The temperature of an ideal monatomic gas is a measure related to the average kinetic energy of its atoms as they move. In Physics and Chemistry, monatomic is a combination of the words "mono" and "atomic" and means "single Atom. This page is about the physical properties of gas as a state of matter The kinetic energy of an object is the extra Energy which it possesses due to its motion In this animation, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure. In the Bohr model of the structure of an Atom, put forward by Niels Bohr in 1913 Electrons orbit a central nucleus. Helium ( He) is a colorless odorless tasteless non-toxic Inert Monatomic Chemical The Standard atmosphere is an international reference pressure defined as 101325 Pa and formerly used as unit of Pressure (symbol atm 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. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Physics the word system has a technical meaning namely it is the portion of the physical Universe chosen for analysis Specifically, temperature is a property of matter. Temperature is one of the principal parameters of thermodynamics. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " On the microscopic scale, temperature is defined as the average energy of microscopic motions of a single particle in the system per degree of freedom. For information on degrees of freedom in other sciences see Degrees of freedom. On the macroscopic scale, temperature is the unique physical property that determines the direction of heat flow between two objects placed in thermal contact. If no heat flow occurs, the two objects have the same temperature; otherwise heat flows from the hotter object to the colder object. These two basic principles are stated in the zeroth law and second law of thermodynamics, respectively. The zeroth law of thermodynamics is a generalized statement about thermal Equilibrium between bodies in contact The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which For a solid, these microscopic motions are principally the vibrations of its atoms about their sites in the solid. For an ideal monatomic gas, the microscopic motions are the translational motions of the constituent gas particles. These four properties that constitute an ideal gas can be easily remembered by the acronym RIPE which stands for - R andom Motion (molecules are in constant random motion For a multiatomic gas, vibrational and rotational motion should be included too. Vibration refers to mechanical Oscillations about an equilibrium point. A rotation is a movement of an object in a circular motion A two- Dimensional object rotates around a center (or point) of rotation

Temperature is measured with thermometers that may be calibrated to a variety of temperature scales. The thermometer is a device that measures Temperature or Temperature gradient using a variety of different principles it comes from the Greek roots Calibration is the process of establishing the relationship between a measuring device and the units of measure Kelvin Celsius (Centigrade Fahrenheit Rankine Delisle Newton Réaumur In most of the world (except for the United States, Jamaica, and a few other countries), the degree Celsius scale is used for most temperature measuring purposes. The United States of America —commonly referred to as the Jamaica (ˈdʒəˈmeɪkə} is an Island nation of the Greater Antilles, in length and as much as in width situated in the Caribbean Sea. The Celsius Temperature scale was previously known as the centigrade scale. 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. The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic 15 °C, or absolute zero. Absolute zero is the point at which molecules do not move (relative to the rest of the body more than they are required to by a quantum mechanical effect called Zero-point Many engineering fields in the U. S. , especially high-tech ones, also use the kelvin and degrees Celsius scales. However, the United States is the last major country in which the degree Fahrenheit temperature scale is used by most lay people, industry, popular meteorology, and government. Fahrenheit is a temperature scale named after Daniel Gabriel Fahrenheit (1686–1736 a German Physicist who proposed it in 1724 Meteorology (from Greek grc μετέωρος metéōros, "high in the sky" and grc -λογία -logia) is the Interdisciplinary 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. Rankine is a thermodynamic (absolute temperature scale named after the Scottish Engineer and Physicist William John Macquorn Rankine Combustion or burning is a complex sequence of Exothermic chemical reactions between a Fuel and an Oxidant accompanied by the production of

Overview

Intuitively, temperature is the measurement of how hot or cold something is, although the most immediate way in which we can measure this, by feeling it, is unreliable, resulting in the phenomenon of felt air temperature, which can differ at varying degrees from actual temperature. Felt air temperature (or apparent air temperature) is the Air Temperature perceived by the body which may differ from the actual temperature 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. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J A quantum mechanical system or particle that is bound, confined spacially can only take on certain discrete values of energy as opposed to classical particles which 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. FLUID ( F ast L ight '''U'''ser '''I'''nterface D esigner is a graphical editor that is used to produce FLTK Source code This article is about the physical phenomenon for the stochastic process see Wiener process. The thermal motions of atoms are very fast and temperatures close to absolute zero are required to directly observe them. Absolute zero is the point at which molecules do not move (relative to the rest of the body more than they are required to by a quantum mechanical effect called Zero-point 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. optical lattice is formed by the Interference of counterpropagating Laser beams which creates a periodic (in space intensity pattern This article covers adiabatic processes in Thermodynamics. For adiabatic processes in Quantum mechanics, see Adiabatic process (quantum mechanics Caesium or cesium (ˈsiːziəm is the Chemical element with the symbol Cs and Atomic number 55 They then turned off the entrapment lasers and directly measured atom velocities of 7 mm per second in order to calculate their temperature.

Molecules, such as O₂, have more degrees of freedom than single atoms: they can have rotational and vibrational motions as well as translational motion. In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by 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 rotation and vibration, will require a higher energy input to change the temperature by a certain amount, i. Diatomic molecules are molecules made only of two Atoms of either the same or different Chemical elements The prefix di- means two in Greek e. it will have a higher heat capacity than a monatomic gas. Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity

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. Absolute zero is the point at which molecules do not move (relative to the rest of the body more than they are required to by a quantum mechanical effect called Zero-point Thermodynamic temperature is the absolute measure of Temperature and is one of the principal parameters of Thermodynamics. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons By definition, absolute zero is a temperature of precisely 0 kelvins (−273. The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic 15 °C or −459. The Celsius Temperature scale was previously known as the centigrade scale. 67 °F). Fahrenheit is a temperature scale named after Daniel Gabriel Fahrenheit (1686–1736 a German Physicist who proposed it in 1724

Details

The formal properties of temperature follow from its mathematical definition (see below for the zeroth law definition and the second law definition) and are studied in thermodynamics and statistical mechanics. In Thermodynamics, the Internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature/entropy or pressure/volume Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically Stress is a measure of the average amount of Force exerted per unit Area. In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical The particle number, N, is the number of so called ' Elementary particles (or elementary constituents in a thermodynamical system. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics

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). In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy 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

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 Convection in the most general terms refers to the movement of molecules within Fluids (i Thermal radiation is Electromagnetic radiation emitted from the surface of an object which is due to the object's Temperature. 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  In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of

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. In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different By contrast, mass, volume, and entropy are extensive properties, and depend on the amount of material in the system. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the

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.

Temperature plays an important role in almost all fields of science, including physics, geology, chemistry, and biology.

Many physical properties of materials including the phase (solid, liquid, gaseous or plasma), density, solubility, vapor pressure, and electrical conductivity depend on the temperature. 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 A solid' object is in the States of matter characterized by resistance to Deformation and changes of Volume. Liquid is one of the principal States of matter. A liquid is a Fluid that has the particles loose and can freely form a distinct surface at the boundaries of This page is about the physical properties of gas as a state of matter In Physics and Chemistry, plasma is an Ionized Gas, in which a certain proportion of Electrons are free rather than being bound The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Solubility is the characteristic Physical property referring to the ability of a given substance the Solute, to dissolve in a Solvent. Vapor pressure (also known as equilibrium vapor pressure or saturation vapor pressure) is the Pressure of a Vapor in equilibrium Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an Electric current. Temperature also plays an important role in determining the rate and extent to which chemical reactions occur. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called 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. The incandescent light bulb, incandescent lamp or incandescent light globe is a source of electric Light that works by Incandescence, (a general Tungsten (ˈtʌŋstən also known as wolfram (/ˈwʊlfrəm/ is a Chemical element that has the symbol W and Atomic number 74 Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700

Temperature-dependence of the speed of sound in air c, density of air ρ and acoustic impedance Z vs. Sound is a vibration that travels through an elastic medium as a Wave. 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 temperature °C

Temperature measurement

Main article: Temperature measurement, see also 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 The International Temperature Scale of 1990 ( ITS-90) is an equipment calibration standard for making measurements on the Kelvin and

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. The thermometer is a device that measures Temperature or Temperature gradient using a variety of different principles it comes from the Greek roots Mercury (ˈmɜrkjʊri also called quicksilver or hydrargyrum, is a Chemical element with the symbol Hg ( Latinized hydrargyrum Ole Christensen Rømer (o(ːlə ˈʁœːˀmɐ in Danish 25 September 1644, Århus – 19 September 1710, Copenhagen) Fahrenheit's scale is still in use, alongside the Celsius scale and the kelvin scale. The Celsius Temperature scale was previously known as the centigrade scale. The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic

Units of temperature

The basic unit of temperature (symbol: T) in the International System of Units (SI) is the kelvin (Symbol: K). The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic The kelvin and Celsius (Centigrade) 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 the point at which molecules do not move (relative to the rest of the body more than they are required to by a quantum mechanical effect called Zero-point In Thermodynamics, the triple point of a substance is the Temperature and Pressure at which three phases (for example Gas, Liquid VSMOW, or Vienna Standard Mean Ocean Water, is an isotopic water standard defined in 1968 by the International Atomic Energy Agency. 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. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons At absolute zero, matter contains no thermal energy. Thermal energy is the sum of the sensible energy and latent 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. The Celsius Temperature scale was previously known as the centigrade scale. 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. Kelvin Celsius (Centigrade Fahrenheit Rankine Delisle Newton Réaumur

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 Physics and Chemistry, plasma is an Ionized Gas, in which a certain proportion of Electrons are free rather than being bound Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. In the study of QCD matter one routinely meets temperatures of the order of a few hundred MeV, equivalent to about 10¹² K. Quark matter or QCD matter (see QCD) refers to any of a number of theorized phases of matter whose degrees of freedom include Quarks and Gluons

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. The Celsius Temperature scale was previously known as the centigrade scale. Freezing Point (Chinese 冰點 Bīngdiǎn is a news journal in the People's Republic of China which has been the subject of controversy over its criticism The boiling point of a liquid is the temperature at which the Vapor pressure of the liquid equals the environmental pressure surrounding the liquid 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.

In the United States, the Fahrenheit scale is widely used. The United States of America —commonly referred to as the Fahrenheit is a temperature scale named after Daniel Gabriel Fahrenheit (1686–1736 a German Physicist who proposed it in 1724 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:

See temperature conversion formulas for conversions between most temperature scales. Kelvin Celsius (Centigrade Fahrenheit Rankine Delisle Newton Réaumur

Negative temperatures

See main article: Negative temperature. In Physics, certain systems can achieve negative temperatures; that is their Thermodynamic temperature can be of a negative quantity

For some systems and specific definitions of temperature, it is possible to obtain a negative temperature. In Physics, certain systems can achieve negative temperatures; that is their Thermodynamic temperature can be of a negative quantity A system with a negative temperature is not colder than absolute zero, but rather it is, in a sense, hotter than infinite temperature. Absolute zero is the point at which molecules do not move (relative to the rest of the body more than they are required to by a quantum mechanical effect called Zero-point Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness ^[2]

Comparison of temperature scales

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. In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and 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.

A basis for the definition of temperature can be obtained from the 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). The zeroth law of thermodynamics is a generalized statement about thermal Equilibrium between bodies in contact In Mathematics, a Binary relation R over a set X is transitive if whenever an element a is related to an element b In Mathematics, an equivalence relation is a Binary relation between two elements of a set which groups them together as being "equivalent" 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.

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. In the social sciences scaling is the process of measuring or ordering entities with respect to Quantitative attributes or traits

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^[3]:

(1)

where 'T is temperature, n is the number of moles of gas and R is the gas constant. The ideal gas law is the Equation of state of a hypothetical Ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834 This article is about proportionality the mathematical relation The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working 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.

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 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. These four properties that constitute an ideal gas can be easily remembered by the acronym RIPE which stands for - R andom Motion (molecules are in constant random motion Kinetic theory (or kinetic theory of gases) attempts to explain Macroscopic properties of Gases such as pressure temperature or volume by considering Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics 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 Maxwell–Boltzmann distribution is a Probability distribution with applications in Physics and Chemistry. The temperature of an ideal gas is related to its average kinetic energy via the equation^[3]:

, where k = R / n (n= Avogadro number, R= ideal gas constant). Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working

In the case of a monoatomic gas, the kinetic energy is:

(Note that a calculation of the kinetic energy of a more complicated object, such as a molecule, is slightly more involved. The kinetic energy of an object is the extra Energy which it possesses due to its motion Additional degrees of freedom are available, so molecular rotation or vibration must be included. For information on degrees of freedom in other sciences see Degrees of freedom. )

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. Neon (ˈniːɒn is the Chemical element that has the symbol Ne and Atomic number 10 Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 This article is about the physical phenomenon for the stochastic process see Wiener process. 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. The ideal gas law is the Equation of state of a hypothetical Ideal gas, first stated by Benoît Paul Émile 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. In Physics, a black body is an object that absorbs all light that falls on it 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 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.

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. Sunlight, in the broad sense is the total spectrum of the Electromagnetic radiation given off by the Sun. 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.

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 the 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. This temperature is thus like a test charge in that it facilitates a measure of the system even though temperature is not strictly defined there. In physical theories, a test particle is an idealized model of an object whose physical properties (usually Mass, Charge, or size) are assumed

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. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy 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.

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. 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. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, q_H and the heat ejected at the low temperature, q_C. The efficiency is the work divided by the heat put into the system or:

(2)

where w_cy is the work done per cycle. We see that the efficiency depends only on q_C/q_H. Because q_C and q_H correspond to heat transfer at the temperatures T_C and T_H, respectively, q_C/q_H should be some function of these temperatures:

(3)

Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Carnot's theorem, also called Carnot's rule is a principle which sets a limit on the maximum amount of efficiency any possible engine can obtain which thus solely depends on 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:

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(T₂)· g(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:

(4)

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

(5)

Notice that for T_C = 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:

(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:

(7)

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

(8)

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

See also

References

• Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed. ). W. H. Freeman Company. ISBN 0-7167-1088-9.  

External links

• An elementary introduction to temperature aimed at a middle school audience
• Why do we have so many temperature scales?
• A Brief History of Temperature Measurement
• What is Temperature? An introductory discussion of temperature as a manifestation of kinetic theory.