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94-439: The average temperature during the summer months on Taipalsaari is the highest among Finnish municipalities. [REDACTED] Media related to Taipalsaari at Wikimedia Commons [REDACTED] Taipalsaari travel guide from Wikivoyage This Southern Finland location article is a stub . You can help Misplaced Pages by expanding it . Temperature Temperature is a physical quantity that quantitatively expresses

188-427: A heuristic tool for solving problems. There was no agreement whether chemical molecules, as measured by atomic weights , were the same as physical molecules, as measured by kinetic theory . Planck's 1920 lecture continued: Nothing can better illustrate the positive and hectic pace of progress which the art of experimenters has made over the past twenty years, than the fact that since that time, not only one, but

282-430: A body in a state of thermodynamic equilibrium is always positive relative to absolute zero. Besides the internationally agreed Kelvin scale, there is also a thermodynamic temperature scale , invented by Lord Kelvin , also with its numerical zero at the absolute zero of temperature, but directly relating to purely macroscopic thermodynamic concepts, including the macroscopic entropy , though microscopically referable to

376-813: A characteristic voltage called the thermal voltage , denoted by V T . The thermal voltage depends on absolute temperature T as V T = k T q = R T F , {\displaystyle V_{\mathrm {T} }={kT \over q}={RT \over F},} where q is the magnitude of the electrical charge on the electron with a value 1.602 176 634 × 10  C . Equivalently, V T T = k q ≈ 8.617333262 × 10 − 5   V / K . {\displaystyle {V_{\mathrm {T} } \over T}={k \over q}\approx 8.617333262\times 10^{-5}\ \mathrm {V/K} .} At room temperature 300 K (27 °C; 80 °F), V T

470-410: A cycle of states of its working body. The engine takes in a quantity of heat Q 1 from a hot reservoir and passes out a lesser quantity of waste heat Q 2 < 0 to a cold reservoir. The net heat energy absorbed by the working body is passed, as thermodynamic work, to a work reservoir, and is considered to be the output of the engine. The cycle is imagined to run so slowly that at each point of

564-402: 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 range that they can be used for thermometry; this was important during the development of thermodynamics and is still of practical importance today. The ideal gas thermometer is, however, not theoretically perfect for thermodynamics. This

658-535: A form of the gas constant R , and macroscopic energies for macroscopic quantities of the substance. The iconic terse form of the equation S = k ln W on Boltzmann's tombstone is in fact due to Planck, not Boltzmann. Planck actually introduced it in the same work as his eponymous h . In 1920, Planck wrote in his Nobel Prize lecture: This constant is often referred to as Boltzmann's constant, although, to my knowledge, Boltzmann himself never introduced it—a peculiar state of affairs, which can be explained by

752-488: A gas can be calculated theoretically from the gas's molecular character, temperature, pressure, and the Boltzmann constant. For a gas of known molecular character and pressure, this provides a relation between temperature and the Boltzmann constant. Those quantities can be known or measured more precisely than can the thermodynamic variables that define the state of a sample of water at its triple point. Consequently, taking

846-510: A great number of methods have been discovered for measuring the mass of a molecule with practically the same accuracy as that attained for a planet. In versions of SI prior to the 2019 revision of the SI , the Boltzmann constant was a measured quantity rather than a fixed value. Its exact definition also varied over the years due to redefinitions of the kelvin (see Kelvin § History ) and other SI base units (see Joule § History ). In 2017,

940-406: A linear relation between their numerical scale readings, but it does require that the relation between their numerical readings shall be strictly monotonic . 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

1034-415: A loss of heat from a closed system, without phase change, without change of volume, and without a change in external force fields acting on it, decreases its temperature. 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

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1128-462: A spatially varying local property in that body, and this is because the temperature is an intensive variable. Temperature is a measure of a quality of a state of a material. 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. The quality of hotness refers to the state of material only in a particular locality, and in general, apart from bodies held in

1222-551: 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 k B T /2 where k B denotes the Boltzmann constant . The translational motion of the particle has three degrees of freedom, so that, except at very low temperatures where quantum effects predominate,

1316-415: 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 connected through the specifically permeable wall 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

1410-400: 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

1504-541: A suitable range of processes. This is a matter for study in non-equilibrium thermodynamics . Boltzmann constant The Boltzmann constant ( k B or k ) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the gas constant , in Planck's law of black-body radiation and Boltzmann's entropy formula , and

1598-435: A system undergoing a first-order phase change such as the melting of ice, as a closed system receives heat, without a change in its volume and without a 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,

1692-511: 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. Except for

1786-460: Is a proportionality factor between temperature and energy, its numerical value depends on the choice of units for energy and temperature. The small numerical value of the Boltzmann constant in SI units means a change in temperature by 1 K only changes a particle's energy by a small amount. A change of 1  °C is defined to be the same as a change of 1 K . The characteristic energy kT

1880-456: Is a more natural form and this rescaled entropy exactly corresponds to Shannon's subsequent information entropy . The characteristic energy kT is thus the energy required to increase the rescaled entropy by one nat . In semiconductors , the Shockley diode equation —the relationship between the flow of electric current and the electrostatic potential across a p–n junction —depends on

1974-520: Is a term encountered in many physical relationships. The Boltzmann constant sets up a relationship between wavelength and temperature (dividing hc / k by a wavelength gives a temperature) with one micrometer being related to 14 387 .777 K , and also a relationship between voltage and temperature ( kT in units of eV corresponds to a voltage) with one volt being related to 11 604 .518 K . The ratio of these two temperatures, 14 387 .777 K  /  11 604 .518 K  ≈ 1.239842,

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2068-485: Is a thermal energy of ⁠ 3 / 2 ⁠   k T per atom. This corresponds very well with experimental data. The thermal energy can be used to calculate the root-mean-square speed of the atoms, which turns out to be inversely proportional to the square root of the atomic mass . The root mean square speeds found at room temperature accurately reflect this, ranging from 1370 m/s for helium , down to 240 m/s for xenon . Kinetic theory gives

2162-409: 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

2256-662: Is approximately 25.85 mV which can be derived by plugging in the values as follows: V T = k T q = 1.38 × 10 − 23   J ⋅ K − 1 × 300   K 1.6 × 10 − 19   C ≃ 25.85   m V {\displaystyle V_{\mathrm {T} }={kT \over q}={\frac {1.38\times 10^{-23}\ \mathrm {J{\cdot }K^{-1}} \times 300\ \mathrm {K} }{1.6\times 10^{-19}\ \mathrm {C} }}\simeq 25.85\ \mathrm {mV} } At

2350-518: Is arbitrary, and 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 run in a fictive continuous cycle of successive processes that traverse

2444-454: 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. In contrast to real materials, the ideal gas does not liquefy or solidify, no matter how cold it is. Alternatively thinking, the ideal gas law, refers to the limit of infinitely high temperature and zero pressure; these conditions guarantee non-interactive motions of

2538-495: 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 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

2632-489: Is disregarded. In an ideal gas , and in other theoretically understood bodies, the Kelvin temperature is defined to be proportional to the average kinetic energy of non-interactively moving microscopic particles, which can be measured by suitable techniques. The proportionality constant is a simple multiple of the Boltzmann constant. If molecules, atoms, or electrons are emitted from material and their velocities are measured,

2726-551: Is exactly equal to −273.15 °C , or −459.67 °F . Referring to the Boltzmann constant , to the Maxwell–Boltzmann distribution , and to the Boltzmann statistical mechanical definition of entropy , as distinct from the Gibbs definition, for independently moving microscopic particles, disregarding interparticle potential energy, by international agreement, a temperature scale is defined and said to be absolute because it

2820-439: Is generally true only for classical systems with a large number of particles , and in which quantum effects are negligible. In classical statistical mechanics , this average is predicted to hold exactly for homogeneous ideal gases . Monatomic ideal gases (the six noble gases) possess three degrees of freedom per atom, corresponding to the three spatial directions. According to the equipartition of energy this means that there

2914-472: Is in common use in the United States. Water freezes at 32 °F and boils at 212 °F at sea-level atmospheric pressure. At the absolute zero of temperature, no energy can be removed from matter as heat, a fact expressed in the third law of thermodynamics . At this temperature, matter contains no macroscopic thermal energy, but still has quantum-mechanical zero-point energy as predicted by

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3008-523: Is independent of the characteristics of particular thermometric substances and thermometer mechanisms. Apart from absolute zero, it does not have a reference temperature. It is known as the Kelvin scale , widely used in science and technology. The kelvin (the unit name is spelled with a lower-case 'k') is the unit of temperature in the International System of Units (SI). The temperature of

3102-455: 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 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

3196-551: Is only one degree of freedom left to arbitrary choice, rather than two as in relative scales. For the Kelvin scale since May 2019, by international convention, the choice has been made to use knowledge of modes of operation of various thermometric devices, relying on microscopic kinetic theories about molecular motion. The numerical scale is settled by a conventional definition of the value of the Boltzmann constant , which relates macroscopic temperature to average microscopic kinetic energy of particles such as molecules. Its numerical value

3290-419: Is said to prevail throughout the body. 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 the 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

3384-501: Is the partition function . Again, it is the energy-like quantity k T that takes central importance. Consequences of this include (in addition to the results for ideal gases above) the Arrhenius equation in chemical kinetics . In statistical mechanics, the entropy S of an isolated system at thermodynamic equilibrium is defined as the natural logarithm of W , the number of distinct microscopic states available to

3478-399: Is the numerical value of hc in units of eV⋅μm. The Boltzmann constant provides a mapping from the characteristic microscopic energy E to the macroscopic temperature scale T = ⁠ E / k ⁠ . In fundamental physics, this mapping is often simplified by using the natural units of setting k to unity. This convention means that temperature and energy quantities have

3572-490: Is used in calculating thermal noise in resistors . The Boltzmann constant has dimensions of energy divided by temperature , the same as entropy and heat capacity . It is named after the Austrian scientist Ludwig Boltzmann . As part of the 2019 revision of the SI , the Boltzmann constant is one of the seven " defining constants " that have been given exact definitions. They are used in various combinations to define

3666-548: The Avogadro constant ) transforms the ideal gas law into an alternative form: p V = N k T , {\displaystyle pV=NkT,} where N is the number of molecules of gas. Given a thermodynamic system at an absolute temperature T , the average thermal energy carried by each microscopic degree of freedom in the system is ⁠ 1 / 2 ⁠   k T (i.e., about 2.07 × 10  J , or 0.013  eV , at room temperature). This

3760-497: The Boltzmann constant , the value of which is defined as fixed by international convention. Since May 2019, the magnitude of the kelvin is defined in relation to microscopic phenomena, characterized in terms of statistical mechanics. Previously, but since 1954, the International System of Units defined a scale and unit for the kelvin as a thermodynamic temperature , by using the reliably reproducible temperature of

3854-525: The Boltzmann constant . That constant refers to chosen kinds of motion of microscopic particles in the constitution of the body. In those kinds of motion, the particles move individually, without mutual interaction. Such motions are typically interrupted by inter-particle collisions, but for temperature measurement, the motions are chosen so that, between collisions, the non-interactive segments of their trajectories are known to be accessible to accurate measurement. For this purpose, interparticle potential energy

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3948-549: The CODATA recommended 1.380 649 × 10  J/K to be the final fixed value of the Boltzmann constant to be used for the International System of Units . As a precondition for redefining the Boltzmann constant, there must be one experimental value with a relative uncertainty below 1 ppm , and at least one measurement from a second technique with a relative uncertainty below 3 ppm. The acoustic gas thermometry reached 0.2 ppm, and Johnson noise thermometry reached 2.8 ppm. Since k

4042-472: The ideal gas law states that, for an ideal gas , the product of pressure p and volume V is proportional to the product of amount of substance n and absolute temperature T : p V = n R T , {\displaystyle pV=nRT,} where R is the molar gas constant ( 8.314 462 618 153 24  J⋅K ⋅ mol ). Introducing the Boltzmann constant as the gas constant per molecule k = R / N A ( N A being

4136-585: The standard state temperature of 298.15 K (25.00 °C; 77.00 °F), it is approximately 25.69 mV . The thermal voltage is also important in plasmas and electrolyte solutions (e.g. the Nernst equation ); in both cases it provides a measure of how much the spatial distribution of electrons or ions is affected by a boundary held at a fixed voltage. The Boltzmann constant is named after its 19th century Austrian discoverer, Ludwig Boltzmann . Although Boltzmann first linked entropy and probability in 1877,

4230-528: The third law of thermodynamics . It would be impossible to extract energy as heat from a body at that temperature. Temperature is important in all fields of natural science , including physics , chemistry , Earth science , astronomy , medicine , biology , ecology , material science , metallurgy , mechanical engineering and geography as well as most aspects of daily life. Many physical processes are related to temperature; some of them are given below: Temperature scales need two values for definition:

4324-602: The triple point of water as a second reference point, the first reference point being 0 K at absolute zero. Historically, the temperature of the triple point of water was defined as exactly 273.16 K. Today it is an empirically measured quantity. The freezing point of water at sea-level atmospheric pressure occurs at very close to 273.15 K ( 0 °C ). There are various 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

4418-459: The uncertainty principle , although this does not enter into the definition of absolute temperature. Experimentally, absolute zero can be approached only very closely; it can never be reached (the lowest temperature attained by experiment is 38 pK). Theoretically, in a body at a temperature of absolute zero, all classical motion of its particles has ceased and they are at complete rest in this classical sense. Absolute zero, defined as 0 K ,

4512-464: The zeroth law of thermodynamics says that they all measure the same quality. This means that for a body in its own state of internal thermodynamic equilibrium, every correctly calibrated thermometer, of whatever kind, that measures the temperature of the body, records one and the same temperature. For a body that is not in its own state of internal thermodynamic equilibrium, different thermometers can record different temperatures, depending respectively on

4606-409: The Boltzmann constant. Taking the value of the Boltzmann constant as a primarily defined reference of exactly defined value, a measurement of the speed of sound can provide a more precise measurement of the temperature of the gas. 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, through a small hole in

4700-480: The Gibbs statistical mechanical definition of entropy for the canonical ensemble , that takes interparticle potential energy into account, as well as independent particle motion so that it can account for measurements of temperatures near absolute zero. This scale has a reference temperature at the triple point of water, the numerical value of which is defined by measurements using the aforementioned internationally agreed Kelvin scale. Many scientific measurements use

4794-409: The Kelvin temperature scale (unit symbol: K), named in honor of the physicist who first defined it . It is an absolute scale. Its numerical zero point, 0 K , is at the absolute zero of temperature. Since May 2019, the kelvin has been defined through particle kinetic theory , and statistical mechanics. In the International System of Units (SI), the magnitude of the kelvin is defined in terms of

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4888-458: The attribute of hotness or coldness. Temperature is measured with a thermometer . It reflects the average kinetic energy of the vibrating and colliding atoms making up a substance. Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with

4982-616: The average pressure p for an ideal gas as p = 1 3 N V m v 2 ¯ . {\displaystyle p={\frac {1}{3}}{\frac {N}{V}}m{\overline {v^{2}}}.} Combination with the ideal gas law p V = N k T {\displaystyle pV=NkT} shows that the average translational kinetic energy is 1 2 m v 2 ¯ = 3 2 k T . {\displaystyle {\tfrac {1}{2}}m{\overline {v^{2}}}={\tfrac {3}{2}}kT.} Considering that

5076-412: The average translational kinetic energy of a freely moving particle in a system with temperature T will be 3 k B T /2 . Molecules, such as oxygen (O 2 ), have more degrees of freedom than single spherical atoms: they undergo rotational and vibrational motions as well as translations. Heating results in an increase of temperature due to an increase in the average translational kinetic energy of

5170-411: 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: The above definition, equation (1), of the absolute temperature, is due to Kelvin. It refers to systems closed to

5264-483: 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 limitations, most generally used practical thermometers are of

5358-408: The constituent molecules. The magnitude of the kelvin is now defined in terms of kinetic theory, derived from the value of the Boltzmann constant . Kinetic theory provides a microscopic account of temperature for some bodies of material, especially gases, based on macroscopic systems' being composed of many microscopic particles, such as molecules and ions of various species, the particles of

5452-501: 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 thermodynamic temperature does in fact have a definite numerical value that has been arbitrarily chosen by tradition and is dependent on the property of 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

5546-410: The containing wall. 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. Temperature is one of the principal quantities in the study of thermodynamics . Formerly,

5640-426: The cycle the working body is in a state of thermodynamic equilibrium. The successive processes of the cycle are thus imagined to run reversibly with no entropy production . Then the quantity of entropy taken in from the hot reservoir when the working body is heated is equal to that passed to the cold reservoir when the working body is cooled. Then the absolute or thermodynamic temperatures, T 1 and T 2 , of

5734-442: The definition just stated, was printed in 1853, a paper read in 1851. Numerical details were formerly settled by making one of the heat reservoirs a cell at the triple point of water, which was defined to have an absolute temperature of 273.16 K. Nowadays, the numerical value is instead obtained from measurement through the microscopic statistical mechanical international definition, as above. In thermodynamic terms, temperature

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5828-863: 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 kinetic theory and thermodynamics. They are more or less ideally realized in practically feasible physical devices and materials. Theoretically based temperature scales are used to provide calibrating standards for practical empirically based thermometers. In physics,

5922-607: The energy associated with each classical degree of freedom ( 1 2 k T {\displaystyle {\tfrac {1}{2}}kT} above) becomes E d o f = 1 2 T {\displaystyle E_{\mathrm {dof} }={\tfrac {1}{2}}T} As another example, the definition of thermodynamic entropy coincides with the form of information entropy : S = − ∑ i P i ln ⁡ P i . {\displaystyle S=-\sum _{i}P_{i}\ln P_{i}.} where P i

6016-426: The fact that Boltzmann, as appears from his occasional utterances, never gave thought to the possibility of carrying out an exact measurement of the constant. This "peculiar state of affairs" is illustrated by reference to one of the great scientific debates of the time. There was considerable disagreement in the second half of the nineteenth century as to whether atoms and molecules were real or whether they were simply

6110-455: The formulation of the first law of thermodynamics. Carnot had no sound understanding of heat and no specific concept of entropy. He wrote of 'caloric' and said that all the caloric that passed from the hot reservoir was passed into the cold reservoir. 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

6204-494: The hotness manifold. 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 . Such heat transfer occurs by conduction or by thermal radiation. Experimental physicists, for example Galileo and Newton , found that there are indefinitely many empirical temperature scales . Nevertheless,

6298-419: 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, the 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, the temperature can be regarded as

6392-409: The internationally agreed conventional temperature scale is called the Kelvin scale. It is calibrated through the internationally agreed and prescribed value of the Boltzmann constant, referring to motions of microscopic particles, such as atoms, molecules, and electrons, constituent in the body whose temperature is to be measured. In contrast with the thermodynamic temperature scale invented by Kelvin,

6486-428: The magnitude of the kelvin was defined in thermodynamic terms, but nowadays, as mentioned above, it is defined in terms of kinetic theory. The thermodynamic temperature is said to be 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

6580-419: The mechanisms of operation of the thermometers. 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. This does not require the two thermometers to have

6674-444: The middle of the nineteenth century. Empirically based temperature scales rely directly on measurements of simple macroscopic 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

6768-435: 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. As noted above, the speed of sound in a gas can be calculated from the gas's molecular character, temperature, pressure, and

6862-408: The most accurate measures of the Boltzmann constant were obtained by acoustic gas thermometry, which determines the speed of sound of a monatomic gas in a triaxial ellipsoid chamber using microwave and acoustic resonances. This decade-long effort was undertaken with different techniques by several laboratories; it is one of the cornerstones of the 2019 revision of the SI. Based on these measurements,

6956-400: The noise-power is directly proportional to the temperature of the resistor and to the value of its resistance and to the noise bandwidth. 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. Historically, till May 2019, the definition of the Kelvin scale

7050-423: The point chosen as zero degrees and the magnitudes of the incremental unit of temperature. The Celsius scale (°C) is used for common temperature measurements in most of the world. It is an empirical scale that developed historically, which led to its zero point 0 °C being defined as the freezing point of water , and 100 °C as the boiling point of water, both at atmospheric pressure at sea level. It

7144-454: The presently conventional Kelvin temperature is not defined through comparison with the temperature of a reference state of a standard body, nor in terms of macroscopic thermodynamics. Apart from the absolute zero of temperature, the Kelvin temperature of a body in a state of internal thermodynamic equilibrium is defined by measurements of suitably chosen of its physical properties, such as have precisely known theoretical explanations in terms of

7238-414: The relation was never expressed with a specific constant until Max Planck first introduced k , and gave a more precise value for it ( 1.346 × 10  J/K , about 2.5% lower than today's figure), in his derivation of the law of black-body radiation in 1900–1901. Before 1900, equations involving Boltzmann factors were not written using the energies per molecule and the Boltzmann constant, but rather using

7332-464: The relevant thermal energy per molecule. More generally, systems in equilibrium at temperature T have probability P i of occupying a state i with energy E weighted by the corresponding Boltzmann factor : P i ∝ exp ⁡ ( − E k T ) Z , {\displaystyle P_{i}\propto {\frac {\exp \left(-{\frac {E}{kT}}\right)}{Z}},} where Z

7426-403: The reservoirs are defined such that 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. Kelvin's original work postulating absolute temperature was published in 1848. It was based on the work of Carnot, before

7520-401: The same dimensions . In particular, the SI unit kelvin becomes superfluous, being defined in terms of joules as 1 K = 1.380 649 × 10  J . With this convention, temperature is always given in units of energy, and the Boltzmann constant is not explicitly needed in formulas. This convention simplifies many physical relationships and formulas. For example, the equipartition formula for

7614-438: The seven SI base units. The Boltzmann constant is defined to be exactly 1.380 649 × 10 joules per kelvin. Boltzmann constant : The Boltzmann constant, k , is one of seven fixed constants defining the International System of Units, the SI, with k = 1.380 649 x 10 J K . The Boltzmann constant is a proportionality constant between the quantities temperature (with unit kelvin) and energy (with unit joule). Macroscopically,

7708-453: 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. 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 the future. The speed of sound in

7802-604: The statistical mechanical entropy equal to the classical thermodynamic entropy of Clausius : Δ S = ∫ d Q T . {\displaystyle \Delta S=\int {\frac {{\rm {d}}Q}{T}}.} One could choose instead a rescaled dimensionless entropy in microscopic terms such that S ′ = ln ⁡ W , Δ S ′ = ∫ d Q k T . {\displaystyle {S'=\ln W},\quad \Delta S'=\int {\frac {\mathrm {d} Q}{kT}}.} This

7896-407: The 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

7990-489: The system given the macroscopic constraints (such as a fixed total energy E ): S = k ln ⁡ W . {\displaystyle S=k\,\ln W.} This equation, which relates the microscopic details, or microstates, of the system (via W ) to its macroscopic state (via the entropy S ), is the central idea of statistical mechanics. Such is its importance that it is inscribed on Boltzmann's tombstone. The constant of proportionality k serves to make

8084-432: The three degrees of freedom for movement of the molecule as a whole. Diatomic gases, for example, possess a total of six degrees of simple freedom per molecule that are related to atomic motion (three translational, two rotational, and one vibrational). At lower temperatures, not all these degrees of freedom may fully participate in the gas heat capacity, due to quantum mechanical limits on the availability of excited states at

8178-428: The transfer of matter and has a 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. Real-world bodies are often not in thermodynamic equilibrium and not homogeneous. For

8272-432: The translational motion velocity vector v has three degrees of freedom (one for each dimension) gives the average energy per degree of freedom equal to one third of that, i.e. ⁠ 1 / 2 ⁠   k T . The ideal gas equation is also obeyed closely by molecular gases; but the form for the heat capacity is more complicated, because the molecules possess additional internal degrees of freedom, as well as

8366-529: The unit symbol °C (formerly called centigrade ), the Fahrenheit scale (°F), and the Kelvin scale (K), with the third being used predominantly for scientific purposes. The kelvin is one of the seven base units in the International System of Units (SI). Absolute zero , i.e., zero kelvin or −273.15 °C, is the lowest point in the thermodynamic temperature scale. Experimentally, it can be approached very closely but not actually reached, as recognized in

8460-428: The value of the Boltzmann constant as a primarily defined reference of exactly defined value, a measurement of the speed of sound can provide a more precise measurement of the temperature of the gas. 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

8554-411: The zeroth law of thermodynamics. 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: Likewise, when

8648-432: Was called a centigrade scale because of the 100-degree interval. 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, so that a temperature increment of one degree Celsius is the same as an increment of one kelvin, though numerically the scales differ by an exact offset of 273.15. The Fahrenheit scale

8742-421: Was defined to be exactly 273.16 K . Since May 2019, that value has not been fixed by definition but is to be measured through microscopic phenomena, involving the Boltzmann constant, as described above. The microscopic statistical mechanical definition does not have a reference temperature. A material on which a macroscopically defined temperature scale may be based is the ideal gas . The pressure exerted by

8836-411: Was that invented by Kelvin, based on a ratio of quantities of energy in processes in an ideal Carnot engine, entirely in terms of macroscopic thermodynamics. That Carnot engine was to work between two temperatures, that of the body whose temperature was to be measured, and a reference, that of a body at the temperature of the triple point of water. Then the reference temperature, that of the triple point,

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