theory

Temperature is a measure of a quality of a state of a material.[38] The quality may be regarded as a more abstract entity than any particular temperature scale that measures it, and is called hotness by some writers.[39] The quality of hotness refers to the state of material only in a particular locality, and in general, apart from bodies held in a steady state of thermodynamic equilibrium, hotness varies from place to place. It is not necessarily the case that a material in a particular place is in a state that is steady and nearly homogeneous enough to allow it to have a well-defined hotness or temperature. Hotness may be represented abstractly as a one-dimensional manifold. Every valid temperature scale has its own one-to-one map into the hotness manifold.[40][41]

When two systems in thermal contact are at the same temperature no heat transfers between them. When a temperature difference does exist heat flows spontaneously from the warmer system to the colder system until they are in thermal equilibrium. Heat transfer occurs by conduction or by thermal radiation.[42][43][44][45][46][47][48][49]

Experimental physicists, for example Galileo and Newton,[50] found that there are indefinitely many empirical temperature scales. Nevertheless, the zeroth law of thermodynamics says that they all measure the same quality.

Bodies in thermodynamic equilibrium

For experimental physics, hotness means that, when comparing any two given bodies in their respective separate thermodynamic equilibria, any two suitably given empirical thermometers with numerical scale readings will agree as to which is the hotter of the two given bodies, or that they have the same temperature.[51] This does not require the two thermometers to have a linear relation between their numerical scale readings, but it does require that the relation between their numerical readings shall be strictly monotonic.[52][53] A definite sense of greater hotness can be had, independently of calorimetry, of thermodynamics, and of properties of particular materials, from Wien's displacement law of thermal radiation: the temperature of a bath of thermal radiation is proportional, by a universal constant, to the frequency of the maximum of its frequency spectrum; this frequency is always positive, but can have values that tend to zero. Thermal radiation is initially defined for a cavity in thermodynamic equilibrium. These physical facts justify a mathematical statement that hotness exists on an ordered one-dimensional manifold. This is a fundamental character of temperature and thermometers for bodies in their own thermodynamic equilibrium.[5][40][41][54][55]

Except for a system undergoing a first-order phase change such as the melting of ice, as a closed system receives heat, without change in its volume and without change in external force fields acting on it, its temperature rises. For a system undergoing such a phase change so slowly that departure from thermodynamic equilibrium can be neglected, its temperature remains constant as the system is supplied with latent heat. Conversely, a loss of heat from a closed system, without phase change, without change of volume, and without change in external force fields acting on it, decreases its temperature.[56]

Bodies in a steady state but not in thermodynamic equilibrium

While for bodies in their own thermodynamic equilibrium states, the notion of temperature requires that all empirical thermometers must agree as to which of two bodies is the hotter or that they are at the same temperature, this requirement is not safe for bodies that are in steady states though not in thermodynamic equilibrium. It can then well be that different empirical thermometers disagree about which is the hotter, and if this is so, then at least one of the bodies does not have a well defined absolute thermodynamic temperature. Nevertheless, any one given body and any one suitable empirical thermometer can still support notions of empirical, non-absolute, hotness and temperature, for a suitable range of processes. This is a matter for study in non-equilibrium thermodynamics.

Bodies not in a steady state

When a body is not in a steady state, then the notion of temperature becomes even less safe than for a body in a steady state not in thermodynamic equilibrium. This is also a matter for study in non-equilibrium thermodynamics.

Thermodynamic equilibrium axiomatics

For axiomatic treatment of thermodynamic equilibrium, since the 1930s, it has become customary to refer to a zeroth law of thermodynamics. The customarily stated minimalist version of such a law postulates only that all bodies, which when thermally connected would be in thermal equilibrium, should be said to have the same temperature by definition, but by itself does not establish temperature as a quantity expressed as a real number on a scale. A more physically informative version of such a law views empirical temperature as a chart on a hotness manifold.[40][55][57] While the zeroth law permits the definitions of many different empirical scales of temperature, the second law of thermodynamics selects the definition of a single preferred, absolute temperature, unique up to an arbitrary scale factor, whence called the thermodynamic temperature.[5][40][58][59][60][61] If internal energy is considered as a function of the volume and entropy of a homogeneous system in thermodynamic equilibrium, thermodynamic absolute temperature appears as the partial derivative of internal energy with respect the entropy at constant volume. Its natural, intrinsic origin or null point is absolute zero at which the entropy of any system is at a minimum. Although this is the lowest absolute temperature described by the model, the third law of thermodynamics postulates that absolute zero cannot be attained by any physical system.

Heat capacity

When an energy transfer to or from a body is only as heat, the state of the body changes. Depending on the surroundings and the walls separating them from the body, various changes are possible in the body. They include chemical reactions, increase of pressure, increase of temperature, and phase change. For each kind of change under specified conditions, the heat capacity is the ratio of the quantity of heat transferred to the magnitude of the change. For example, if the change is an increase in temperature at constant volume, with no phase change and no chemical change, then the temperature of the body rises and its pressure increases. The quantity of heat transferred, ΔQ, divided by the observed temperature change, ΔT, is the body's heat capacity at constant volume:

If heat capacity is measured for a well defined amount of substance, the specific heat is the measure of the heat required to increase the temperature of such a unit quantity by one unit of temperature. For example, to raise the temperature of water by one kelvin (equal to one degree Celsius) requires 4186 joules per kilogram (J/kg).


A typical Celsius thermometer measures a winter day temperature of −17 °C

Temperature measurement using modern scientific thermometers and temperature scales goes back at least as far as the early 18th century, when Gabriel Fahrenheit adapted a thermometer (switching to mercury) and a scale both developed by Ole Christensen Rømer. Fahrenheit's scale is still in use in the United States for non-scientific applications.

Temperature is measured with thermometers that may be calibrated to a variety of temperature scales. In most of the world (except for Belize, Myanmar, Liberia and the United States), the Celsius scale is used for most temperature measuring purposes. Most scientists measure temperature using the Celsius scale and thermodynamic temperature using the Kelvin scale, which is the Celsius scale offset so that its null point is 0 K = −273.15 °C, or absolute zero. Many engineering fields in the US, notably high-tech and US federal specifications (civil and military), also use the Kelvin and Celsius scales. Other engineering fields in the US also rely upon the Rankine scale (a shifted Fahrenheit scale) when working in thermodynamic-related disciplines such as combustion.


The basic unit of temperature in the International System of Units (SI) is the Kelvin. It has the symbol K.

For everyday applications, it is often convenient to use the Celsius scale, in which 0 °C corresponds very closely to the freezing point of water and 100 °C is its boiling point at sea level. Because liquid droplets commonly exist in clouds at sub-zero temperatures, 0 °C is better defined as the melting point of ice. In this scale a temperature difference of 1 degree Celsius is the same as a 1kelvin increment, but the scale is offset by the temperature at which ice melts (273.15 K).

By international agreement[62] the Kelvin and Celsius scales are defined by two fixing points: absolute zero and the triple point of Vienna Standard Mean Ocean Water, which is water specially prepared with a specified blend of hydrogen and oxygen isotopes. Absolute zero is defined as precisely 0 K and −273.15 °C. It is the temperature at which all classical translational motion of the particles comprising matter ceases and they are at complete rest in the classical model. Quantum-mechanically, however, zero-point motion remains and has an associated energy, the zero-point energy. Matter is in its ground state,[63] and contains no thermal energy. The triple point of water is defined as 273.16 K and 0.01 °C. This definition serves the following purposes: it fixes the magnitude of the kelvin as being precisely 1 part in 273.16 parts of the difference between absolute zero and the triple point of water; it establishes that one kelvin has precisely the same magnitude as one degree on the Celsius scale; and it establishes the difference between the null points of these scales as being 273.15 K (0 K = −273.15 °C and 273.16 K = 0.01 °C).

In the United States, the Fahrenheit scale is widely used. On this scale the freezing point of water corresponds to 32 °F and the boiling point to 212 °F. The Rankine scale, still used in fields of chemical engineering in the US, is an absolute scale based on the Fahrenheit increment.


The following table shows the temperature conversion formulas for conversions to and from the Celsius scale.

Temperature conversions
from Celsius to Celsius
Fahrenheit [°F] = [°C] × ​95 + 32 [°C] = ([°F] − 32) × ​59
Kelvin [K] = [°C] + 273.15 [°C] = [K] − 273.15
Rankine [°R] = ([°C] + 273.15) × ​95 [°C] = ([°R] − 491.67) × ​59
Delisle [°De] = (100 − [°C]) × ​32 [°C] = 100 − [°De] × ​23
Newton [°N] = [°C] × ​33100 [°C] = [°N] × ​10033
Réaumur [°Ré] = [°C] × ​45 [°C] = [°Ré] × ​54
Rømer [°Rø] = [°C] × ​2140 + 7.5 [°C] = ([°Rø] − 7.5) × ​4021

Plasma physics

The field of plasma physics deals with phenomena of electromagnetic nature that involve very high temperatures. It is customary to express temperature as energy in units of electronvolts (eV) or kiloelectronvolts (keV). The energy, which has a different dimension from temperature, is then calculated as the product of the Boltzmann constant and temperature, . Then, 1 eV corresponds to 11605 K. In the study of QCD matter one routinely encounters temperatures of the order of a few hundred MeV, equivalent to about 1012 K.

Theoretical foundation

Historically, there are several scientific approaches to the explanation of temperature: the classical thermodynamic description based on macroscopic empirical variables that can be measured in a laboratory; the kinetic theory of gases which relates the macroscopic description to the probability distribution of the energy of motion of gas particles; and a microscopic explanation based on statistical physics and quantum mechanics. In addition, rigorous and purely mathematical treatments have provided an axiomatic approach to classical thermodynamics and temperature.[64] Statistical physics provides a deeper understanding by describing the atomic behavior of matter, and derives macroscopic properties from statistical averages of microscopic states, including both classical and quantum states. In the fundamental physical description, using natural units, temperature may be measured directly in units of energy. However, in the practical systems of measurement for science, technology, and commerce, such as the modern metric system of units, the macroscopic and the microscopic descriptions are interrelated by the Boltzmann constant, a proportionality factor that scales temperature to the microscopic mean kinetic energy.

The microscopic description in statistical mechanics is based on a model that analyzes a system into its fundamental particles of matter or into a set of classical or quantum-mechanical oscillators and considers the system as a statistical ensemble of microstates. As a collection of classical material particles, temperature is a measure of the mean energy of motion, called kinetic energy, of the particles, whether in solids, liquids, gases, or plasmas. The kinetic energy, a concept of classical mechanics, is half the mass of a particle times its speed squared. In this mechanical interpretation of thermal motion, the kinetic energies of material particles may reside in the velocity of the particles of their translational or vibrational motion or in the inertia of their rotational modes. In monatomic perfect gases and, approximately, in most gases, temperature is a measure of the mean particle kinetic energy. It also determines the probability distribution function of the energy. In condensed matter, and particularly in solids, this purely mechanical description is often less useful and the oscillator model provides a better description to account for quantum mechanical phenomena. Temperature determines the statistical occupation of the microstates of the ensemble. The microscopic definition of temperature is only meaningful in the thermodynamic limit, meaning for large ensembles of states or particles, to fulfill the requirements of the statistical model.

In the context of thermodynamics, the kinetic energy is also referred to as thermal energy. The thermal energy may be partitioned into independent components attributed to the degrees of freedom of the particles or to the modes of oscillators in a thermodynamic system. In general, the number of these degrees of freedom that are available for the equipartitioning of energy depends on the temperature, i.e. the energy region of the interactions under consideration. For solids, the thermal energy is associated primarily with the vibrations of its atoms or molecules about their equilibrium position. In an ideal monatomic gas, the kinetic energy is found exclusively in the purely translational motions of the particles. In other systems, vibrational and rotational motions also contribute degrees of freedom.

Kinetic theory of gases

Translational motion
A theoretical understanding of temperature in an ideal gas can be obtained from the Kinetic theory.

Maxwell and Boltzmann developed a kinetic theory that yields a fundamental understanding of temperature in gases.[65] This theory also explains the ideal gas law and the observed heat capacity of monatomic (or 'noble') gases.[66][67][68]

Gas thermometer and absolute zero
Plots of pressure vs temperature for three different gas samples extrapolated to absolute zero

The ideal gas law is based on observed empirical relationships between pressure (p), volume (V), and temperature (T), and was recognized long before the kinetic theory of gases was developed (see Boyle's and Charles's laws). The ideal gas law states:[69]

where n is the number of moles of gas and R = 8.3144598(48) J⋅mol−1⋅K−1[70] is the gas constant.

This relationship gives us our first hint that there is an absolute zero on the temperature scale, because it only holds if the temperature is measured on an absolute scale such as Kelvin's. The ideal gas law allows one to measure temperature on this absolute scale using the gas thermometer. The temperature in kelvins can be defined as the pressure in pascals of one mole of gas in a container of one cubic meter, divided by the gas constant.

Although it is not a particularly convenient device, the gas thermometer provides an essential theoretical basis by which all thermometers can be calibrated. As a practical matter, it is not possible to use a gas thermometer to measure absolute zero temperature since the gases tend to condense into a liquid long before the temperature reaches zero. It is possible, however, to extrapolate to absolute zero by using the ideal gas law, as shown in the figure.

The kinetic theory assumes that pressure is caused by the force associated with individual atoms striking the walls, and that all energy is translational kinetic energy. Using a sophisticated symmetry argument,[71] Boltzmann deduced what is now called the Maxwell–Boltzmann probability distribution function for the velocity of particles in an ideal gas. From that probability distribution function, the average kinetic energy (per particle) of a monatomic ideal gas is[67][72]

where the Boltzmann constant k is the ideal gas constant divided by the Avogadro number, and is the root-mean-square speed. Thus the ideal gas law states that internal energy is directly proportional to temperature.[73] This direct proportionality between temperature and internal energy is a special case of the equipartition theorem, and holds only in the classical limit of an ideal gas. It does not hold for most substances, although it is true that temperature is a monotonic (non-decreasing) function of internal energy.

Zeroth law of thermodynamics

When two otherwise isolated bodies are connected together by a rigid physical path impermeable to matter, there is spontaneous transfer of energy as heat from the hotter to the colder of them. Eventually, they reach a state of mutual thermal equilibrium, in which heat transfer has ceased, and the bodies' respective state variables have settled to become unchanging.

One statement of the zeroth law of thermodynamics is that if two systems are each in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other.

This statement helps to define temperature but it does not, by itself, complete the definition. An empirical temperature is a numerical scale for the hotness of a thermodynamic system. Such hotness may be defined as existing on a one-dimensional manifold, stretching between hot and cold. Sometimes the zeroth law is stated to include the existence of a unique universal hotness manifold, and of numerical scales on it, so as to provide a complete definition of empirical temperature.[57] To be suitable for empirical thermometry, a material must have a monotonic relation between hotness and some easily measured state variable, such as pressure or volume, when all other relevant coordinates are fixed. An exceptionally suitable system is the ideal gas, which can provide a temperature scale that matches the absolute Kelvin scale. The Kelvin scale is defined on the basis of the second law of thermodynamics.

Second law of thermodynamics

In the previous section certain properties of temperature were expressed by the zeroth law of thermodynamics. It is also possible to define temperature in terms of the second law of thermodynamics which deals with entropy. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability.

For example, in a series of coin tosses, a perfectly ordered system would be one in which either every toss comes up heads or every toss comes up tails. This means that for a perfectly ordered set of coin tosses, there is only one set of toss outcomes possible: the set in which 100% of tosses come up the same. On the other hand, there are multiple combinations that can result in disordered or mixed systems, where some fraction are heads and the rest tails. A disordered system can be 90% heads and 10% tails, or it could be 98% heads and 2% tails, etcetera. As the number of coin tosses increases, the number of possible combinations corresponding to imperfectly ordered systems increases. For a very large number of coin tosses, the combinations to ~50% heads and ~50% tails dominate and obtaining an outcome significantly different from 50/50 becomes extremely unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy.

It has been previously stated that temperature governs the transfer of heat between two systems and it was just shown that the universe tends to progress so as to maximize entropy, which is expected of any natural system. Thus, it is expected that there is some relationship between temperature and entropy. To find this relationship, the relationship between heat, work and temperature is first considered. A heat engine is a device for converting thermal energy into mechanical energy, resulting in the performance of work, and analysis of the Carnot heat engine provides the necessary relationships. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, qH and the heat ejected at the low temperature, qC. The efficiency is the work divided by the heat put into the system:


where wcy is the work done per cycle. The efficiency depends only on qC/qH. Because qC and qH correspond to heat transfer at the temperatures TC and TH respectively, qC/qH should be some function of these temperatures:


Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between T1 and T3 must have the same efficiency as one consisting of two cycles, one between T1 and T2, and the second between T2 and T3. This can only be the case if

which implies

Since the first function is independent of T2, this temperature must cancel on the right side, meaning f(T1,T3) is of the form g(T1)/g(T3) (i.e. f(T1,T3) = f(T1,T2)f(T2,T3) = g(T1)/g(T2g(T2)/g(T3) = g(T1)/g(T3)), where g is a function of a single temperature. A temperature scale can now be chosen with the property that


Substituting (4) back into (2) gives a relationship for the efficiency in terms of temperature:


For TC = 0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K. Since an efficiency greater than 100% violates the first law of thermodynamics, this implies that 0 K is the minimum possible temperature. In fact the lowest temperature ever obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 5 from the middle portion and rearranging gives

where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by


where the subscript indicates a reversible process. The change of this state function around any cycle is zero, as is necessary for any state function. This function corresponds to the entropy of the system, which was described previously. Rearranging Equation 6 gives a new definition for temperature in terms of entropy and heat:


For a system, where entropy S(E) is a function of its energy E, the temperature T is given by


i.e. the reciprocal of the temperature is the rate of increase of entropy with respect to energy.

Definition from statistical mechanics

Statistical mechanics defines temperature based on a system's fundamental degrees of freedom. Eq.(10) is the defining relation of temperature. Eq. (9) can be derived from the principles underlying the fundamental thermodynamic relation.

Generalized temperature from single-particle statistics

It is possible to extend the definition of temperature even to systems of few particles, like in a quantum dot. The generalized temperature is obtained by considering time ensembles instead of configuration-space ensembles given in statistical mechanics in the case of thermal and particle exchange between a small system of fermions (N even less than 10) with a single/double-occupancy system. The finite quantum grand canonical ensemble,[74] obtained under the hypothesis of ergodicity and orthodicity,[75] allows expressing the generalized temperature from the ratio of the average time of occupation and of the single/double-occupancy system:[76]

where EF is the Fermi energy. This generalized temperature tends to the ordinary temperature when N goes to infinity.

Negative temperature

On the empirical temperature scales, which are not referenced to absolute zero, a negative temperature is one below the zero-point of the scale used. For example, dry ice has a sublimation temperature of −78.5 °C which is equivalent to −109.3 °F. On the absolute kelvin scale, however, this temperature is 194.6 K. On the absolute scale of thermodynamic temperature, strictly defined by the condition of thermodynamic equilibrium, no body, nor any component of a body, can be colder than one with a temperature of 0 K, as indicated below. Indeed, no body can be brought to exactly 0 K by any finite practicable process; this is stated in the third law of thermodynamics.

Temperature is strictly defined for a body in its own state of internal thermodynamic equilibrium, and in this definition, on an absolute scale, it is always positive. In an apparent contradiction of this reliable and valid rule, a so-called negative absolute "temperature" may be approximately defined for a component of a body that is not in its own state of internal thermodynamic equilibrium: a component of the body may have a negative approximate "temperature" while the rest of the components of the body have positive approximate absolute temperatures. The component with negative "temperature" is, perhaps counterintuitively, hotter, not colder, than a body with the same magnitude of positive absolute temperature. Such a non-equilibrium situation is either transient in time or is maintained by external factors that drive a flow of energy through the body of interest. An example of such a component is a spin system within a body, as follows.

In the quantum mechanical description of electron and nuclear spin systems that have a limited number of possible states, and therefore a discrete upper limit of energy they can attain, it is possible to obtain a negative temperature, which is numerically indeed less than absolute zero. However, this is not the macroscopic temperature of the material, but instead the temperature of only very specific degrees of freedom, that are isolated from others and do not exchange energy by virtue of the equipartition theorem.

A negative temperature is experimentally achieved with suitable radio frequency techniques that cause a population inversion of spin states from the ground state. As the energy in the system increases upon population of the upper states, the entropy increases as well, as the system becomes less ordered, but attains a maximum value when the spins are evenly distributed among ground and excited states, after which it begins to decrease, once again achieving a state of higher order as the upper states begin to fill exclusively. At the point of maximum entropy, the temperature function shows the behavior of a singularity, because the slope of the entropy function decreases to zero at first and then turns negative. Since temperature is the inverse of the derivative of the entropy, the temperature formally goes to infinity at this point, and switches to negative infinity as the slope turns negative. At energies higher than this point, the spin degree of freedom therefore exhibits formally a negative thermodynamic temperature. As the energy increases further by continued population of the excited state, the negative temperature approaches zero asymptotically.[77] As the energy of the system increases in the population inversion, a system with a negative temperature is not colder than absolute zero, but rather it has a higher energy than at positive temperature, and may be said to be in fact hotter at negative temperatures. When brought into contact with a system at a positive temperature, energy will be transferred from the negative temperature regime to the positive temperature region.


Temperature Peak emittance wavelength[78]
of black-body radiation
Kelvin Celsius
Absolute zero
(precisely by definition)
0 K −273.15 °C cannot be defined
Coldest temperature
100 pK −273.149999999900 °C 29000 km
Bose–Einstein condensate[80]
450 pK −273.14999999955 °C 6400 km
One millikelvin
(precisely by definition)
0.001 K −273.149 °C 2.89777 m
(radio, FM band)[81]
Cosmic microwave background
(2013 measurement)
2.7260 K −270.424 °C 0.00106301 m
(millimeter-wavelength microwave)
Water triple point
(precisely by definition)
273.16 K 0.01 °C 10608.3 nm
(long-wavelength IR)
Water boiling point[A] 373.1339 K 99.9839 °C 7766.03 nm
(mid-wavelength IR)
Iron melting point 1811 K 1538 °C 1600 nm
(far infrared)
Incandescent lamp[B] 2500 K 2200 °C 1160 nm
(near infrared)[C]
Sun's visible surface[D][82] 5778 K 5505 °C 501.5 nm
(green-blue light)
Lightning bolt
28 kK 28000 °C 100 nm
(far ultraviolet light)
Sun's core[E] 16 MK 16 million °C 0.18 nm (X-rays)
Thermonuclear weapon
(peak temperature)[E][83]
350 MK 350 million °C 8.3×10−3 nm
(gamma rays)
Sandia National Labs'
Z machine[E][84]
2 GK 2 billion °C 1.4×10−3 nm
(gamma rays)[F]
Core of a high-mass
star on its last day
3 GK 3 billion °C 1×10−3 nm
(gamma rays)
Merging binary neutron
350 GK 350 billion °C 8×10−6 nm
(gamma rays)
Relativistic Heavy
Ion Collider
1 TK 1 trillion °C 3×10−6 nm
(gamma rays)
CERN's proton vs
nucleus collisions[E][88]
10 TK 10 trillion °C 3×10−7 nm
(gamma rays)
Universe 5.391×10−44 s
after the Big Bang[E]
1.417×1032 K
(Planck temperature)
1.417×1032 °C 1.616×10−27 nm
(Planck length)[89]
  • A For Vienna Standard Mean Ocean Water at one standard atmosphere (101.325 kPa) when calibrated strictly per the two-point definition of thermodynamic temperature.
  • B The 2500 K value is approximate. The 273.15 K difference between K and °C is rounded to 300 K to avoid false precision in the Celsius value.
  • C For a true black-body (which tungsten filaments are not). Tungsten filament emissivity is greater at shorter wavelengths, which makes them appear whiter.
  • D Effective photosphere temperature. The 273.15 K difference between K and °C is rounded to 273 K to avoid false precision in the Celsius value.
  • E The 273.15 K difference between K and °C is within the precision of these values.
  • F For a true black-body (which the plasma was not). The Z machine's dominant emission originated from 40 MK electrons (soft x-ray emissions) within the plasma.

See also

  • Thermometer CF.svg Temperature portal

Notes and references

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  78. ^ The cited emission wavelengths are for black bodies in equilibrium. CODATA 2006 recommended value of 2.8977685(51)×10−3 m K used for Wien displacement law constant b.
  79. ^ "World record in low temperatures". Archived from the original on 2009-06-18. Retrieved 2009-05-05.
  80. ^ A temperature of 450 ±80 pK in a Bose–Einstein condensate (BEC) of sodium atoms was achieved in 2003 by researchers at MIT. Citation: Cooling Bose–Einstein Condensates Below 500 Picokelvin, A.E. Leanhardt et al., Science 301, 12 Sept. 2003, p. 1515. It's noteworthy that this record's peak emittance black-body wavelength of 6,400 kilometers is roughly the radius of Earth.
  81. ^ The peak emittance wavelength of 2.89777 m is a frequency of 103.456 MHz
  82. ^ Measurement was made in 2002 and has an uncertainty of ±3 kelvins. A 1989 measurement Archived 2010-02-11 at the Wayback Machine produced a value of 5,777.0±2.5 K. Citation: Overview of the Sun (Chapter 1 lecture notes on Solar Physics by Division of Theoretical Physics, Dept. of Physical Sciences, University of Helsinki).
  83. ^ The 350 MK value is the maximum peak fusion fuel temperature in a thermonuclear weapon of the Teller–Ulam configuration (commonly known as a hydrogen bomb). Peak temperatures in Gadget-style fission bomb cores (commonly known as an atomic bomb) are in the range of 50 to 100 MK. Citation: Nuclear Weapons Frequently Asked Questions, 3.2.5 Matter At High Temperatures. Link to relevant Web page. Archived 2007-05-03 at the Wayback Machine All referenced data was compiled from publicly available sources.
  84. ^ Peak temperature for a bulk quantity of matter was achieved by a pulsed-power machine used in fusion physics experiments. The term bulk quantity draws a distinction from collisions in particle accelerators wherein high temperature applies only to the debris from two subatomic particles or nuclei at any given instant. The >2 GK temperature was achieved over a period of about ten nanoseconds during shot Z1137. In fact, the iron and manganese ions in the plasma averaged 3.58±0.41 GK (309±35 keV) for 3 ns (ns 112 through 115). Ion Viscous Heating in a Magnetohydrodynamically Unstable Z Pinch at Over 2×109 Kelvin, M.G. Haines et al., Physical Review Letters 96 (2006) 075003. Link to Sandia's news release. Archived 2010-05-30 at the Wayback Machine
  85. ^ Core temperature of a high–mass (>8–11 solar masses) star after it leaves the main sequence on the Hertzsprung–Russell diagram and begins the alpha process (which lasts one day) of fusing silicon–28 into heavier elements in the following steps: sulfur–32 → argon–36 → calcium–40 → titanium–44 → chromium–48 → iron–52 → nickel–56. Within minutes of finishing the sequence, the star explodes as a Type II supernova. Citation: Stellar Evolution: The Life and Death of Our Luminous Neighbors (by Arthur Holland and Mark Williams of the University of Michigan). Link to Web site Archived 2009-01-16 at the Wayback Machine. More informative links can be found here "Archived copy". Archived from the original on 2013-04-11. Retrieved 2016-02-08.CS1 maint: Archived copy as title (link), and here "Archived copy". Archived from the original on 2011-08-14. Retrieved 2016-02-08.CS1 maint: Archived copy as title (link), and a concise treatise on stars by NASA is here "Archived copy". Archived from the original on 2010-10-24. Retrieved 2010-10-12.CS1 maint: Archived copy as title (link). "Stellar". Archived from the original on January 16, 2009. Retrieved 2010-10-12.CS1 maint: BOT: original-url status unknown (link)
  86. ^ Based on a computer model that predicted a peak internal temperature of 30 MeV (350 GK) during the merger of a binary neutron star system (which produces a gamma–ray burst). The neutron stars in the model were 1.2 and 1.6 solar masses respectively, were roughly 20 km in diameter, and were orbiting around their barycenter (common center of mass) at about 390 Hz during the last several milliseconds before they completely merged. The 350 GK portion was a small volume located at the pair's developing common core and varied from roughly 1 to 7 km across over a time span of around 5 ms. Imagine two city-sized objects of unimaginable density orbiting each other at the same frequency as the G4 musical note (the 28th white key on a piano). It's also noteworthy that at 350 GK, the average neutron has a vibrational speed of 30% the speed of light and a relativistic mass (m) 5% greater than its rest mass (m0).  Torus Formation in Neutron Star Mergers and Well-Localized Short Gamma-Ray Bursts Archived 2017-11-22 at the Wayback Machine, R. Oechslin et al. of Max Planck Institute for Astrophysics. Archived 2005-04-03 at the Wayback Machine, arXiv:astro-ph/0507099 v2, 22 Feb. 2006. An html summary Archived 2010-11-09 at the Wayback Machine.
  87. ^ Results of research by Stefan Bathe using the PHENIX Archived 2008-11-20 at the Wayback Machine detector on the Relativistic Heavy Ion Collider Archived 2016-03-03 at the Wayback Machine at Brookhaven National Laboratory Archived 2012-06-24 at the Wayback Machine in Upton, New York. Bathe has studied gold-gold, deuteron-gold, and proton-proton collisions to test the theory of quantum chromodynamics, the theory of the strong force that holds atomic nuclei together. Link to news release. Archived 2009-02-11 at the Wayback Machine
  88. ^ How do physicists study particles? Archived 2007-10-11 at the Wayback Machine by CERN Archived 2012-07-07 at the Wayback Machine.
  89. ^ The Planck frequency equals 1.85487(14)×1043 Hz (which is the reciprocal of one Planck time). Photons at the Planck frequency have a wavelength of one Planck length. The Planck temperature of 1.41679(11)×1032 K equates to a calculated /T = λmax wavelength of 2.04531(16)×10−26 nm. However, the actual peak emittance wavelength quantizes to the Planck length of 1.61624(12)×10−26 nm.

Bibliography of cited references

  • Adkins, C.J. (1968/1983). Equilibrium Thermodynamics, (1st edition 1968), third edition 1983, Cambridge University Press, Cambridge UK, ISBN 0-521-25445-0.
  • Buchdahl, H.A. (1966). The Concepts of Classical Thermodynamics, Cambridge University Press, Cambridge.
  • Middleton, W.E.K. (1966). A History of the Thermometer and its Use in Metrology, Johns Hopkins Press, Baltimore.
  • Miller, J (2013). "Cooling molecules the optoelectric way". Physics Today. 66 (1): 12–14. Bibcode:2013PhT....66a..12M. doi:10.1063/pt.3.1840.
  • Partington, J.R. (1949). An Advanced Treatise on Physical Chemistry, volume 1, Fundamental Principles. The Properties of Gases, Longmans, Green & Co., London, pp. 175–177.
  • Pippard, A.B. (1957/1966). Elements of Classical Thermodynamics for Advanced Students of Physics, original publication 1957, reprint 1966, Cambridge University Press, Cambridge UK.
  • Quinn, T.J. (1983). Temperature, Academic Press, London, ISBN 0-12-569680-9.
  • Schooley, J.F. (1986). Thermometry, CRC Press, Boca Raton, ISBN 0-8493-5833-7.
  • Roberts, J.K., Miller, A.R. (1928/1960). Heat and Thermodynamics, (first edition 1928), fifth edition, Blackie & Son Limited, Glasgow.
  • Thomson, W. (Lord Kelvin) (1848). On an absolute thermometric scale founded on Carnot's theory of the motive power of heat, and calculated from Regnault's observations, Proc. Camb. Phil. Soc. (1843/1863) 1, No. 5: 66–71.
  • Thomson, W. (Lord Kelvin) (March 1851). "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam". Transactions of the Royal Society of Edinburgh. XX (part II): 261–268, 289–298.
  • Truesdell, C.A. (1980). The Tragicomical History of Thermodynamics, 1822–1854, Springer, New York, ISBN 0-387-90403-4.
  • Tschoegl, N.W. (2000). Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, ISBN 0-444-50426-5.
  • Zeppenfeld, M.; Englert, B.G.U.; Glöckner, R.; Prehn, A.; Mielenz, M.; Sommer, C.; van Buuren, L.D.; Motsch, M.; Rempe, G. (2012). "Sysiphus cooling of electrically trapped polyatomic molecules". Nature. 491 (7425): 570–573. arXiv:1208.0046. Bibcode:2012Natur.491..570Z. doi:10.1038/nature11595. PMID 23151480.

Further reading

  • Chang, Hasok (2004). Inventing Temperature: Measurement and Scientific Progress. Oxford: Oxford University Press. ISBN 978-0-19-517127-3.
  • Zemansky, Mark Waldo (1964). Temperatures Very Low and Very High. Princeton, NJ: Van Nostrand.

External links

Absolute zero

Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as 0. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15° on the Celsius scale (International System of Units), which equals −459.67° on the Fahrenheit scale (United States customary units or Imperial units). The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition.

It is commonly thought of as the lowest temperature possible, but it is not the lowest enthalpy state possible, because all real substances begin to depart from the ideal gas when cooled as they approach the change of state to liquid, and then to solid; and the sum of the enthalpy of vaporization (gas to liquid) and enthalpy of fusion (liquid to solid) exceeds the ideal gas's change in enthalpy to absolute zero. In the quantum-mechanical description, matter (solid) at absolute zero is in its ground state, the point of lowest internal energy.

The laws of thermodynamics indicate that absolute zero cannot be reached using only thermodynamic means, because the temperature of the substance being cooled approaches the temperature of the cooling agent asymptotically, and a system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state at absolute zero. The kinetic energy of the ground state cannot be removed.

Scientists and technologists routinely achieve temperatures close to absolute zero, where matter exhibits quantum effects such as superconductivity and superfluidity.

Atmosphere of Earth

The atmosphere of Earth is the layer of gases, commonly known as air, that surrounds the planet Earth and is retained by Earth's gravity. The atmosphere of Earth protects life on Earth by creating pressure allowing for liquid water to exist on the Earth's surface, absorbing ultraviolet solar radiation, warming the surface through heat retention (greenhouse effect), and reducing temperature extremes between day and night (the diurnal temperature variation).

By volume, dry air contains 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.04% carbon dioxide, and small amounts of other gases. Air also contains a variable amount of water vapor, on average around 1% at sea level, and 0.4% over the entire atmosphere. Air content and atmospheric pressure vary at different layers, and air suitable for use in photosynthesis by terrestrial plants and breathing of terrestrial animals is found only in Earth's troposphere and in artificial atmospheres.

The atmosphere has a mass of about 5.15×1018 kg, three quarters of which is within about 11 km (6.8 mi; 36,000 ft) of the surface. The atmosphere becomes thinner and thinner with increasing altitude, with no definite boundary between the atmosphere and outer space. The Kármán line, at 100 km (62 mi), or 1.57% of Earth's radius, is often used as the border between the atmosphere and outer space. Atmospheric effects become noticeable during atmospheric reentry of spacecraft at an altitude of around 120 km (75 mi). Several layers can be distinguished in the atmosphere, based on characteristics such as temperature and composition.

The study of Earth's atmosphere and its processes is called atmospheric science (aerology). Early pioneers in the field include Léon Teisserenc de Bort and Richard Assmann.

Boiling point

The boiling point of a substance is the temperature at which the vapor pressure of the liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.

The boiling point of a liquid varies depending upon the surrounding environmental pressure. A liquid in a partial vacuum has a lower boiling point than when that liquid is at atmospheric pressure. A liquid at high pressure has a higher boiling point than when that liquid is at atmospheric pressure. For example, water boils at 100 °C (212 °F) at sea level, but at 93.4 °C (200.1 °F) at 1,905 metres (6,250 ft) altitude. For a given pressure, different liquids will boil at different temperatures.

The normal boiling point (also called the atmospheric boiling point or the atmospheric pressure boiling point) of a liquid is the special case in which the vapor pressure of the liquid equals the defined atmospheric pressure at sea level, 1 atmosphere. At that temperature, the vapor pressure of the liquid becomes sufficient to overcome atmospheric pressure and allow bubbles of vapor to form inside the bulk of the liquid. The standard boiling point has been defined by IUPAC since 1982 as the temperature at which boiling occurs under a pressure of 1 bar.The heat of vaporization is the energy required to transform a given quantity (a mol, kg, pound, etc.) of a substance from a liquid into a gas at a given pressure (often atmospheric pressure).

Liquids may change to a vapor at temperatures below their boiling points through the process of evaporation. Evaporation is a surface phenomenon in which molecules located near the liquid's edge, not contained by enough liquid pressure on that side, escape into the surroundings as vapor. On the other hand, boiling is a process in which molecules anywhere in the liquid escape, resulting in the formation of vapor bubbles within the liquid.


The Celsius scale, also known as the centigrade scale, is a temperature scale used by the International System of Units (SI). As an SI derived unit, it is used by all countries except the United States, the Bahamas, Belize, the Cayman Islands and Liberia. It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale or a unit to indicate a difference between two temperatures or an uncertainty. Before being renamed to honor Anders Celsius in 1948, the unit was called centigrade, from the Latin centum, which means 100, and gradus, which means steps.

From 1743, the Celsius scale is based on 0 °C for the freezing point of water and 100 °C for the boiling point of water at 1 atm pressure. Prior to 1743, the scale was also based on the boiling and melting points of water, but the values were reversed (i.e. the boiling point was at 0 degrees and the melting point was at 100 degrees). The 1743 scale reversal was proposed by Jean-Pierre Christin.

By international agreement, since 1954 the unit degree Celsius and the Celsius scale are defined by absolute zero and the triple point of Vienna Standard Mean Ocean Water (VSMOW), a specially purified water. This definition also precisely relates the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature with symbol K. Absolute zero, the lowest temperature possible, is defined as being exactly 0 K and −273.15 °C. The temperature of the triple point of water is defined as exactly 273.16 K (0.01 °C). This means that a temperature difference of one degree Celsius and that of one kelvin are exactly the same.On May 20, 2019, the degree Kelvin, and along with it the degree Celsius, will again be re-defined so that its value will be determined by definition of the Boltzmann constant.


Climate is the statistics of weather over long periods of time. It is measured by assessing the patterns of variation in temperature, humidity, atmospheric pressure, wind, precipitation, atmospheric particle count and other meteorological variables in a given region over long periods of time. Climate differs from weather, in that weather only describes the short-term conditions of these variables in a given region.

A region's climate is generated by the climate system, which has five components: atmosphere, hydrosphere, cryosphere, lithosphere, and biosphere.The climate of a location is affected by its latitude, terrain, and altitude, as well as nearby water bodies and their currents. Climates can be classified according to the average and the typical ranges of different variables, most commonly temperature and precipitation. The most commonly used classification scheme was the Köppen climate classification. The Thornthwaite system, in use since 1948, incorporates evapotranspiration along with temperature and precipitation information and is used in studying biological diversity and how climate change affects it. The Bergeron and Spatial Synoptic Classification systems focus on the origin of air masses that define the climate of a region.

Paleoclimatology is the study of ancient climates. Since direct observations of climate are not available before the 19th century, paleoclimates are inferred from proxy variables that include non-biotic evidence such as sediments found in lake beds and ice cores, and biotic evidence such as tree rings and coral. Climate models are mathematical models of past, present and future climates. Climate change may occur over long and short timescales from a variety of factors; recent warming is discussed in global warming. Global warming results in redistributions. For example, "a 3°C change in mean annual temperature corresponds to a shift in isotherms of approximately 300–400 km in latitude (in the temperate zone) or 500 m in elevation. Therefore, species are expected to move upwards in elevation or towards the poles in latitude in response to shifting climate zones".

Color temperature

Not to be confused with warm and cool colors.

The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of a color comparable to that of the light source. Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics, horticulture, and other fields. In practice, color temperature is meaningful only for light sources that do in fact correspond somewhat closely to the radiation of some black body, i.e., light in a range going from red to orange to yellow to white to blueish white; it does not make sense to speak of the color temperature of, e.g., a green or a purple light. Color temperature is conventionally expressed in kelvins, using the symbol K, a unit of measure for absolute temperature.

Color temperatures over 5000 K are called "cool colors" (bluish), while lower color temperatures (2700–3000 K) are called "warm colors" (yellowish). "Warm" in this context is an analogy to radiated heat flux of traditional incandescent lighting rather than temperature. The spectral peak of warm-coloured light is closer to infrared, and most natural warm-coloured light sources emit significant infrared radiation. The fact that "warm" lighting in this sense actually has a "cooler" color temperature often leads to confusion.


In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system (such as its volume, pressure and temperature). Under the assumption that each microstate is equally probable, the entropy is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant kB. Formally (assuming equiprobable microstates),

Macroscopic systems typically have a very large number Ω of possible microscopic configurations. For example, the entropy of an ideal gas is proportional to the number of gas molecules N. Roughly twenty liters of gas at room temperature and atmospheric pressure has N6×1023 (Avogadro's number). At equilibrium, each of the Ω ≈ eN configurations can be regarded as random and equally likely.[citation needed]

The second law of thermodynamics states that the entropy of an isolated system never decreases. Such systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy. Non-isolated systems may lose entropy, provided their environment's entropy increases by at least that amount so that the total entropy increases. Entropy is a function of the state of the system, so the change in entropy of a system is determined by its initial and final states. In the idealization that a process is reversible, the entropy does not change, while irreversible processes always increase the total entropy.

Because it is determined by the number of random microstates, entropy is related to the amount of additional information needed to specify the exact physical state of a system, given its macroscopic specification. For this reason, it is often said that entropy is an expression of the disorder, or randomness of a system, or of the lack of information about it[citation needed]. The concept of entropy plays a central role in information theory.

Boltzmann's constant, and therefore entropy, have dimensions of energy divided by temperature, which has a unit of joules per kelvin (J⋅K−1) in the International System of Units (or kg⋅m2⋅s−2⋅K−1 in terms of base units). The entropy of a substance is usually given as an intensive property—either entropy per unit mass (SI unit: J⋅K−1⋅kg−1) or entropy per unit amount of substance (SI unit: J⋅K−1⋅mol−1).


The Fahrenheit scale is a temperature scale based on one proposed in 1724 by Dutch–German–Polish physicist Daniel Gabriel Fahrenheit (1686–1736). It uses the degree Fahrenheit (symbol: °F) as the unit. Several accounts of how he originally defined his scale exist. The lower defining point, 0 °F, was established as the freezing temperature of a solution of brine made from equal parts of ice, water and salt (ammonium chloride). Further limits were established as the melting point of ice (32 °F) and his best estimate of the average human body temperature (96 °F, about 2.6 °F less than the modern value due to a later redefinition of the scale). The scale is now usually defined by two fixed points: the temperature at which water freezes into ice is defined as 32 °F, and the boiling point of water is defined to be 212 °F, a 180 °F separation, as defined at sea level and standard atmospheric pressure.

At the end of the 2010s, Fahrenheit was used as the official temperature scale only in the United States (including its unincorporated territories), its freely associated states in the Western Pacific (Palau, the Federated States of Micronesia and the Marshall Islands), the Bahamas, the Cayman Islands and Liberia. Antigua and Barbuda and other islands which use the same meteorological service, such as Anguilla, the British Virgin Islands, Montserrat and Saint Kitts and Nevis, as well as Bermuda, Belize and the Turks and Caicos Islands, use Fahrenheit and Celsius. All other countries in the world officially now use the Celsius scale, named after Swedish astronomer Anders Celsius.


Fever, also known as pyrexia and febrile response, is defined as having a temperature above the normal range due to an increase in the body's temperature set point. There is not a single agreed-upon upper limit for normal temperature with sources using values between 37.5 and 38.3 °C (99.5 and 100.9 °F). The increase in set point triggers increased muscle contractions and causes a feeling of cold. This results in greater heat production and efforts to conserve heat. When the set point temperature returns to normal, a person feels hot, becomes flushed, and may begin to sweat. Rarely a fever may trigger a febrile seizure. This is more common in young children. Fevers do not typically go higher than 41 to 42 °C (105.8 to 107.6 °F).A fever can be caused by many medical conditions ranging from non serious to life threatening. This includes viral, bacterial and parasitic infections such as the common cold, urinary tract infections, meningitis, malaria and appendicitis among others. Non-infectious causes include vasculitis, deep vein thrombosis, side effects of medication, and cancer among others. It differs from hyperthermia, in that hyperthermia is an increase in body temperature over the temperature set point, due to either too much heat production or not enough heat loss.Treatment to reduce fever is generally not required. Treatment of associated pain and inflammation, however, may be useful and help a person rest. Medications such as ibuprofen or paracetamol (acetaminophen) may help with this as well as lower temperature. Measures such as putting a cool damp cloth on the forehead and having a slightly warm bath are not useful and may simply make a person more uncomfortable. Children younger than three months require medical attention, as might people with serious medical problems such as a compromised immune system or people with other symptoms. Hyperthermia does require treatment.Fever is one of the most common medical signs. It is part of about 30% of healthcare visits by children and occurs in up to 75% of adults who are seriously sick. While fever is a useful defense mechanism, treating fever does not appear to worsen outcomes. Fever is viewed with greater concern by parents and healthcare professionals than it usually deserves, a phenomenon known as fever phobia.

Flash point

The flash point of a volatile material is the lowest temperature at which vapours of the material will ignite, when given an ignition source.

The flash point is sometimes confused with the autoignition temperature, the temperature that results in spontaneous autoignition. The fire point is the lowest temperature at which vapors of the material will keep burning after the ignition source is removed. The fire point is higher than the flash point, because at the flash point more vapor may not be produced rapidly enough to sustain combustion. Neither flash point nor fire point depends directly on the ignition source temperature, but ignition source temperature is far higher than either the flash or fire point.

Global warming

Global warming is a long-term rise in the average temperature of the Earth's climate system, an aspect of climate change shown by temperature measurements and by multiple effects of the warming. The term commonly refers to the mainly human-caused observed warming since pre-industrial times and its projected continuation, though there were also much earlier periods of global warming. In the modern context the terms global warming and climate change are commonly used interchangeably, but climate change includes both global warming and its effects, such as changes to precipitation and impacts that differ by region. Many of the observed warming changes since the 1950s are unprecedented in the instrumental temperature record, and in historical and paleoclimate proxy records of climate change over thousands to millions of years.In 2013, the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report concluded, "It is extremely likely that human influence has been the dominant cause of the observed warming since the mid-20th century." The largest human influence has been the emission of greenhouse gases such as carbon dioxide, methane, and nitrous oxide. Climate model projections summarized in the report indicated that during the 21st century, the global surface temperature is likely to rise a further 0.3 to 1.7 °C (0.5 to 3.1 °F) to 2.6 to 4.8 °C (4.7 to 8.6 °F) depending on the rate of greenhouse gas emissions and on climate feedback effects. These findings have been recognized by the national science academies of the major industrialized nations and are not disputed by any scientific body of national or international standing.Future climate change effects are expected to include rising sea levels, ocean acidification, regional changes in precipitation, and expansion of deserts in the subtropics. Surface temperature increases are greatest in the Arctic, with the continuing retreat of glaciers, permafrost, and sea ice. Predicted regional precipitation effects include more frequent extreme weather events such as heat waves, droughts, wildfires, heavy rainfall with floods, and heavy snowfall. Effects directly significant to humans are predicted to include the threat to food security from decreasing crop yields, and the abandonment of populated areas due to rising sea levels. Environmental impacts appear likely to include the extinction or relocation of ecosystems as they adapt to climate change, with coral reefs, mountain ecosystems, and Arctic ecosystems most immediately threatened. Because the climate system has a large "inertia" and greenhouse gases will remain in the atmosphere for a long time, climatic changes and their effects will continue to become more pronounced for many centuries even if further increases to greenhouse gases stop.Possible societal responses to global warming include mitigation by emissions reduction, adaptation to its effects, and possible future climate engineering. Most countries are parties to the United Nations Framework Convention on Climate Change (UNFCCC), whose ultimate objective is to prevent dangerous anthropogenic climate change. Parties to the UNFCCC have agreed that deep cuts in emissions are required and that global warming should be limited to well below 2.0 °C (3.6 °F) compared to pre-industrial levels, with efforts made to limit warming to 1.5 °C (2.7 °F). Some scientists call into question climate adaptation feasibility, with higher emissions scenarios, or the two degree temperature target.Public reactions to global warming and concern about its effects are also increasing. A global 2015 Pew Research Center report showed that a median of 54% of all respondents asked consider it "a very serious problem". Significant regional differences exist, with Americans and Chinese (whose economies are responsible for the greatest annual CO2 emissions) among the least concerned.

Greenhouse effect

The greenhouse effect is the process by which radiation from a planet's atmosphere warms the planet's surface to a temperature above what it would be without its atmosphere.If a planet's atmosphere contains radiatively active gases (i.e., greenhouse gases) they will radiate energy in all directions. Part of this radiation is directed towards the surface, warming it.

The intensity of the downward radiation – that is, the strength of the greenhouse effect – will depend on the atmosphere's temperature and on the amount of greenhouse gases that the atmosphere contains.

Earth’s natural greenhouse effect is critical to supporting life. Human activities, mainly the burning of fossil fuels and clearing of forests, have strengthened the greenhouse effect and caused global warming.The term "greenhouse effect" is a misnomer that arose from a faulty analogy with the effect of sunlight passing through glass and warming a greenhouse. The way a greenhouse retains heat is fundamentally different, as a greenhouse works mostly by reducing airflow so that warm air is kept inside.

Heat capacity

Heat capacity or thermal capacity is a measurable physical quantity equal to the ratio of the heat added to (or removed from) an object to the resulting temperature change. The unit of heat capacity is joule per kelvin , or kilogram metre squared per kelvin second squared in SI units. The dimensional form is L2MT−2Θ−1. Specific heat is the amount of heat needed to raise the temperature of one kilogram of mass by 1 kelvin.

Heat capacity is an extensive property of matter, meaning that it is proportional to the size of the system. When expressing the same phenomenon as an intensive property, the heat capacity is divided by the amount of substance, mass, or volume, thus the quantity is independent of the size or extent of the sample. The molar heat capacity is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the specific heat capacity, often called simply specific heat, is the heat capacity per unit mass of a material. Nonetheless some authors use the term specific heat to refer to the ratio of the specific heat capacity of a substance at any given temperature to the specific heat capacity of another substance at a reference temperature, much in the fashion of specific gravity. In some engineering contexts, the volumetric heat capacity is used.

Temperature reflects the average randomized kinetic energy of constituent particles of matter (i.e., atoms or molecules) relative to the centre of mass of the system, while heat is the transfer of energy across a system boundary into the body other than by work or matter transfer. Translation, rotation, and vibration of atoms represent the degrees of freedom of motion which classically contribute to the heat capacity of gases, while only vibrations are needed to describe the heat capacities of most solids, as shown by the Dulong–Petit law. Other contributions can come from magnetic and electronic degrees of freedom in solids, but these rarely make substantial contributions.

For quantum mechanical reasons, at any given temperature, some of these degrees of freedom may be unavailable, or only partially available, to store thermal energy. In such cases, the heat capacity is a fraction of the maximum. As the temperature approaches absolute zero, the heat capacity of a system approaches zero because of loss of available degrees of freedom. Quantum theory can be used to quantitatively predict the heat capacity of simple systems.


Hypothermia is reduced body temperature that happens when a body dissipates more heat than it absorbs. In humans, it is defined as a body core temperature below 35.0 °C (95.0 °F). Symptoms depend on the temperature. In mild hypothermia there is shivering and mental confusion. In moderate hypothermia shivering stops and confusion increases. In severe hypothermia, there may be paradoxical undressing, in which a person removes their clothing, as well as an increased risk of the heart stopping.Hypothermia has two main types of causes. It classically occurs from exposure to extreme cold. It may also occur from any condition that decreases heat production or increases heat loss. Commonly this includes alcohol intoxication but may also include low blood sugar, anorexia, and advanced age. Body temperature is usually maintained near a constant level of 36.5–37.5 °C (97.7–99.5 °F) through thermoregulation. Efforts to increase body temperature involve shivering, increased voluntary activity, and putting on warmer clothing. Hypothermia may be diagnosed based on either a person's symptoms in the presence of risk factors or by measuring a person's core temperature.The treatment of mild hypothermia involves warm drinks, warm clothing, and physical activity. In those with moderate hypothermia, heating blankets and warmed intravenous fluids are recommended. People with moderate or severe hypothermia should be moved gently. In severe hypothermia, extracorporeal membrane oxygenation (ECMO) or cardiopulmonary bypass may be useful. In those without a pulse, cardiopulmonary resuscitation (CPR) is indicated along with the above measures. Rewarming is typically continued until a person's temperature is greater than 32 °C (90 °F). If there is no improvement at this point or the blood potassium level is greater than 12 mmol/liter at any time, resuscitation may be discontinued.Hypothermia is the cause of at least 1,500 deaths a year in the United States. It is more common in older people and males. One of the lowest documented body temperatures from which someone with accidental hypothermia has survived is 13.0 °C (55.4 °F) in a near-drowning of a 7-year-old girl in Sweden. Survival after more than six hours of CPR has been described. For those for whom ECMO or bypass is used, survival is around 50%. Deaths due to hypothermia have played an important role in many wars. The term is from Greek ὑπο, hupo, meaning "under", and θερμία, thermía, meaning "heat". The opposite of hypothermia is hyperthermia, an increased body temperature due to failed thermoregulation.


The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin (symbol: K) is the base unit of temperature in the International System of Units (SI).

Until 2018, the kelvin was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F). In other words, it was defined such that the triple point of water is exactly 273.16 K.

On 16 November 2018, a new definition was adopted, in terms of a fixed value of the Boltzmann constant. For legal metrology purposes, the new definition will officially come into force on 20 May 2019 (the 130th anniversary of the Metre Convention).The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907), who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or written as a degree. The kelvin is the primary unit of temperature measurement in the physical sciences, but is often used in conjunction with the degree Celsius, which has the same magnitude. The definition implies that absolute zero (0 K) is equivalent to −273.15 °C (−459.67 °F).

Relative humidity

Relative humidity (RH) is the ratio of the partial pressure of water vapor to the equilibrium vapor pressure of water at a given temperature. Relative humidity depends on temperature and the pressure of the system of interest. The same amount of water vapor results in higher relative humidity in cool air than warm air. A related parameter is that of dewpoint.

Standard conditions for temperature and pressure

Standard conditions for temperature and pressure are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST), although these are not universally accepted standards. Other organizations have established a variety of alternative definitions for their standard reference conditions.

In chemistry, IUPAC changed the definition of standard temperature and pressure (STP) in 1982:

Until 1982, STP was defined as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of exactly 1 atm (101.325 kPa).

Since 1982, STP is defined as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of exactly 105 Pa (100 kPa, 1 bar).STP should not be confused with the standard state commonly used in thermodynamic evaluations of the Gibbs energy of a reaction.

NIST uses a temperature of 20 °C (293.15 K, 68 °F) and an absolute pressure of 1 atm (14.696 psi, 101.325 kPa). This standard is also called normal temperature and pressure (abbreviated as NTP).

The International Standard Metric Conditions for natural gas and similar fluids are 288.15 K (15.00 °C; 59.00 °F) and 101.325 kPa.In industry and commerce, standard conditions for temperature and pressure are often necessary to define the standard reference conditions to express the volumes of gases and liquids and related quantities such as the rate of volumetric flow (the volumes of gases vary significantly with temperature and pressure) – standard cubic meters per second (sm3/s), and normal cubic meters per second (nm3/s). However, many technical publications (books, journals, advertisements for equipment and machinery) simply state "standard conditions" without specifying them, often leading to confusion and errors. Good practice always incorporates the reference conditions of temperature and pressure.


A thermometer is a device that measures temperature or a temperature gradient. A thermometer has two important elements: (1) a temperature sensor (e.g. the bulb of a mercury-in-glass thermometer or the digital sensor in an infrared thermometer) in which some change occurs with a change in temperature; and (2) some means of converting this change into a numerical value (e.g. the visible scale that is marked on a mercury-in-glass thermometer or the digital readout on an infrared model). Thermometers are widely used in technology and industry to monitor processes, in meteorology, in medicine, and in scientific research.

Some of the principles of the thermometer were known to Greek philosophers of two thousand years ago. The modern thermometer gradually evolved from the thermoscope with the addition of a scale in the early 17th century and standardisation through the 17th and 18th centuries.


Thermoregulation is the ability of an organism to keep its body temperature within certain boundaries, even when the surrounding temperature is very different. A thermoconforming organism, by contrast, simply adopts the surrounding temperature as its own body temperature, thus avoiding the need for internal thermoregulation. The internal thermoregulation process is one aspect of homeostasis: a state of dynamic stability in an organism's internal conditions, maintained far from thermal equilibrium with its environment (the study of such processes in zoology has been called physiological ecology). If the body is unable to maintain a normal temperature and it increases significantly above normal, a condition known as hyperthermia occurs. For humans, this occurs when the body is exposed to constant temperatures of approximately 55 °C (131 °F), and with prolonged exposure (longer than a few hours) at this temperature and up to around 75 °C (167 °F) death is almost inevitable. Humans may also experience lethal hyperthermia when the wet bulb temperature is sustained above 35 °C (95 °F) for six hours. The opposite condition, when body temperature decreases below normal levels, is known as hypothermia. It results when the homeostatic control mechanisms of heat within the body malfunction, causing the body to lose heat faster than producing it. Normal body temperature is around 37 °C (99 °F), and hypothermia sets in when the core body temperature gets lower than 35 °C (95 °F). Usually caused by prolonged exposure to cold temperatures, hypothermia is usually treated by methods that attempt to raise the body temperature back to a normal range.It was not until the introduction of thermometers that any exact data on the temperature of animals could be obtained. It was then found that local differences were present, since heat production and heat loss vary considerably in different parts of the body, although the circulation of the blood tends to bring about a mean temperature of the internal parts. Hence it is important to identify the parts of the body that most closely reflect the temperature of the internal organs. Also, for such results to be comparable, the measurements must be conducted under comparable conditions. The rectum has traditionally been considered to reflect most accurately the temperature of internal parts, or in some cases of sex or species, the vagina, uterus or bladder.Occasionally the temperature of the urine as it leaves the urethra may be of use in measuring body temperature. More often the temperature is taken in the mouth, axilla, ear or groin.Some animals undergo one of various forms of dormancy where the thermoregulation process temporarily allows the body temperature to drop, thereby conserving energy. Examples include hibernating bears and torpor in bats.

Meteorological data and variables
Scales of temperature

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