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Encyclopedia > Temperature
The temperature of an ideal monatomic gas is a measure related to the average kinetic energy of its atoms as they move. In this animation, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure. These room-temperature atoms have a certain, average speed (slowed down here two trillion fold).

Temperature is a physical property of a system that underlies the common notions of hot and cold; something that is hotter generally has the greater temperature. Temperature is one of the principal parameters of thermodynamics. On the microscopic scale, temperature is defined as simply the average energy of microscopic motions of a single particle in the system per degree of freedom. On the bulk scale, common to non-scientists, temperature is defined as that unique physical property that is shared between two otherwise entirely unlike things that happen to be in thermal equilibrium with each other (meaning, no net heat energy is exchanged between them). For a solid, these microscopic motions are principally the vibrations of the constituent atoms about their sites in the solid. For an ideal monatomic gas, the microscopic motions are the translational motions of the constituent gas particles. For multiatomic gas vibrational and rotational motion should be included too. Look up temperature in Wiktionary, the free dictionary. ... Image File history File links This is a lossless scalable vector image. ... Image File history File links Translational_motion. ... Image File history File links Translational_motion. ... In physics and chemistry, monatomic is a combination of the words mono and atomic, and means single atom. ... Gas phase particles (atoms, molecules, or ions) move around freely Gas is one of the four major states of matter, consisting of freely moving atoms or molecules without a definite shape and without a definite volume. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. ... General Name, symbol, number helium, He, 2 Chemical series noble gases Group, period, block 18, 1, s Appearance colorless Standard atomic weight 4. ... Standard atmosphere (symbol: atm) is a unit of pressure. ... One million million (1,000,000,000,000) is the natural number following 999,999,999,999 and preceding 1,000,000,000,001. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... A physical system is a system that is comprised of matter and energy. ... Thermodynamics (from the Greek Î¸ÎµÏÎ¼Î·, therme, meaning heat and Î´Ï…Î½Î±Î¼Î¹Ï‚, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ... Look up vibration in Wiktionary, the free dictionary. ... This article is about rotation as a movement of a physical body. ...

Temperature is measured with thermometers that may be calibrated to a variety of temperature scales. In most of the world (except for the United States, Jamaica, and a few other countries), the Celsius scale is used for most temperature measuring purposes. The entire scientific world (the U.S. included) measures temperature using the Celsius scale and thermodynamic temperature using the kelvin scale, which is just the Celsius scale shifted downwards so that 0 K[1]= -273.15 °C, or absolute zero. Many engineering fields in the U.S., especially high-tech ones, also use the kelvin and Celsius scales. The bulk of the U.S. however, (its lay people, industry, popular meteorology, and government) relies upon the Fahrenheit scale. Other engineering fields in the U.S. also rely upon the Rankine scale (a shifted Fahrenheit scale) when working in thermodynamic-related disciplines such as combustion. A common mercury thermometer A thermometer is a device that measures temperature or temperature gradient, using a variety of different principles. ... calibration refers to the process of determining the relation between the output (or response) of a measuring instrument and the value of the input quantity or attribute, a measurement standard. ... // Comparison of temperature scales Â¹ Normal human body temperature is 36. ... Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ... For other uses, see Kelvin (disambiguation). ... For other uses, see Absolute Zero (disambiguation). ... // Meteorology (from Greek: Î¼ÎµÏ„Î­Ï‰ÏÎ¿Î½, meteoron, high in the sky; and Î»ÏŒÎ³Î¿Ï‚, logos, knowledge) is the interdisciplinary scientific study of the atmosphere that focuses on weather processes and forecasting. ... For other uses, see Fahrenheit (disambiguation). ... For the idealized thermodynamic cycle for a steam engine, see Rankine cycle. ... This article is about the chemical reaction combustion. ...

Intuitively, temperature is a measure of how hot or cold something is. On the molecular level, temperature is the result of the motion of particles which make up a substance. Temperature increases as the energy of this motion increases. The motion may be the translational motion of the particle, or the internal energy of the particle due to molecular vibration or the excitation of an electron energy level. Although very specialized laboratory equipment is required to directly detect the translational thermal motions, thermal collisions by atoms or molecules with small particles suspended in a fluid produces Brownian motion that can be seen with an ordinary microscope. The thermal motions of atoms are very fast and temperatures close to absolute zero are required to directly observe them. For instance, when scientists at the NIST achieved a record-setting cold temperature of 700 nK (1 nK = 10−9 K) in 1994, they used optical lattice laser equipment to adiabatically cool caesium atoms. They then turned off the entrapment lasers and directly measured atom velocities of 7 mm per second in order to calculate their temperature. For other uses, see Electron (disambiguation). ... A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... Three different views of Brownian motion, with 32 steps, 256 steps, and 2048 steps denoted by progressively lighter colors. ... For other uses, see Absolute Zero (disambiguation). ... NIST logo The National Institute of Standards and Technology (NIST, formerly known as The National Bureau of Standards) is a non-regulatory agency of the United States Department of Commerceâ€™s Technology Administration. ... An optical lattice is formed by using counterpropagating laser beams to create a periodic (in space) intensity pattern. ... In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid. ... General Name, Symbol, Number caesium, Cs, 55 Chemical series alkali metals Group, Period, Block 1, 6, s Appearance silvery gold Standard atomic weight 132. ...

Molecules, such as O2, have more degrees of freedom than single atoms: they can have rotational and vibrational motions as well as translational motion. An increase in temperature will cause the average translational energy to increase. It will also cause the energy associated with vibrational and rotational modes to increase. Thus a diatomic gas, with extra degrees of freedom like rotation and vibration, will require a higher energy input to change the temperature by a certain amount, i.e. it will have a higher heat capacity than a monatomic gas. 3D (left and center) and 2D (right) representations of the terpenoid molecule atisane. ... The phrase degrees of freedom is used in three different branches of science: in physics and physical chemistry, in mechanical and aerospace engineering, and in statistics. ... A computer rendering of the Nitrogen Molecule, which is a diatomic molecule. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

The process of cooling involves removing energy from a system. When there is no more energy able to be removed, the system is said to be at absolute zero, which is the point on the thermodynamic (absolute) temperature scale where all kinetic motion in the particles comprising matter ceases and they are at complete rest in the “classic” (non-quantum mechanical) sense. By definition, absolute zero is a temperature of precisely 0 kelvins (−273.15 °C or −459.67 °F). For other uses, see Absolute Zero (disambiguation). ... Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... For other uses, see Kelvin (disambiguation). ... Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ... For other uses, see Fahrenheit (disambiguation). ...

## Details

Conjugate variables
of thermodynamics
Pressure Volume
(Stress) (Strain)
Temperature Entropy
Chem. potential Particle no.

Contrary to other thermodynamic quantities such as entropy and heat, whose microscopic definitions are valid even far away from thermodynamic equilibrium, temperature being an average energy per particle can only be defined at thermodynamic equilibrium, or at least local thermodynamic equilibrium (see below). For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. ...

As a system receives heat, its temperature rises; similarly, a loss of heat from the system tends to decrease its temperature (at the--uncommon--exception of negative temperature; see below).

When two systems are at the same temperature, no heat transfer occurs between them. When a temperature difference does exist, heat will tend to move from the higher-temperature system to the lower-temperature system, until they are at thermal equilibrium. This heat transfer may occur via conduction, convection or radiation or combinations of them (see heat for additional discussion of the various mechanisms of heat transfer) and some ions may vary . Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter, from a region of higher temperature to a region of lower temperature, and hence acts to even out temperature differences. ... Convection in the most general terms refers to the movement of currents within fluids (i. ... Radiant heat redirects here. ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ...

Temperature is also related to the amount of internal energy and enthalpy of a system: the higher the temperature of a system, the higher its internal energy and enthalpy. In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... t In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or Î”H, or rarely as Ï‡) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ...

Temperature is an intensive property of a system, meaning that it does not depend on the system size, the amount or type of material in the system, the same as for the pressure and density. By contrast, mass, volume, and entropy are extensive properties, and depend on the amount of material in the system. An intensive property is sometimes defined as a ratio of two extensive properties. ... This article is about pressure in the physical sciences. ... For other uses, see Density (disambiguation). ... For other uses, see Mass (disambiguation). ... For other uses, see Volume (disambiguation). ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... In physics and chemistry an intensive property (also called a bulk property) of a system is a physical property of the system that does not depend on the system size or the amount of material in the system. ...

## The role of temperature in nature

Water freezes at 0 °C. The frost shown here is at -17 °C.
A map of mean temperatures as a function of location.

Many physical properties of materials including the phase (solid, liquid, gaseous or plasma), density, solubility, vapor pressure, and electrical conductivity depend on the temperature. Temperature also plays an important role in determining the rate and extent to which chemical reactions occur. This is one reason why the human body has several elaborate mechanisms for maintaining the temperature at 37 °C, since temperatures only a few degrees higher can result in harmful reactions with serious consequences. Temperature also controls the type and quantity of thermal radiation emitted from a surface. One application of this effect is the incandescent light bulb, in which a tungsten filament is electrically heated to a temperature at which significant quantities of visible light are emitted. In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i. ... This box:      For other uses, see Solid (disambiguation). ... For other uses, see Liquid (disambiguation). ... Gas phase particles (atoms, molecules, or ions) move around freely Gas is one of the four major states of matter, consisting of freely moving atoms or molecules without a definite shape and without a definite volume. ... For other uses, see Plasma. ... For other uses, see Density (disambiguation). ... Solubility is a chemical property referring to the ability for a given substance, the solute, to dissolve in a solvent. ... Vapor pressure is the pressure of a vapor in equilibrium with its non-vapor phases. ... Not to be confused with electrical conductance, a measure of an objects or circuits ability to conduct an electric current between two points, which is dependent on the electrical conductivity and the geometric dimensions of the conducting object. ... For other uses, see Chemical reaction (disambiguation). ... Light bulb redirects here. ... For other uses, see Tungsten (disambiguation). ... Electricity (from New Latin Ä“lectricus, amberlike) is a general term for a variety of phenomena resulting from the presence and flow of electric charge. ... For other uses, see Light (disambiguation). ...

Temperature-dependence of the speed of sound in air c, density of air ρ and acoustic impedance Z vs. temperature °C This page is about the physical speed of sound waves in a medium. ... The acoustic impedance Z (or sound impedance) is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments. ...

 Impact of temperature on speed of sound, air density and acoustic impedance T in °C c in m/s ρ in kg/m³ Z in N·s/m³ −10 325.4 1.341 436.5 −5 328.5 1.316 432.4 0 331.5 1.293 428.3 5 334.5 1.269 424.5 10 337.5 1.247 420.7 15 340.5 1.225 417.0 20 343.4 1.204 413.5 25 346.3 1.184 410.0 30 349.2 1.164 406.6

## Temperature measurement

Main article: Temperature measurement, see also The International Temperature Scale. A medical/clinical thermometer showing the temperature of 38. ... ITS-90 is the current version of the International Temperature Scale. ...

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, alongside the Celsius scale and the kelvin scale. A common mercury thermometer A thermometer is a device that measures temperature or temperature gradient, using a variety of different principles. ... Daniel Gabriel Fahrenheit (24 May 1686 â€“ 16 September 1736) was a German physicist and engineer who worked most of his life in the Dutch Republic. ... This article is about the element. ... Ole RÃ¸mer. ... Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ... For other uses, see Kelvin (disambiguation). ...

### Units of temperature

The basic unit of temperature (symbol: T) in the International System of Units (SI) is the kelvin (Symbol: K). The kelvin and Celsius scales are, by international agreement, defined by two points: absolute zero, and the triple point of Vienna Standard Mean Ocean Water (water specially prepared with a specified blend of hydrogen and oxygen isotopes). Absolute zero is defined as being precisely 0 K and −273.15 °C. Absolute zero is where all kinetic motion in the particles comprising matter ceases and they are at complete rest in the “classic” (non-quantum mechanical) sense. At absolute zero, matter contains no thermal energy. Also, the triple point of water is defined as being precisely 273.16 K and 0.01 °C. This definition does three things: 1) it fixes the magnitude of the kelvin unit as being precisely 1 part in 273.16 parts the difference between absolute zero and the triple point of water; 2) it establishes that one kelvin has precisely the same magnitude as a one degree increment on the Celsius scale; and 3) it establishes the difference between the two scales’ null points as being precisely 273.15 kelvins (0 K = −273.15 °C and 273.16 K = 0.01 °C). Formulas for converting from these defining units of temperature to other scales can be found at Temperature conversion formulas. Look up si, Si, SI in Wiktionary, the free dictionary. ... For other uses, see Kelvin (disambiguation). ... For other uses, see Absolute Zero (disambiguation). ... In physics, the triple point of a substance is the temperature and pressure at which three phases (gas, liquid, and solid) of that substance may coexist in thermodynamic equilibrium. ... VSMOW, or Vienna Standard Mean Ocean Water, is an isotopic water standard defined in 1968 by the International Atomic Energy Agency. ... Kinetic energy (also called vis viva, or living force) is energy possessed by a body by virtue of its motion. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ... Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ... // Comparison of temperature scales Â¹ Normal human body temperature is 36. ...

In the field of plasma physics, because of the high temperatures encountered and the electromagnetic nature of the phenomena involved, it is customary to express temperature in electronvolts (eV) or kiloelectronvolts (keV), where 1 eV = 11,604 K. In the study of QCD matter one routinely meets temperatures of the order of a few hundred MeV, equivalent to about 1012 K. A Plasma lamp In physics and chemistry, a plasma is an ionized gas, and is usually considered to be a distinct phase of matter. ... Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. ... The electronvolt (symbol eV) is a unit of energy. ... Quark matter or QCD matter refers to any of a number of phases of matter whose degrees of freedom include quarks and gluons. ... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...

For everyday applications, it's very often convenient to use the Celsius scale, in which 0 °C corresponds to the temperature at which water freezes and 100 °C corresponds to the boiling point of water at sea level. In this scale a temperature difference of 1 degree is the same as a 1 K temperature difference, so the scale is essentially the same as the kelvin scale, but offset by the temperature at which water freezes (273.15 K). Thus the following equation can be used to convert from degrees Celsius to kelvins. Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ... Freezing point can refer to several things: For the chemistry term, see Melting point. ... Italic text This article is about the boiling point of liquids. ...

$mathrm{K = [^circ C] left(frac{1 , K}{1, ^circ C}right) + 273.15, K}$

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 following formula can be used to convert from Fahrenheit to Celsius: For other uses, see Fahrenheit (disambiguation). ...

$mathrm{ !^circ C = frac{5, ^circ C}{9, ^circ F}( ^circ F - 32 ^circ )}$

See temperature conversion formulas for conversions between most temperature scales. // Comparison of temperature scales Â¹ Normal human body temperature is 36. ...

### Negative temperatures

See main article: Negative temperature.

For some systems and specific definitions of temperature, it is possible to obtain a negative temperature. A system with a negative temperature is not colder than absolute zero, but rather it is, in a sense, hotter than infinite temperature.[citation needed] In physics, certain systems can achieve negative temperatures; that is, their thermodynamic temperature can be a negative quantity. ... In physics, certain systems can achieve negative temperatures; that is, their thermodynamic temperature can be a negative quantity. ... For other uses, see Absolute Zero (disambiguation). ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ...

## Comparison of temperature scales

Comparison of temperature scales
Comment Kelvin Celsius Fahrenheit Rankine Delisle Newton Réaumur Rømer
Absolute zero 0 −273.15 −459.67 0 559.725 −90.14 −218.52 −135.90
Lowest recorded surface temperature on Earth
(Vostok, Antarctica - July 21, 1983)
184 −89 −128.2 331.47 283.5 −29.37 −71.2 −39.225
Celsius / Fahrenheit's "cross-over" temperature 233.15 −40 –40 419.67 . . . .
Fahrenheit's ice/salt mixture 255.37 −17.78 0 459.67 176.67 −5.87 −14.22 −1.83
Water melts (at standard pressure) 273.15 0 32 491.67 150 0 0 7.5
Average surface temperature on Earth 288 15 59 518.67 127.5 4.95 12 15.375
Average human body temperature ¹ 309.95 36.8 98.24 557.91 94.8 12.144 29.44 26.82
Highest recorded surface temperature on Earth
(Al 'Aziziyah, Libya - September 13, 1922)
331 58 136.4 596.07 63 19.14 46.4 37.95
Water boils (at standard pressure) 373.1339 99.9839 211.97102 671.64102 0 33 80 60
Titanium melts 1941 1668 3034 3494 −2352 550 1334 883
The surface of the Sun 5800 5526 9980 10440 −8140 1823 4421 2909

¹ Normal human body temperature is 36.6 °C ±0.7 °C, or 98.2 °F ±1.3 °F. The commonly given value 98.6 °F is simply the exact conversion of the nineteenth-century German standard of 37 °C. Since it does not list an acceptable range, it could therefore be said to have excess (invalid) precision. Here's a list of various measurements.
Some numbers in this table have been rounded off. For other uses, see Kelvin (disambiguation). ... Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ... For other uses, see Fahrenheit (disambiguation). ... For the idealized thermodynamic cycle for a steam engine, see Rankine cycle. ... The Delisle scale is a temperature scale invented in 1732 by the French astronomer Joseph-Nicolas Delisle (1688&#8211;1768). ... Around 1700, Isaac Newton (1642&#8211;1727) applied his mind to the problem of heat. ... The degree RÃ©aumur is a unit of temperature named after RenÃ© Antoine Ferchault de RÃ©aumur, who first proposed it in 1731. ... RÃ¸mer is a disused temperature scale named after the Danish astronomer Ole Christensen RÃ¸mer, who proposed it in 1701. ... For other uses, see Absolute Zero (disambiguation). ... Vostok, Antarctica is a Russian research station located near the Geomagnetic South Pole (see South Pole), at the center of the East Antarctic Ice Sheet. ... is the 202nd day of the year (203rd in leap years) in the Gregorian calendar. ... Year 1983 (MCMLXXXIII) was a common year starting on Saturday (link displays the 1983 Gregorian calendar). ... In chemistry and other sciences, STP or standard temperature and pressure is a standard set of conditions for experimental measurements, to enable comparisons to be made between sets of data. ... The average surface temperature of the earth is defined as the combined temperature of near-surface air temperature over land and sea surface temperature. ... Al Aziziyah is one of the municipalities of Libya, located in the north of the country. ... is the 256th day of the year (257th in leap years) in the Gregorian calendar. ... Year 1922 (MCMXXII) was a common year starting on Sunday (link will display full calendar) of the Gregorian calendar. ... In chemistry and other sciences, STP or standard temperature and pressure is a standard set of conditions for experimental measurements, to enable comparisons to be made between sets of data. ... General Name, symbol, number titanium, Ti, 22 Chemical series transition metals Group, period, block 4, 4, d Appearance silvery metallic Standard atomic weight 47. ... The photosphere of an astronomical object is the region at which the optical depth becomes one for a photon of wavelength equal to 5000 angstroms. ... Normal human body temperature is a concept that depends on the place in the body at which the measurement is made. ...

## Theoretical foundation of temperature

### Zeroth-law definition of temperature

While most people have a basic understanding of the concept of temperature, its formal definition is rather complicated. Before jumping to a formal definition, let us consider the concept of thermal equilibrium. If two systems with fixed volumes are brought together in thermal contact, changes most likely will take place in the properties of both systems. These changes are caused by the transfer of heat between the systems. A state must be reached in which no further changes occur, to put the objects into thermal equilibrium. In thermodynamics, a thermodynamic system is in thermodynamic equilibrium if its energy distribution equals a Maxwell-Boltzmann-distribution. ...

Now a basis for the definition of temperature can be obtained from the so-called zeroth law of thermodynamics which states that if two systems, A and B, are in thermal equilibrium and a third system C is in thermal equilibrium with system A then systems B and C will also be in thermal equilibrium (being in thermal equilibrium is a transitive relation; moreover, it is an equivalence relation). This is an empirical fact, based on observation rather than theory. Since A, B, and C are all in thermal equilibrium, it is reasonable to say each of these systems shares a common value of some property. We call this property temperature. The zeroth law of thermodynamics may be succintly stated as: If two thermodynamic systems A and B are in thermal equilibrium, and B and C are also in thermal equilibrium, then A and C are in thermal equilibrium. ... In mathematics, a binary relation R over a set X is transitive if it holds for all a, b, and c in X, that if a is related to b and b is related to c, then a is related to c. ... In mathematics, an equivalence relation is a binary relation between two elements of a set which groups them together as being equivalent in some way. ...

Generally, it is not convenient to place any two arbitrary systems in thermal contact to see if they are in thermal equilibrium and thus have the same temperature. Also, it would only provide an ordinal scale. Scaling is the measurement of a variable in such a way that it can be expressed on a continuum. ...

Therefore, it is useful to establish a temperature scale based on the properties of some reference system. Then, a measuring device can be calibrated based on the properties of the reference system and used to measure the temperature of other systems. One such reference system is a fixed quantity of gas. The ideal gas law indicates that the product of the pressure and volume (P · V) of a gas is directly proportional to the temperature: Isotherms of an ideal gas The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by BenoÃ®t Paul Ã‰mile Clapeyron in 1834. ... This article is about proportionality, the mathematical relation. ...

$P cdot V = n cdot R cdot T$ (1)

where 'T is temperature, n is the number of moles of gas and R is the gas constant. Thus, one can define a scale for temperature based on the corresponding pressure and volume of the gas: the temperature in kelvins is the pressure in pascals of one mole of gas in a container of one cubic metre, divided by 8.31... In practice, such a gas thermometer is not very convenient, but other measuring instruments can be calibrated to this scale. The mole (symbol: mol) is one of the seven SI base units and is commonly used in chemistry. ... The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ...

It is also interesting to note that pressure, volume, and the number of moles of a substance are all inherently greater than or equal to zero. This suggests that temperature must also be greater than or equal to zero. As a practical matter it is not possible to use a gas thermometer to measure absolute zero temperature since the gasses tend to condense into a liquid long before the temperature reaches zero. It is possible, however, to extrapolate how many degrees below the present temperature the absolute zero is from the temperature range where Equation 1 works.

### Temperature in gases

For an ideal gas the kinetic theory of gases uses statistical mechanics to relate the temperature to the average kinetic energy of the atoms in the system. This average energy is independent of particle mass, which seems counter-intuitive to many people. Temperature is related only to the average kinetic energy of the particles in a gas - each particle has its own energy which may or may not correspond to the average; the distribution of energies (and thus speeds) of the particles in any gas are given by the Maxwell-Boltzmann distribution. The temperature of an ideal gas is related to its average kinetic energy via the equation:
An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ... Kinetic theory or kinetic theory of gases attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecular composition and motion. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

$overline{E}_k = begin{matrix} frac{3}{2} end{matrix} kT$, where k = nR / NA (n= number of moles, R= ideal gas constant, NA = Avogadro's number).

In the case of a monoatomic gas, the kinetic energy is:
Molar gas constant (also known as universal gas constant, usually denoted by symbol R) is the constant occurring in the universal gas equation, i. ... Avogadros number, also called Avogadros constant (NA), named after Amedeo Avogadro, is formally defined to be the number of carbon-12 atoms in 12 grams (0. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ...

$E_k = begin{matrix} frac{1}{2} end{matrix} mv^2$

(Note that a calculation of the kinetic energy of a more complicated object, such as a molecule, is slightly more involved. Additional degrees of freedom are available, so molecular rotation or vibration must be included.)

The second law of thermodynamics states that any two given systems when interacting with each other will later reach the same average energy per particle (and hence the same temperature). In a mixture of particles of various mass, the heaviest particles will move more slowly than lighter counterparts, but will still have the same average energy. A neon atom moves slower relative to a hydrogen molecule of the same kinetic energy; a pollen particle moves in a slow Brownian motion among fast moving water molecules, etc. A visual illustration of this from Oklahoma State University makes the point more clear. Particles with different mass have different velocity distributions, but the average kinetic energy is the same because of the ideal gas law. Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters. ... For other uses, see Neon (disambiguation). ... This article is about the chemistry of hydrogen. ... Three different views of Brownian motion, with 32 steps, 256 steps, and 2048 steps denoted by progressively lighter colors. ... Isotherms of an ideal gas The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by BenoÃ®t Paul Ã‰mile Clapeyron in 1834. ...

### Temperature of the vacuum

It is possible to use the zeroth law definition of temperature to assign a temperature to something we don't normally associate temperatures with, like a perfect vacuum. Because all objects emit black body radiation, a thermometer in a vacuum away from thermally radiating sources will radiate away its own thermal energy; decreasing in temperature indefinitely until it reaches the zero-point energy limit. At that point it can be said to be in equilibrium with the vacuum and by definition at the same temperature. If we could find a gas that behaved ideally all the way down to absolute zero the kinetic theory of gases tells us that it would achieve zero kinetic energy per particle, and thereby achieve absolute zero temperature. Thus, by the zeroth law a perfect, isolated vacuum is at absolute zero temperature. Note that in order to behave ideally in this context it is necessary for the atoms of the gas to have no zero point energy. It will turn out not to matter that this is not possible because the second law definition of temperature will yield the same result for any unique vacuum state. As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ... In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system. ...

More realistically, no such ideal vacuum exists. For instance a thermometer in a vacuum chamber which is maintained at some finite temperature (say, chamber is in the lab at room temperature) will equilibrate with the thermal radiation it receives from the chamber and with time reaches the temperature of the chamber. If a thermometer orbiting the Earth is exposed to a sunlight, then it equilibrates at the temperature at which power received by the thermometer from the Sun is exactly equal to the power radiated away by thermal radiation of the thermometer. For a black body this equilibrium temperature is about 281 K (+8 C). Earth average temperature (which is maintained by similar balance) is close to this temperature. Prism splitting light High Resolution Solar Spectrum Sunlight in the broad sense is the total spectrum of the electromagnetic radiation given off by the Sun. ...

A thermometer isolated from solar radiation (in the shade of the Earth, for example) is still exposed to thermal radiation of Earth - thus will show some equilibrium temperature at which it receives and radiates equal amount of energy. If this thermometer is close to Earth then its equilibrium temperature is about 236 K (-37 C) provided that Earth surface is at 281 K.

A thermometer far away from Solar system still receives Cosmic microwave background radiation. Equilibrium temperature of such thermometer is about 2.725 K, which is the temperature of a photon gas constituting black body microwave background radiation at present state of expansion of Universe. This temperature is sometimes referred to as the temperature of space. CMB redirects here. ...

### Second-law definition of temperature

In the previous section temperature was defined in terms of the Zeroth Law of thermodynamics. It is also possible to define temperature in terms of the second law of thermodynamics, which deals with entropy. Entropy is a measure of the disorder in a system. 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. Consider 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 came up the same. The second law of thermodynamics is an expression of the universal law of increasing entropy. ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ...

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 40% heads and 60% tails, et cetera. 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 number of combinations corresponding to ~50% heads and ~50% tails dominates 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.

We previously stated that temperature controls the flow of heat between two systems and we have just shown that the universe, and we would expect any natural system, tends to progress so as to maximize entropy. Thus, we would expect there to be some relationship between temperature and entropy. In order to find this relationship let's first consider the relationship between heat, work and temperature. A heat engine is a device for converting heat into mechanical work and analysis of the Carnot heat engine provides the necessary relationships we seek. 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 or: A heat engine is a physical or theoretical device that converts thermal energy to mechanical output. ... A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. ...

$textrm{efficiency} = frac {w_{cy}}{q_H} = frac{q_H-q_C}{q_H} = 1 - frac{q_C}{q_H}$ (2)

where wcy is the work done per cycle. We see that 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:

$frac{q_C}{q_H} = f(T_H,T_C)$ (3)

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: A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. ...

$q_{13} = frac{q_1 q_2} {q_2 q_3}$

which implies:

q13 = f(T1,T3) = f(T1,T2)f(T2,T3)

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. We can now choose a temperature scale with the property that:

$frac{q_C}{q_H} = frac{T_C}{T_H}$ (4)

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

$textrm{efficiency} = 1 - frac{q_C}{q_H} = 1 - frac{T_C}{T_H}$ (5)

Notice that 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:

$frac {q_H}{T_H} - frac{q_C}{T_C} = 0$

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

$dS = frac {dq_mathrm{rev}}{T}$ (6)

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 we described previously. We can rearranging Equation 6 to get a new definition for temperature in terms of entropy and heat:

$T = frac{dq_mathrm{rev}}{dS}$ (7)

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

$frac{1}{T} = frac{dS}{dE}$ (8)

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

## References

1. ^ This means "zero kelvin": using the degree symbol for an absolute temperature (as in 0°K) is a common error
• Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9.

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