1.
Thermodynamic temperature
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Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is defined by the law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, absolute zero, the constituents of matter have minimal motion. In the quantum-mechanical description, matter at absolute zero is in its ground state, the International System of Units specifies a particular scale for thermodynamic temperature. It uses the Kelvin scale for measurement and selects the point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically, the Rankine scale, using the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United States in some engineering fields. ITS-90 gives a means of estimating the thermodynamic temperature to a very high degree of accuracy. Internal energy is called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a degree of freedom. At equilibrium, each degree of freedom will have on average the energy, k B T /2 where k B is the Boltzmann constant. Temperature is a measure of the random submicroscopic motions and vibrations of the constituents of matter. These motions comprise the internal energy of a substance, more specifically, the thermodynamic temperature of any bulk quantity of matter is the measure of the average kinetic energy per classical degree of freedom of its constituent particles. Translational motions are almost always in the classical regime, translational motions are ordinary, whole-body movements in three-dimensional space in which particles move about and exchange energy in collisions. Figure 1 below shows translational motion in gases, Figure 4 below shows translational motion in solids, Zero kinetic energy remains in a substance at absolute zero. Throughout the scientific world where measurements are made in SI units, many engineering fields in the U. S. however, measure thermodynamic temperature using the Rankine scale. By international agreement, the kelvin and its scale are defined by two points, absolute zero, and the triple point of Vienna Standard Mean Ocean Water. Absolute zero, the lowest possible temperature, is defined as being precisely 0 K, the triple point of water is defined as being precisely 273.16 K and 0.01 °C. This definition does three things, It fixes the magnitude of the unit as being precisely 1 part in 273.15 kelvins
2.
Enthalpy
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Enthalpy /ˈɛnθəlpi/ is a measurement of energy in a thermodynamic system. It is the thermodynamic quantity equivalent to the heat content of a system. It is equal to the energy of the system plus the product of pressure. Enthalpy is defined as a function that depends only on the prevailing equilibrium state identified by the systems internal energy, pressure. The unit of measurement for enthalpy in the International System of Units is the joule, but other historical, conventional units are still in use, such as the British thermal unit and the calorie. At constant pressure, the enthalpy change equals the energy transferred from the environment through heating or work other than expansion work, the total enthalpy, H, of a system cannot be measured directly. The same situation exists in classical mechanics, only a change or difference in energy carries physical meaning. Enthalpy itself is a potential, so in order to measure the enthalpy of a system, we must refer to a defined reference point, therefore what we measure is the change in enthalpy. The ΔH is a change in endothermic reactions, and negative in heat-releasing exothermic processes. For processes under constant pressure, ΔH is equal to the change in the energy of the system. This means that the change in enthalpy under such conditions is the heat absorbed by the material through a reaction or by external heat transfer. Enthalpies for chemical substances at constant pressure assume standard state, most commonly 1 bar pressure, standard state does not, strictly speaking, specify a temperature, but expressions for enthalpy generally reference the standard heat of formation at 25 °C. Enthalpy of ideal gases and incompressible solids and liquids does not depend on pressure, unlike entropy, real materials at common temperatures and pressures usually closely approximate this behavior, which greatly simplifies enthalpy calculation and use in practical designs and analyses. The word enthalpy stems from the Ancient Greek verb enthalpein, which means to warm in and it combines the Classical Greek prefix ἐν- en-, meaning to put into, and the verb θάλπειν thalpein, meaning to heat. The word enthalpy is often attributed to Benoît Paul Émile Clapeyron. This misconception was popularized by the 1927 publication of The Mollier Steam Tables, however, neither the concept, the word, nor the symbol for enthalpy existed until well after Clapeyrons death. The earliest writings to contain the concept of enthalpy did not appear until 1875, however, Gibbs did not use the word enthalpy in his writings. The actual word first appears in the literature in a 1909 publication by J. P. Dalton
3.
Entropy
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In statistical thermodynamics, entropy is a measure of the number of microscopic configurations Ω that a thermodynamic system can have when in a state as specified by some macroscopic variables. Formally, S = k B ln Ω, for example, gas in a container with known volume, pressure, and temperature could have an enormous number of possible configurations of the collection of individual gas molecules. Each instantaneous configuration of the gas may be regarded as random, Entropy may be understood as a measure of disorder within a macroscopic system. The second law of thermodynamics states that an isolated systems entropy never decreases, such systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy. Non-isolated systems may lose entropy, provided their environments entropy increases by at least that amount, since entropy is a function of the state of the system, a change in entropy of a system is determined by its initial and final states. This applies whether the process is reversible or irreversible, however, irreversible processes increase the combined entropy of the system and its environment. The above definition is called the macroscopic definition of entropy because it can be used without regard to any microscopic description of the contents of a system. The concept of entropy has found to be generally useful and has several other formulations. Entropy was discovered when it was noticed to be a quantity that behaves as a function of state and it has the dimension of energy divided by temperature, which has a unit of joules per kelvin in the International System of Units. But the entropy of a substance is usually given as an intensive property—either entropy per unit mass or entropy per unit amount of substance. In statistical mechanics this reflects that the state of a system is generally non-degenerate. Understanding the role of entropy in various processes requires an understanding of how. It is often said that entropy is an expression of the disorder, or randomness of a system, the second law is now often seen as an expression of the fundamental postulate of statistical mechanics through the modern definition of entropy. In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy and he made the analogy with that of how water falls in a water wheel. This was an insight into the second law of thermodynamics. g. Clausius described entropy as the transformation-content, i. e. dissipative energy use and this was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass. Later, scientists such as Ludwig Boltzmann, Josiah Willard Gibbs, henceforth, the essential problem in statistical thermodynamics, i. e. according to Erwin Schrödinger, has been to determine the distribution of a given amount of energy E over N identical systems. Carathéodory linked entropy with a definition of irreversibility, in terms of trajectories
4.
Ideal gas
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An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interaction is perfectly elastic collision. The ideal gas concept is useful because it obeys the ideal gas law, an equation of state. One mole of a gas has a volume of 22.710947 litres at STP as defined by IUPAC since 1982. At normal conditions such as temperature and pressure, most real gases behave qualitatively like an ideal gas. Many gases such as nitrogen, oxygen, hydrogen, noble gases, the ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size become important. It also fails for most heavy gases, such as many refrigerants, at high pressures, the volume of a real gas is often considerably greater than that of an ideal gas. At low temperatures, the pressure of a gas is often considerably less than that of an ideal gas. At some point of low temperature and high pressure, real gases undergo a phase transition, the model of an ideal gas, however, does not describe or allow phase transitions. These must be modeled by more complex equations of state, the deviation from the ideal gas behaviour can be described by a dimensionless quantity, the compressibility factor, Z. The ideal gas model has been explored in both the Newtonian dynamics and in quantum mechanics, the ideal gas model has also been used to model the behavior of electrons in a metal, and it is one of the most important models in statistical mechanics. There are three classes of ideal gas, the classical or Maxwell–Boltzmann ideal gas, the ideal quantum Bose gas, composed of bosons. The classical ideal gas can be separated into two types, The classical thermodynamic ideal gas and the ideal quantum Boltzmann gas. The ideal quantum Boltzmann gas overcomes this limitation by taking the limit of the quantum Bose gas, the behavior of a quantum Boltzmann gas is the same as that of a classical ideal gas except for the specification of these constants. The ideal gas law is an extension of experimentally discovered gas laws, real fluids at low density and high temperature approximate the behavior of a classical ideal gas. This deviation is expressed as a compressibility factor, the classical thermodynamic properties of an ideal gas can be described by two equations of state. Multiplying the equations representing the three laws, V ∗ V ∗ V = k b a Gives, V ∗ V ∗ V =, under ideal conditions, V = R, that is, P V = n R T. The other equation of state of an ideal gas must express Joules law, in order to switch from macroscopic quantities to microscopic ones, we use n R = N k B where N is the number of gas particles kB is the Boltzmann constant. The probability distribution of particles by velocity or energy is given by the Maxwell speed distribution, the assumption of spherical particles is necessary so that there are no rotational modes allowed, unlike in a diatomic gas
5.
Ideal gas law
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The ideal gas law is the equation of state of a hypothetical ideal gas. It is an approximation of the behavior of many gases under many conditions. It was first stated by Émile Clapeyron in 1834 as a combination of the empirical Boyles law, Charless law and it can also be derived microscopically from kinetic theory, as was achieved by August Krönig in 1856 and Rudolf Clausius in 1857. The state of an amount of gas is determined by its pressure, volume, the modern form of the equation relates these simply in two main forms. The temperature used in the equation of state is an absolute temperature, in SI units, P is measured in pascals, V is measured in cubic metres, n is measured in moles, and T in kelvins. R has the value 8.314 J/ ≈2 cal/, how much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, a form of the ideal gas law may be useful. The chemical amount is equal to the mass of the gas divided by the molar mass. By replacing n with m/M and subsequently introducing density ρ = m/V, we get, defining the specific gas constant Rspecific as the ratio R/M, P = ρ R specific T. This form of the gas law is very useful because it links pressure, density. Alternatively, the law may be written in terms of the specific volume v and it is common, especially in engineering applications, to represent the specific gas constant by the symbol R. In such cases, the gas constant is usually given a different symbol such as R ¯ to distinguish it. In any case, the context and/or units of the gas constant should make it clear as to whether the universal or specific gas constant is being referred to. KB =R/NA The number density contrasts to the formulation, which uses n, the number of moles and V. This relation implies that R = NAkB, where NA is Avogadros constant, in extreme conditions the principles of statistical mechanics may break down as some of the assumptions relating a real life example to an ideal gas become untrue. In SI units, P is measured in pascals, V in cubic metres, Y is a dimensionless number, KB has the value 1. 38·10−23 J/K in SI units. According to the assumptions of the theory of gases, we assumed that there are no inter molecular attractions between the molecules of an ideal gas its potential energy is zero. Hence, all the energy possessed by the gas is kinetic energy, E =32 R T This is the kinetic energy of one mole of a gas
6.
Celsius
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Celsius, also known as centigrade, is a metric scale and unit of measurement for temperature. As an SI derived unit, it is used by most countries in the world and it is named after the Swedish astronomer Anders Celsius, who developed a similar temperature scale. The degree Celsius can refer to a temperature on the Celsius scale as well as a unit to indicate a temperature interval. Before being renamed to honour Anders Celsius in 1948, the unit was called centigrade, from the Latin centum, which means 100, and gradus, which means steps. The scale is based on 0° for the point of water. This scale is widely taught in schools today, by international agreement the unit degree Celsius and the Celsius scale are currently defined by two different temperatures, absolute zero, and the triple point of VSMOW. This definition also precisely relates the Celsius scale to the Kelvin scale, absolute zero, the lowest temperature possible, is defined as being precisely 0 K and −273.15 °C. The temperature of the point of water is defined as precisely 273.16 K at 611.657 pascals pressure. This definition fixes the magnitude of both the degree Celsius and the kelvin as precisely 1 part in 273.16 of the difference between absolute zero and the point of water. Thus, it sets the magnitude of one degree Celsius and that of one kelvin as exactly the same, additionally, it establishes the difference between the two scales null points as being precisely 273.15 degrees. In his paper Observations of two persistent degrees on a thermometer, he recounted his experiments showing that the point of ice is essentially unaffected by pressure. He also determined with precision how the boiling point of water varied as a function of atmospheric pressure. He proposed that the point of his temperature scale, being the boiling point. This pressure is known as one standard atmosphere, the BIPMs 10th General Conference on Weights and Measures later defined one standard atmosphere to equal precisely 1013250dynes per square centimetre. On 19 May 1743 he published the design of a mercury thermometer, in 1744, coincident with the death of Anders Celsius, the Swedish botanist Carolus Linnaeus reversed Celsiuss scale. In it, Linnaeus recounted the temperatures inside the orangery at the University of Uppsala Botanical Garden, since the 19th century, the scientific and thermometry communities worldwide referred to this scale as the centigrade scale. Temperatures on the scale were often reported simply as degrees or. More properly, what was defined as centigrade then would now be hectograde.2 gradians, for scientific use, Celsius is the term usually used, with centigrade otherwise continuing to be in common but decreasing use, especially in informal contexts in English-speaking countries
7.
International System of Units
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The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
8.
Fahrenheit
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Fahrenheit is a temperature scale based on one proposed in 1724 by the physicist Daniel Gabriel Fahrenheit, after whom the scale is named. It uses the degree Fahrenheit as the unit, several accounts of how he originally defined his scale exist. The lower defining point,0 °F, was established as the temperature of a solution of brine made from parts of ice. Further limits were established as the point of ice and his best estimate of the average human body temperature. All other countries in the world now use the Celsius scale, defined since 1954 by absolute zero being −273.15 °C, on the Fahrenheit scale, the freezing point of water is 32 degrees Fahrenheit and the boiling point is 212 °F. This puts the boiling and freezing points of water exactly 180 degrees apart, therefore, a degree on the Fahrenheit scale is 1⁄180 of the interval between the freezing point and the boiling point. On the Celsius scale, the freezing and boiling points of water are 100 degrees apart, a temperature interval of 1 °F is equal to an interval of 5⁄9 degrees Celsius. The Fahrenheit and Celsius scales intersect at −40°, absolute zero is −273.15 °C or −459.67 °F. For an exact conversion, the formulas can be applied. Again, f is the value in Fahrenheit and c the value in Celsius, f °Fahrenheit to c °Celsius, C °Celsius to f °Fahrenheit, −40 = f. Fahrenheit proposed his temperature scale in 1724, basing it on two points of temperature. In his initial scale, the point is determined by placing the thermometer in a mixture of ice, water. This is a mixture which stabilizes its temperature automatically, that stable temperature was defined as 0 °F. The second point,96 degrees, was approximately the human bodys temperature, in any case, the definition of the Fahrenheit scale has changed since. According to a letter Fahrenheit wrote to his friend Herman Boerhaave, his scale was built on the work of Ole Rømer, whom he had met earlier. In Rømers scale, brine freezes at zero, water freezes and melts at 7.5 degrees, body temperature is 22.5, Fahrenheit multiplied each value by four in order to eliminate fractions and increase the granularity of the scale. Fahrenheit observed that water boils at about 212 degrees using this scale, under this system, the Fahrenheit scale is redefined slightly so that the freezing point of water is exactly 32 °F, and the boiling point is exactly 212 °F or 180 degrees higher. It is for this reason that human body temperature is approximately 98° on the revised scale
9.
United States customary units
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United States customary units are a system of measurements commonly used in the United States. The United States customary system developed from English units which were in use in the British Empire before the US declared its independence, however, the British system of measures was overhauled in 1824 to create the imperial system, changing the definitions of some units. Therefore, while many U. S. units are similar to their Imperial counterparts. The majority of U. S. customary units were redefined in terms of the meter and these definitions were refined by the international yard and pound agreement of 1959. Americans primarily use customary units in commercial activities, as well as for personal and social use, in science, medicine, many sectors of industry and some of government, metric units are used. The International System of Units, the form of the metric system, is preferred for many uses by the U. S. National Institute of Standards. The United States system of units is similar to the British imperial system, both systems are derived from English units, a system which had evolved over the millennia before American independence, and which had its roots in Roman and Anglo-Saxon units. The customary system was championed by the U. S. -based International Institute for Preserving and Perfecting Weights, advocates of the customary system saw the French Revolutionary, or metric, system as atheistic. An auxiliary of the Institute in Ohio published a poem with wording such as down with every metric scheme and A perfect inch, one adherent of the customary system called it a just weight and a just measure, which alone are acceptable to the Lord. The U. S. government passed the Metric Conversion Act of 1975, the legislation states that the federal government has a responsibility to assist industry as it voluntarily converts to the metric system, i. e. metrification. This is most evident in U. S. labeling requirements on food products, according to the CIA Factbook, the United States is one of three nations that have not adopted the metric system as their official system of weights and measures. U. S. customary units are used on consumer products. Metric units are standard in science, medicine, as well as many sectors of industry and government, the metric system also lacks a parallel to the foot. Frequently, however, these units designate quite different sizes, for example, the mile ranged by country from one-half to five U. S. miles, foot and pound also had varying definitions. Historically, a range of non-SI units were used in the U. S. and in Britain. This article deals only with the commonly used or officially defined in the U. S. For measuring length, the U. S. customary system uses the inch, foot, yard, and mile, since July 1,1959, these have been defined on the basis of 1 yard =0.9144 meters except for some applications in surveying. The U. S. the United Kingdom and other Commonwealth countries agreed on this definition, the NAD27 was replaced in the 1980s by the North American Datum of 1983, which is defined in meters
10.
Imperial units
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The system of imperial units or the imperial system is the system of units first defined in the British Weights and Measures Act of 1824, which was later refined and reduced. The Imperial units replaced the Winchester Standards, which were in effect from 1588 to 1825, the system came into official use across the British Empire. The imperial system developed from what were first known as English units, the Weights and Measures Act of 1824 was initially scheduled to go into effect on 1 May 1825. However, the Weights and Measures Act of 1825 pushed back the date to 1 January 1826, the 1824 Act allowed the continued use of pre-imperial units provided that they were customary, widely known, and clearly marked with imperial equivalents. Apothecaries units are mentioned neither in the act of 1824 nor 1825, at the time, apothecaries weights and measures were regulated in England, Wales, and Berwick-upon-Tweed by the London College of Physicians, and in Ireland by the Dublin College of Physicians. In Scotland, apothecaries units were unofficially regulated by the Edinburgh College of Physicians, the three colleges published, at infrequent intervals, pharmacopoeiae, the London and Dublin editions having the force of law. The Medical Act of 1858 transferred to The Crown the right to publish the official pharmacopoeia and to regulate apothecaries weights, Metric equivalents in this article usually assume the latest official definition. Before this date, the most precise measurement of the imperial Standard Yard was 0.914398416 metres, in 1824, the various different gallons in use in the British Empire were replaced by the imperial gallon, a unit close in volume to the ale gallon. It was originally defined as the volume of 10 pounds of distilled water weighed in air with brass weights with the standing at 30 inches of mercury at a temperature of 62 °F. The Weights and Measures Act of 1985 switched to a gallon of exactly 4.54609 l and these measurements were in use from 1826, when the new imperial gallon was defined, but were officially abolished in the United Kingdom on 1 January 1971. In the USA, though no longer recommended, the system is still used occasionally in medicine. The troy pound was made the unit of mass by the 1824 Act, however, its use was abolished in the UK on 1 January 1879, with only the troy ounce. The Weights and Measures Act 1855 made the pound the primary unit of mass. In all the systems, the unit is the pound. For the yard, the length of a pendulum beating seconds at the latitude of Greenwich at Mean Sea Level in vacuo was defined as 39.01393 inches, the imperial system is one of many systems of English units. Although most of the units are defined in more than one system, some units were used to a much greater extent, or for different purposes. The distinctions between these systems are not drawn precisely. One such distinction is that between these systems and older British/English units/systems or newer additions, the US customary system is historically derived from the English units that were in use at the time of settlement
11.
Kelvin
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The kelvin is a unit of measure for temperature based upon an absolute scale. It is one of the seven units in the International System of Units and is assigned the unit symbol K. The kelvin is defined as the fraction 1⁄273.16 of the temperature of the triple point of water. In other words, it is defined such that the point of water is exactly 273.16 K. The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Lord Kelvin, unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or typeset as a degree. The kelvin is the unit of temperature measurement in the physical sciences, but is often used in conjunction with the Celsius degree. The definition implies that absolute zero is equivalent to −273.15 °C, Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale, when spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm. When reference is made to the Kelvin scale, the word kelvin—which is normally a noun—functions adjectivally to modify the noun scale and is capitalized, as with most other SI unit symbols there is a space between the numeric value and the kelvin symbol. Before the 13th CGPM in 1967–1968, the unit kelvin was called a degree and it was distinguished from the other scales with either the adjective suffix Kelvin or with absolute and its symbol was °K. The latter term, which was the official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale. Before the 13th CGPM, the form was degrees absolute. The 13th CGPM changed the name to simply kelvin. Its measured value was 7002273160280000000♠0.01028 °C with an uncertainty of 60 µK, the use of SI prefixed forms of the degree Celsius to express a temperature interval has not been widely adopted. In 2005 the CIPM embarked on a program to redefine the kelvin using a more experimentally rigorous methodology, the current definition as of 2016 is unsatisfactory for temperatures below 20 K and above 7003130000000000000♠1300 K. In particular, the committee proposed redefining the kelvin such that Boltzmanns constant takes the exact value 6977138065049999999♠1. 3806505×10−23 J/K, from a scientific point of view, this will link temperature to the rest of SI and result in a stable definition that is independent of any particular substance. From a practical point of view, the redefinition will pass unnoticed, the kelvin is often used in the measure of the colour temperature of light sources. Colour temperature is based upon the principle that a black body radiator emits light whose colour depends on the temperature of the radiator, black bodies with temperatures below about 7003400000000000000♠4000 K appear reddish, whereas those above about 7003750000000000000♠7500 K appear bluish
12.
Enthalpy of vaporization
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The enthalpy of vaporization is a function of the pressure at which that transformation takes place. The heat of vaporization is temperature-dependent, though a constant heat of vaporization can be assumed for small temperature ranges, the heat of vaporization diminishes with increasing temperature and it vanishes completely at a certain point called the critical temperature. Above the critical temperature, the liquid and vapor phases are indistinguishable, values are usually quoted in J/mol or kJ/mol, although kJ/kg or J/g, and older units like kcal/mol, cal/g and Btu/lb are sometimes still used, among others. The increase in the energy can be viewed as the energy required to overcome the intermolecular interactions in the liquid. Hence helium has a particularly low enthalpy of vaporization,0.0845 kJ/mol, as the van der Waals forces between helium atoms are particularly weak. This is particularly true of metals, which often form covalently bonded molecules in the gas phase, in these cases, the enthalpy of atomization must be used to obtain a true value of the bond energy. An alternative description is to view the enthalpy of condensation as the heat which must be released to the surroundings to compensate for the drop in entropy when a gas condenses to a liquid. These two definitions are equivalent, the point is the temperature at which the increased entropy of the gas phase overcomes the intermolecular forces. Estimation of the enthalpy of vaporization of electrolyte solutions can be carried out using equations based on the chemical thermodynamic models. The vaporization of metals is a key step in metal vapor synthesis, gmelin-Handbuch der anorganischen Chemie /08 a. NIST Chemistry WebBook Young, Francis W. Sears, Mark W. Zemansky, Hugh D
13.
Enthalpy of fusion
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This energy includes the contribution required to make room for any associated change in volume by displacing its environment against ambient pressure. The temperature at which the transition occurs is the melting point. By convention, the pressure is assumed to be 1 atm unless otherwise specified, the enthalpy of fusion is a latent heat, because during melting the introduction of heat cannot be observed as a temperature change, as the temperature remains constant during the process. The latent heat of fusion is the change of any amount of substance when it melts. The liquid phase has an internal energy than the solid phase. When liquid water is cooled, its temperature falls steadily until it drops just below the line of freezing point at 0 °C, the temperature then remains constant at the freezing point while the water crystallizes. Once the water is frozen, its temperature continues to fall. The enthalpy of fusion is almost always a quantity, helium is the only known exception. Helium-3 has an enthalpy of fusion at temperatures below 0.3 K. Helium-4 also has a very slightly negative enthalpy of fusion below 0.77 K. This means that, at appropriate constant pressures, these substances freeze with the addition of heat, in the case of 4He, this pressure range is between 24.992 and 25.00 atm. These values are mostly from the CRC Handbook of Chemistry and Physics, the conversion between cal/g and J/g in the above table uses the thermochemical calorie =4.184 joules rather than the International Steam Table calorie =4.1868 joules. 1) To heat 1 kg of water from 283.15 K to 303.15 K requires 83.6 kJ, however, to melt ice also requires energy. This error can be reduced when a heat capacity parameter is taken into account. H. Freeman and Company, p.236, ISBN 0-7167-7355-4 Ott, bevan, Boerio-Goates, Juliana, Chemical Thermodynamics, Advanced Applications, Academic Press, ISBN 0-12-530985-6
14.
Quantum mechanics
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Quantum mechanics, including quantum field theory, is a branch of physics which is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, derives from quantum mechanics as an approximation valid only at large scales, early quantum theory was profoundly reconceived in the mid-1920s. The reconceived theory is formulated in various specially developed mathematical formalisms, in one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. In 1803, Thomas Young, an English polymath, performed the famous experiment that he later described in a paper titled On the nature of light. This experiment played a role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays, Plancks hypothesis that energy is radiated and absorbed in discrete quanta precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, ludwig Boltzmann independently arrived at this result by considerations of Maxwells equations. However, it was only at high frequencies and underestimated the radiance at low frequencies. Later, Planck corrected this model using Boltzmanns statistical interpretation of thermodynamics and proposed what is now called Plancks law, following Max Plancks solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, robert Andrews Millikan studied the photoelectric effect experimentally, and Albert Einstein developed a theory for it. In 1913, Peter Debye extended Niels Bohrs theory of structure, introducing elliptical orbits. This phase is known as old quantum theory, according to Planck, each energy element is proportional to its frequency, E = h ν, where h is Plancks constant. Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the reality of the radiation itself. In fact, he considered his quantum hypothesis a mathematical trick to get the right rather than a sizable discovery. He won the 1921 Nobel Prize in Physics for this work, lower energy/frequency means increased time and vice versa, photons of differing frequencies all deliver the same amount of action, but do so in varying time intervals. High frequency waves are damaging to human tissue because they deliver their action packets concentrated in time, the Copenhagen interpretation of Niels Bohr became widely accepted. In the mid-1920s, developments in mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the old quantum theory, out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons
15.
Ground state
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The ground state of a quantum mechanical system is its lowest-energy state, the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with greater than the ground state. In the quantum theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate, many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state, according to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state, thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a crystal lattice, have a unique ground state. It is also possible for the highest excited state to have zero temperature for systems that exhibit negative temperature. In 1D, the state of the Schrödinger equation has no nodes. This can be proved considering the energy of a state with a node at x =0, i. e. ψ =0. Consider the average energy in this state ⟨ ψ | H | ψ ⟩ = ∫ d x where V is the potential, now consider a small interval around x =0, i. e. x ∈. Take a new wave function ψ ′ to be defined as ψ ′ = ψ, x < − ϵ and ψ ′ = − ψ, x > ϵ, if ϵ is small enough then this is always possible to do so that ψ ′ is continuous. Note that the energy density | d ψ ′ d x |2 < | d ψ d x |2 everywhere because of the normalization. For definiteness let us choose V ≥0, then it is clear that outside the interval x ∈ the potential energy density is smaller for the ψ ′ because | ψ ′ | < | ψ | there. Therefore, the energy is unchanged up to order ϵ2 if we deform the state with a node ψ into a state without a node ψ ′. We can therefore remove all nodes and reduce the energy, which implies that the wave function cannot have a node. The wave function of the state of a particle in a one-dimensional well is a half-period sine wave which goes to zero at the two edges of the well. The wave function of the state of a hydrogen atom is a spherically-symmetric distribution centred on the nucleus. The electron is most likely to be found at a distance from the equal to the Bohr radius
16.
Internal energy
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It keeps account of the gains and losses of energy of the system that are due to changes in its internal state. The internal energy of a system can be changed by transfers of matter or heat or by doing work, when matter transfer is prevented by impermeable containing walls, the system is said to be closed. Then the first law of thermodynamics states that the increase in energy is equal to the total heat added plus the work done on the system by its surroundings. If the containing walls pass neither matter nor energy, the system is said to be isolated, the first law of thermodynamics may be regarded as establishing the existence of the internal energy. The internal energy is one of the two cardinal state functions of the variables of a thermodynamic system. The internal energy of a state of a system cannot be directly measured. Such a chain, or path, can be described by certain extensive state variables of the system, namely, its entropy, S, its volume, V. The internal energy, U, is a function of those, sometimes, to that list are appended other extensive state variables, for example electric dipole moment. Customarily, thermodynamic descriptions include only items relevant to the processes under study, Thermodynamics is chiefly concerned only with changes in the internal energy, not with its absolute value. The internal energy is a function of a system, because its value depends only on the current state of the system. It is the one and only cardinal thermodynamic potential, through it, by use of Legendre transforms, are mathematically constructed the other thermodynamic potentials. These are functions of variable lists in which some extensive variables are replaced by their conjugate intensive variables, Legendre transformation is necessary because mere substitutive replacement of extensive variables by intensive variables does not lead to thermodynamic potentials. Mere substitution leads to a less informative formula, an equation of state, though it is a macroscopic quantity, internal energy can be explained in microscopic terms by two theoretical virtual components. One is the kinetic energy due to the microscopic motion of the systems particles. The other is the energy associated with the microscopic forces, including the chemical bonds. If thermonuclear reactions are specified as a topic of concern, then the static rest mass energy of the constituents of matter is also counted. There is no simple relation between these quantities of microscopic energy and the quantities of energy gained or lost by the system in work, heat. The SI unit of energy is the joule, sometimes it is convenient to use a corresponding density called specific internal energy which is internal energy per unit of mass of the system in question
17.
Asymptote
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In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, in some contexts, such as algebraic geometry, an asymptote is defined as a line which is tangent to a curve at infinity. The word asymptote is derived from the Greek ἀσύμπτωτος which means not falling together, + σύν together + πτωτ-ός fallen. The term was introduced by Apollonius of Perga in his work on conic sections, there are potentially three kinds of asymptotes, horizontal, vertical and oblique asymptotes. For curves given by the graph of a function y = ƒ, vertical asymptotes are vertical lines near which the function grows without bound. Asymptotes convey information about the behavior of curves in the large, the study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis. The idea that a curve may come close to a line without actually becoming the same may seem to counter everyday experience. The representations of a line and a curve as marks on a piece of paper or as pixels on a screen have a positive width. So if they were to be extended far enough they would seem to merge, but these are physical representations of the corresponding mathematical entities, the line and the curve are idealized concepts whose width is 0. Therefore, the understanding of the idea of an asymptote requires an effort of reason rather than experience, consider the graph of the function f =1 x shown to the right. The coordinates of the points on the curve are of the form where x is an other than 0. But no matter how large x becomes, its reciprocal 1 x is never 0, so the curve extends farther and farther upward as it comes closer and closer to the y-axis. Thus, both the x and y-axes are asymptotes of the curve and these ideas are part of the basis of concept of a limit in mathematics, and this connection is explained more fully below. The asymptotes most commonly encountered in the study of calculus are of curves of the form y = ƒ and these can be computed using limits and classified into horizontal, vertical and oblique asymptotes depending on its orientation. Horizontal asymptotes are lines that the graph of the function approaches as x tends to +∞ or −∞. As the name indicate they are parallel to the x-axis, vertical asymptotes are vertical lines near which the function grows without bound. Oblique asymptotes are diagonal lines so that the difference between the curve and the line approaches 0 as x tends to +∞ or −∞, more general type of asymptotes can be defined in this case. Only open curves that have some infinite branch, can have an asymptote, no closed curve can have an asymptote
18.
Kinetic energy
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In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes, the same amount of work is done by the body in decelerating from its current speed to a state of rest. In classical mechanics, the energy of a non-rotating object of mass m traveling at a speed v is 12 m v 2. In relativistic mechanics, this is an approximation only when v is much less than the speed of light. The standard unit of energy is the joule. The adjective kinetic has its roots in the Greek word κίνησις kinesis, the dichotomy between kinetic energy and potential energy can be traced back to Aristotles concepts of actuality and potentiality. The principle in classical mechanics that E ∝ mv2 was first developed by Gottfried Leibniz and Johann Bernoulli, Willem s Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, Émilie du Châtelet recognized the implications of the experiment and published an explanation. The terms kinetic energy and work in their present scientific meanings date back to the mid-19th century, early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled Du Calcul de lEffet des Machines outlining the mathematics of kinetic energy. William Thomson, later Lord Kelvin, is given the credit for coining the term kinetic energy c, energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, and rest energy. These can be categorized in two classes, potential energy and kinetic energy. Kinetic energy is the movement energy of an object, Kinetic energy can be transferred between objects and transformed into other kinds of energy. Kinetic energy may be best understood by examples that demonstrate how it is transformed to, for example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance, the chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms, for example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling, the energy is not destroyed, it has only been converted to another form by friction
19.
Superconductivity
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It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8,1911, in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a mechanical phenomenon. It is characterized by the Meissner effect, the ejection of magnetic field lines from the interior of the superconductor as it transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be simply as the idealization of perfect conductivity in classical physics. The electrical resistance of a metallic conductor decreases gradually as temperature is lowered, in ordinary conductors, such as copper or silver, this decrease is limited by impurities and other defects. Even near absolute zero, a sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature, an electric current flowing through a loop of superconducting wire can persist indefinitely with no power source. In 1986, it was discovered that some cuprate-perovskite ceramic materials have a temperature above 90 K. Such a high temperature is theoretically impossible for a conventional superconductor. There are many criteria by which superconductors are classified, by theory of operation, It is conventional if it can be explained by the BCS theory or its derivatives, or unconventional, otherwise. By material, Superconductor material classes include chemical elements, alloys, ceramics, on the other hand, there is a class of properties that are independent of the underlying material. For instance, all superconductors have exactly zero resistivity to low applied currents when there is no magnetic field present or if the field does not exceed a critical value. The resistance of the sample is given by Ohms law as R = V / I, if the voltage is zero, this means that the resistance is zero. Superconductors are also able to maintain a current with no applied voltage whatsoever, experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years, theoretical estimates for the lifetime of a persistent current can exceed the estimated lifetime of the universe, depending on the wire geometry and the temperature. In a normal conductor, an electric current may be visualized as a fluid of electrons moving across an ionic lattice. As a result, the energy carried by the current is constantly being dissipated and this is the phenomenon of electrical resistance and Joule heating. The situation is different in a superconductor, in a conventional superconductor, the electronic fluid cannot be resolved into individual electrons
20.
Superfluidity
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Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without loss of kinetic energy. When stirred a superfluid forms cellular vortices that continue to rotate indefinitely, superfluidity occurs in two isotopes of helium when they are liquified by cooling to cryogenic temperatures. It is also a property of other exotic states of matter theorized to exist in astrophysics, high-energy physics. Superfluidity was originally discovered in liquid helium, by Pyotr Kapitsa and it has since been described through phenomenology and microscopic theories. In liquid helium-4, the superfluidity occurs at far higher temperatures than it does in helium-3, each atom of helium-4 is a boson particle, by virtue of its integer spin. A helium-3 atom is a particle, it can form bosons only by pairing with itself at much lower temperatures. The discovery of superfluidity in helium-3 was the basis for the award of the 1996 Nobel Prize in Physics and this process is similar to the electron pairing in superconductivity. Superfluidity in an ultracold fermionic gas was experimentally proven by Wolfgang Ketterle, such vortices had previously been observed in an ultracold bosonic gas using 87Rb in 2000, and more recently in two-dimensional gases. As early as 1999 Lene Hau created such a condensate using sodium atoms for the purpose of slowing light, with a double light-roadblock setup, we can generate controlled collisions between shock waves resulting in completely unexpected, nonlinear excitations. We have observed hybrid structures consisting of vortex rings embedded in dark solitonic shells, the vortex rings act as phantom propellers leading to very rich excitation dynamics. The idea that superfluidity exists inside neutron stars was first proposed by Arkady Migdal, superfluid vacuum theory is an approach in theoretical physics and quantum mechanics where the physical vacuum is viewed as superfluid. The ultimate goal of the approach is to develop scientific models that unify quantum mechanics with gravity and this makes SVT a candidate for the theory of quantum gravity and an extension of the Standard Model. Boojum Condensed matter physics Macroscopic quantum phenomena Quantum hydrodynamics Slow light Supersolid Guénault, annett, James F. Superconductivity, superfluids, and condensates. The Universe in a helium droplet
21.
Adiabatic process
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In thermodynamics, an adiabatic process is one that occurs without transfer of heat or matter between a thermodynamic system and its surroundings. In an adiabatic process, energy is transferred only as work, the adiabatic process provides a rigorous conceptual basis for the theory used to expound the first law of thermodynamics, and as such it is a key concept in thermodynamics. The adiabatic flame temperature is the temperature that would be achieved by a if the process of combustion took place in the absence of heat loss to the surroundings. A process that does not involve the transfer of heat or matter into or out of a system, so that Q =0, is called an adiabatic process, the assumption that a process is adiabatic is a frequently made simplifying assumption. Even though the cylinders are not insulated and are quite conductive, the same can be said to be true for the expansion process of such a system. The assumption of adiabatic isolation of a system is a useful one, the behaviour of actual machines deviates from these idealizations, but the assumption of such perfect behaviour provide a useful first approximation of how the real world works. According to Laplace, when sound travels in a gas, there is no loss of heat in the medium and the propagation of sound is adiabatic. For this adiabatic process, the modulus of elasticity E = γP where γ is the ratio of specific heats at constant pressure and at constant volume, such a process is called an isentropic process and is said to be reversible. Fictively, if the process is reversed, the energy added as work can be recovered entirely as work done by the system, if the walls of a system are not adiabatic, and energy is transferred in as heat, entropy is transferred into the system with the heat. Such a process is neither adiabatic nor isentropic, having Q >0, naturally occurring adiabatic processes are irreversible. The transfer of energy as work into an isolated system can be imagined as being of two idealized extreme kinds. In one such kind, there is no entropy produced within the system, in nature, this ideal kind occurs only approximately, because it demands an infinitely slow process and no sources of dissipation. The other extreme kind of work is work, for which energy is added as work solely through friction or viscous dissipation within the system. The second law of thermodynamics observes that a process, of transfer of energy as work, always consists at least of isochoric work. Every natural process, adiabatic or not, is irreversible, with ΔS >0, the adiabatic compression of a gas causes a rise in temperature of the gas. Adiabatic expansion against pressure, or a spring, causes a drop in temperature, in contrast, free expansion is an isothermal process for an ideal gas. Adiabatic heating occurs when the pressure of a gas is increased from work done on it by its surroundings and this finds practical application in diesel engines which rely on the lack of quick heat dissipation during their compression stroke to elevate the fuel vapor temperature sufficiently to ignite it. Adiabatic heating occurs in the Earths atmosphere when an air mass descends, for example, in a wind, Foehn wind
22.
Crystal
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A crystal or crystalline solid is a solid material whose constituents are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, the scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification, the word crystal derives from the Ancient Greek word κρύσταλλος, meaning both ice and rock crystal, from κρύος, icy cold, frost. Examples of large crystals include snowflakes, diamonds, and table salt, most inorganic solids are not crystals but polycrystals, i. e. many microscopic crystals fused together into a single solid. Examples of polycrystals include most metals, rocks, ceramics, a third category of solids is amorphous solids, where the atoms have no periodic structure whatsoever. Examples of amorphous solids include glass, wax, and many plastics, Crystals are often used in pseudoscientific practices such as crystal therapy, and, along with gemstones, are sometimes associated with spellwork in Wiccan beliefs and related religious movements. The scientific definition of a crystal is based on the arrangement of atoms inside it. A crystal is a solid where the form a periodic arrangement. For example, when liquid water starts freezing, the change begins with small ice crystals that grow until they fuse. Most macroscopic inorganic solids are polycrystalline, including almost all metals, ceramics, ice, rocks, solids that are neither crystalline nor polycrystalline, such as glass, are called amorphous solids, also called glassy, vitreous, or noncrystalline. These have no periodic order, even microscopically, there are distinct differences between crystalline solids and amorphous solids, most notably, the process of forming a glass does not release the latent heat of fusion, but forming a crystal does. A crystal structure is characterized by its cell, a small imaginary box containing one or more atoms in a specific spatial arrangement. The unit cells are stacked in three-dimensional space to form the crystal, the symmetry of a crystal is constrained by the requirement that the unit cells stack perfectly with no gaps. There are 219 possible crystal symmetries, called space groups. These are grouped into 7 crystal systems, such as cubic crystal system or hexagonal crystal system, Crystals are commonly recognized by their shape, consisting of flat faces with sharp angles. Euhedral crystals are those with obvious, well-formed flat faces, anhedral crystals do not, usually because the crystal is one grain in a polycrystalline solid. The flat faces of a crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal. This occurs because some surface orientations are more stable than others, as a crystal grows, new atoms attach easily to the rougher and less stable parts of the surface, but less easily to the flat, stable surfaces
23.
Max Planck
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Max Karl Ernst Ludwig Planck, FRS was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. However, his name is known on a broader academic basis, through the renaming in 1948 of the German scientific institution. The MPS now includes 83 institutions representing a range of scientific directions. Planck came from a traditional, intellectual family and his paternal great-grandfather and grandfather were both theology professors in Göttingen, his father was a law professor in Kiel and Munich. Planck was born in Kiel, Holstein, to Johann Julius Wilhelm Planck and his second wife and he was baptised with the name of Karl Ernst Ludwig Marx Planck, of his given names, Marx was indicated as the primary name. However, by the age of ten he signed with the name Max and he was the 6th child in the family, though two of his siblings were from his fathers first marriage. Among his earliest memories was the marching of Prussian and Austrian troops into Kiel during the Second Schleswig War in 1864 and it was from Müller that Planck first learned the principle of conservation of energy. Planck graduated early, at age 17 and this is how Planck first came in contact with the field of physics. Planck was gifted when it came to music and he took singing lessons and played piano, organ and cello, and composed songs and operas. However, instead of music he chose to study physics, the Munich physics professor Philipp von Jolly advised Planck against going into physics, saying, in this field, almost everything is already discovered, and all that remains is to fill a few holes. Planck replied that he did not wish to discover new things, but only to understand the fundamentals of the field. Under Jollys supervision, Planck performed the experiments of his scientific career, studying the diffusion of hydrogen through heated platinum. In 1877 he went to the Friedrich Wilhelms University in Berlin for a year of study with physicists Hermann von Helmholtz and Gustav Kirchhoff and mathematician Karl Weierstrass. He wrote that Helmholtz was never quite prepared, spoke slowly, miscalculated endlessly and he soon became close friends with Helmholtz. While there he undertook a program of mostly self-study of Clausiuss writings, in October 1878 Planck passed his qualifying exams and in February 1879 defended his dissertation, Über den zweiten Hauptsatz der mechanischen Wärmetheorie. He briefly taught mathematics and physics at his school in Munich. In June 1880, he presented his thesis, Gleichgewichtszustände isotroper Körper in verschiedenen Temperaturen. With the completion of his thesis, Planck became an unpaid private lecturer in Munich
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Third law of thermodynamics
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Entropy is related to the number of accessible microstates, and for a system consisting of many particles, quantum mechanics indicates that there is only one unique state with minimum energy. The constant value is called the entropy of the system. Here a condensed system refers to liquids and solids, a classical formulation by Nernst is, It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations. It was proven in 2017 by Masanes and Oppenheim, the 3rd law was developed by the chemist Walther Nernst during the years 1906–12, and is therefore often referred to as Nernsts theorem or Nernsts postulate. The third law of thermodynamics states that the entropy of a system at zero is a well-defined constant. This is because a system at zero temperature exists in its ground state, in 1912 Nernst stated the law thus, It is impossible for any procedure to lead to the isotherm T =0 in a finite number of steps. An alternative version of the law of thermodynamics as stated by Gilbert N. This version states not only ΔS will reach zero at 0 K, some crystals form defects which causes a residual entropy. This residual entropy disappears when the barriers to transitioning to one ground state are overcome. With the development of mechanics, the third law of thermodynamics changed from a fundamental law to a derived law. The counting of states is from the state of absolute zero. In simple terms, the law states that the entropy of a perfect crystal of a pure substance approaches zero as the temperature approaches zero. The alignment of a perfect crystal leaves no ambiguity as to the location and orientation of each part of the crystal, as the energy of the crystal is reduced, the vibrations of the individual atoms are reduced to nothing, and the crystal becomes the same everywhere. The third law provides a reference point for the determination of entropy at any other temperature. The entropy of a system, determined relative to this point, is then the absolute entropy of that system. Mathematically, the entropy of any system at zero temperature is the natural log of the number of ground states times Boltzmanns constant kB = 6977137999999999999♠1. 38×10−23 J K−1. The entropy of a crystal lattice as defined by Nernsts theorem is zero provided that its ground state is unique. As a result, the initial value of zero is selected S0 =0 is used for convenience
25.
Walther Nernst
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Nernst helped establish the modern field of physical chemistry and contributed to electrochemistry, thermodynamics and solid state physics. He is also known for developing the Nernst equation, Nernst was born in Briesen in West Prussia as son of Gustav Nernst and Ottilie Nerger. His father was a country judge, Nernst had three older sisters and one younger brother. The third sister died due to cholera, Nernst went to elementary school at Graudenz. He studied physics and mathematics at the universities of Zürich, Berlin, Graz and Würzburg, in 1889, he finished his habilitation at University of Leipzig. It was said that Nernst was mechanically minded in that he was thinking of ways to apply new discoveries to industry. Nernsts hobbies included hunting and fishing, Nernst married in 1892 to Emma Lohmeyer with whom he had two sons and three daughters. Both of Nernsts sons died fighting in World War I and he was a colleague of Svante Arrhenius, and suggested setting fire to unused coal seams to increase the global temperature. He was a critic of Adolf Hitler and Nazism. In 1933, the rise of Nazism led to the end of Nernsts career as a scientist, Nernst died in 1941 and is buried near Max Planck, Otto Hahn and Max von Laue in Göttingen, Germany. After some work at Leipzig, he founded the Institute of Physical Chemistry and Electrochemistry at Göttingen, Nernst invented, in 1897 an electric lamp, using an incandescent ceramic rod. His invention, known as the Nernst lamp, was the successor to the lamp of Edison. Nernst researched osmotic pressure and electrochemistry, in 1905, he established what he referred to as his New Heat Theorem, later known as the Third law of thermodynamics. This is the work for which he is best remembered, as it provided a means of determining free energies of reactions from heat measurements. Theodore Richards claimed Nernst had stolen the idea from him, in 1911, with Max Planck, he was the main organizer of the first Solvay Conference in Brussels. In 1912, the impressionist painter Max Liebermann painted his portrait, in 1914 Nernst showed his support for German militarism by signing the Manifesto of the Ninety-Three. He also accepted the post of Staff Scientific Advisor in the Imperial German Army, in 1918, after studying photochemistry, he proposed the atomic chain reaction theory. The atomic chain reaction theory stated that when a reaction in which atoms are formed
26.
Nernst heat theorem
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The Nernst heat theorem was formulated by Walther Nernst early in the twentieth century and was used in the development of the third law of thermodynamics. The Nernst heat theorem says that as absolute zero is approached and this can be expressed mathematically as follow lim T →0 Δ S =0 The above equation is a modern statement of the theorem. Nernst often used a form that avoided the concept of entropy, another way of looking at the theorem is to start with the definition of the Gibbs free energy, G = H - TS, where H stands for enthalpy. For a change from reactants to products at constant temperature and pressure the equation becomes Δ G = Δ H − T Δ S. In the limit of T =0 the equation reduces to just ΔG = ΔH, as illustrated in the figure shown here, however, it is known from thermodynamics that the slope of the ΔG curve is -ΔS. Since the slope shown here reaches the limit of 0 as T →0 then the implication is that ΔS →0. Theodore William Richards Entropy Denbigh, Kenneth, - See especially pages 421 –424 Nernst heat theorem
27.
Isothermal process
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An isothermal process is a change of a system, in which the temperature remains constant, ΔT =0. In contrast, a process is where a system exchanges no heat with its surroundings. In other words, in a process, the value ΔT =0 and therefore ΔU =0 but Q ≠0, while in an adiabatic process. Isothermal processes can occur in any kind of system that has some means of regulating the temperature, including highly structured machines, some parts of the cycles of some heat engines are carried out isothermally. In the thermodynamic analysis of reactions, it is usual to first analyze what happens under isothermal conditions. Phase changes, such as melting or evaporation, are also isothermal processes when, as is usually the case, isothermal processes are often used and a starting point in analyzing more complex, non-isothermal processes. Isothermal processes are of special interest for ideal gases and this is a consequence of Joules second law which states that the internal energy of a fixed amount of an ideal gas depends only on its temperature. Thus, in a process the internal energy of an ideal gas is constant. This is a result of the fact that in a gas there are no intermolecular forces. Note that this is only for ideal gases, the internal energy depends on pressure as well as on temperature for liquids, solids. In the isothermal compression of a gas there is work is done on the system to decrease the volume, doing work on the gas increases the internal energy and will tend to increase the temperature. To maintain the constant temperature energy must leave the system as heat, if the gas is ideal, the amount of energy entering the environment is equal to the work done on the gas, because internal energy does not change. For details of the calculations, see calculation of work, for an adiabatic process, in which no heat flows into or out of the gas because its container is well insulated, Q =0. If there is no work done, i. e. a free expansion. For an ideal gas, this means that the process is also isothermal, thus, specifying that a process is isothermal is not sufficient to specify a unique process. For the special case of a gas to which Boyles law applies, the value of the constant is nRT, where n is the number of moles of gas present and R is the ideal gas constant. In other words, the gas law pV = nRT applies. This means that p = n R T V = constant V holds, the family of curves generated by this equation is shown in the graph in Figure 1
28.
Lattice (group)
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In geometry and group theory, a lattice in R n is a subgroup of R n which is isomorphic to Z n, and which spans the real vector space R n. In other words, for any basis of R n, the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice, a lattice may be viewed as a regular tiling of a space by a primitive cell. Lattices have many significant applications in mathematics, particularly in connection to Lie algebras, number theory. More generally, lattice models are studied in physics, often by the techniques of computational physics, a lattice is the symmetry group of discrete translational symmetry in n directions. A pattern with this lattice of translational symmetry cannot have more, as a group a lattice is a finitely-generated free abelian group, and thus isomorphic to Z n. A lattice in the sense of a 3-dimensional array of regularly spaced points coinciding with e. g, a simple example of a lattice in R n is the subgroup Z n. More complicated examples include the E8 lattice, which is a lattice in R8, the period lattice in R2 is central to the study of elliptic functions, developed in nineteenth century mathematics, it generalises to higher dimensions in the theory of abelian functions. Lattices called root lattices are important in the theory of simple Lie algebras, for example, a typical lattice Λ in R n thus has the form Λ = where is a basis for R n. Different bases can generate the lattice, but the absolute value of the determinant of the vectors vi is uniquely determined by Λ. If one thinks of a lattice as dividing the whole of R n into equal polyhedra and this is why d is sometimes called the covolume of the lattice. If this equals 1, the lattice is called unimodular, minkowskis theorem relates the number d and the volume of a symmetric convex set S to the number of lattice points contained in S. The number of lattice points contained in an all of whose vertices are elements of the lattice is described by the polytopes Ehrhart polynomial. Formulas for some of the coefficients of this polynomial involve d as well, Lattice basis reduction is the problem of finding a short and nearly orthogonal lattice basis. The Lenstra-Lenstra-Lovász lattice basis reduction algorithm approximates such a basis in polynomial time, it has found numerous applications. There are five 2D lattice types as given by the crystallographic restriction theorem, below, the wallpaper group of the lattice is given in IUC notation, Orbifold notation, and Coxeter notation, along with a wallpaper diagram showing the symmetry domains. Note that a pattern with this lattice of translational symmetry cannot have more, a full list of subgroups is available. For example below the hexagonal/triangular lattice is given twice, with full 6-fold, if the symmetry group of a pattern contains an n-fold rotation then the lattice has n-fold symmetry for even n and 2n-fold for odd n. For the classification of a lattice, start with one point
29.
Symmetry
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Symmetry in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, symmetry has a precise definition, that an object is invariant to any of various transformations. Although these two meanings of symmetry can sometimes be told apart, they are related, so they are discussed together. The opposite of symmetry is asymmetry, a geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion. This means that an object is symmetric if there is a transformation that moves individual pieces of the object, an object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape. An object has symmetry if it can be translated without changing its overall shape. An object has symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis. An object has symmetry if it does not change shape when it is expanded or contracted. Fractals also exhibit a form of symmetry, where small portions of the fractal are similar in shape to large portions. Other symmetries include glide reflection symmetry and rotoreflection symmetry, a dyadic relation R is symmetric if and only if, whenever its true that Rab, its true that Rba. Thus, is the age as is symmetrical, for if Paul is the same age as Mary. Symmetric binary logical connectives are and, or, biconditional, nand, xor, the set of operations that preserve a given property of the object form a group. In general, every kind of structure in mathematics will have its own kind of symmetry, examples include even and odd functions in calculus, the symmetric group in abstract algebra, symmetric matrices in linear algebra, and the Galois group in Galois theory. In statistics, it appears as symmetric probability distributions, and as skewness, symmetry in physics has been generalized to mean invariance—that is, lack of change—under any kind of transformation, for example arbitrary coordinate transformations. This concept has one of the most powerful tools of theoretical physics. See Noethers theorem, and also, Wigners classification, which says that the symmetries of the laws of physics determine the properties of the found in nature. Important symmetries in physics include continuous symmetries and discrete symmetries of spacetime, internal symmetries of particles, in biology, the notion of symmetry is mostly used explicitly to describe body shapes. Bilateral animals, including humans, are more or less symmetric with respect to the plane which divides the body into left
30.
Orthogonality
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The concept of orthogonality has been broadly generalized in mathematics, as well as in areas such as chemistry, and engineering. The word comes from the Greek ὀρθός, meaning upright, and γωνία, the ancient Greek ὀρθογώνιον orthogōnion and classical Latin orthogonium originally denoted a rectangle. Later, they came to mean a right triangle, in the 12th century, the post-classical Latin word orthogonalis came to mean a right angle or something related to a right angle. In geometry, two Euclidean vectors are orthogonal if they are perpendicular, i. e. they form a right angle, two vectors, x and y, in an inner product space, V, are orthogonal if their inner product ⟨ x, y ⟩ is zero. This relationship is denoted x ⊥ y, two vector subspaces, A and B, of an inner product space, V, are called orthogonal subspaces if each vector in A is orthogonal to each vector in B. The largest subspace of V that is orthogonal to a subspace is its orthogonal complement. Given a module M and its dual M∗, an element m′ of M∗, two sets S′ ⊆ M∗ and S ⊆ M are orthogonal if each element of S′ is orthogonal to each element of S. A term rewriting system is said to be if it is left-linear and is non-ambiguous. Orthogonal term rewriting systems are confluent, a set of vectors in an inner product space is called pairwise orthogonal if each pairing of them is orthogonal. Such a set is called an orthogonal set, nonzero pairwise orthogonal vectors are always linearly independent. In certain cases, the normal is used to mean orthogonal. For example, the y-axis is normal to the curve y = x2 at the origin, however, normal may also refer to the magnitude of a vector. In particular, a set is called if it is an orthogonal set of unit vectors. As a result, use of the normal to mean orthogonal is often avoided. The word normal also has a different meaning in probability and statistics, a vector space with a bilinear form generalizes the case of an inner product. When the bilinear form applied to two results in zero, then they are orthogonal. The case of a pseudo-Euclidean plane uses the term hyperbolic orthogonality, in the diagram, axes x′ and t′ are hyperbolic-orthogonal for any given ϕ. In 2-D or higher-dimensional Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i. e. they make an angle of 90°, hence orthogonality of vectors is an extension of the concept of perpendicular vectors into higher-dimensional spaces
31.
Cartesian coordinate system
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Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair. The coordinates can also be defined as the positions of the projections of the point onto the two axis, expressed as signed distances from the origin. One can use the principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes. In general, n Cartesian coordinates specify the point in an n-dimensional Euclidean space for any dimension n and these coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes. The invention of Cartesian coordinates in the 17th century by René Descartes revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes can be described by Cartesian equations, algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2, centered at the origin of the plane, a familiar example is the concept of the graph of a function. Cartesian coordinates are also tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering. They are the most common system used in computer graphics, computer-aided geometric design. Nicole Oresme, a French cleric and friend of the Dauphin of the 14th Century, used similar to Cartesian coordinates well before the time of Descartes. The adjective Cartesian refers to the French mathematician and philosopher René Descartes who published this idea in 1637 and it was independently discovered by Pierre de Fermat, who also worked in three dimensions, although Fermat did not publish the discovery. Both authors used a single axis in their treatments and have a length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes La Géométrie was translated into Latin in 1649 by Frans van Schooten and these commentators introduced several concepts while trying to clarify the ideas contained in Descartes work. Many other coordinate systems have developed since Descartes, such as the polar coordinates for the plane. The development of the Cartesian coordinate system would play a role in the development of the Calculus by Isaac Newton. The two-coordinate description of the plane was later generalized into the concept of vector spaces. Choosing a Cartesian coordinate system for a one-dimensional space – that is, for a straight line—involves choosing a point O of the line, a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative, we say that the line is oriented from the negative half towards the positive half
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Chemical substance
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A chemical substance is a form of matter that has constant chemical composition and characteristic properties. It cannot be separated into components by physical methods, i. e. without breaking chemical bonds. Chemical substances can be chemical elements, chemical compounds, ions or alloys, Chemical substances are often called pure to set them apart from mixtures. A common example of a substance is pure water, it has the same properties. Other chemical substances commonly encountered in pure form are diamond, gold, table salt, however, in practice, no substance is entirely pure, and chemical purity is specified according to the intended use of the chemical. Chemical substances exist as solids, liquids, gases, or plasma, Chemical substances may be combined or converted to others by means of chemical reactions. Forms of energy, such as light and heat, are not matter, a chemical substance may well be defined as any material with a definite chemical composition in an introductory general chemistry textbook. According to this definition a chemical substance can either be a chemical element or a pure chemical compound. But, there are exceptions to this definition, a substance can also be defined as a form of matter that has both definite composition and distinct properties. The chemical substance index published by CAS also includes several alloys of uncertain composition, in geology, substances of uniform composition are called minerals, while physical mixtures of several minerals are defined as rocks. Many minerals, however, mutually dissolve into solid solutions, such that a rock is a uniform substance despite being a mixture in stoichiometric terms. Feldspars are an example, anorthoclase is an alkali aluminium silicate. In law, chemical substances may include both pure substances and mixtures with a composition or manufacturing process. For example, the EU regulation REACH defines monoconstituent substances, multiconstituent substances and substances of unknown or variable composition, the latter two consist of multiple chemical substances, however, their identity can be established either by direct chemical analysis or reference to a single manufacturing process. For example, charcoal is a complex, partially polymeric mixture that can be defined by its manufacturing process. Therefore, although the chemical identity is unknown, identification can be made to a sufficient accuracy. The CAS index also includes mixtures, polymers almost always appear as mixtures of molecules of multiple molar masses, each of which could be considered a separate chemical substance. However, the polymer may be defined by a precursor or reaction
33.
Graphite
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Graphite, archaically referred to as plumbago, is a crystalline form of carbon, a semimetal, a native element mineral, and one of the allotropes of carbon. Graphite is the most stable form of carbon under standard conditions, therefore, it is used in thermochemistry as the standard state for defining the heat of formation of carbon compounds. Highly ordered pyrolytic graphite or more correctly highly oriented pyrolytic graphite refers to graphite with a spread between the graphite sheets of less than 1°. The name graphite fiber is sometimes used to refer to carbon fibers or carbon fiber-reinforced polymer. Graphite occurs in rocks as a result of the reduction of sedimentary carbon compounds during metamorphism. It also occurs in rocks and in meteorites. Minerals associated with graphite include quartz, calcite, micas and tourmaline, in meteorites it occurs with troilite and silicate minerals. Small graphitic crystals in meteoritic iron are called cliftonite, Graphite is not mined in the United States, but U. S. production of synthetic graphite in 2010 was 134 kt valued at $1.07 billion. Graphite has a layered, planar structure, the individual layers are called graphene. In each layer, the atoms are arranged in a honeycomb lattice with separation of 0.142 nm. Atoms in the plane are bonded covalently, with three of the four potential bonding sites satisfied. The fourth electron is free to migrate in the plane, making graphite electrically conductive, however, it does not conduct in a direction at right angles to the plane. Bonding between layers is via weak van der Waals bonds, which allows layers of graphite to be easily separated, the two known forms of graphite, alpha and beta, have very similar physical properties, except for that the graphene layers stack slightly differently. The alpha graphite may be flat or buckled. The alpha form can be converted to the form through mechanical treatment. The acoustic and thermal properties of graphite are highly anisotropic, since phonons propagate quickly along the tightly-bound planes, graphites high thermal stability and electrical and thermal conductivity facilitate its widespread use as electrodes and refractories in high temperature material processing applications. However, in oxygen containing atmospheres graphite readily oxidizes to form CO2 at temperatures of 700 °C, Graphite is an electric conductor, consequently, useful in such applications as arc lamp electrodes. It can conduct electricity due to the vast electron delocalization within the carbon layers and these valence electrons are free to move, so are able to conduct electricity
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Carbon
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Carbon is a chemical element with symbol C and atomic number 6. It is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds, three isotopes occur naturally, 12C and 13C being stable, while 14C is a radioactive isotope, decaying with a half-life of about 5,730 years. Carbon is one of the few elements known since antiquity, Carbon is the 15th most abundant element in the Earths crust, and the fourth most abundant element in the universe by mass after hydrogen, helium, and oxygen. It is the second most abundant element in the body by mass after oxygen. The atoms of carbon can bond together in different ways, termed allotropes of carbon, the best known are graphite, diamond, and amorphous carbon. The physical properties of carbon vary widely with the allotropic form, for example, graphite is opaque and black while diamond is highly transparent. Graphite is soft enough to form a streak on paper, while diamond is the hardest naturally occurring material known, graphite is a good electrical conductor while diamond has a low electrical conductivity. Under normal conditions, diamond, carbon nanotubes, and graphene have the highest thermal conductivities of all known materials, all carbon allotropes are solids under normal conditions, with graphite being the most thermodynamically stable form. They are chemically resistant and require high temperature to react even with oxygen, the most common oxidation state of carbon in inorganic compounds is +4, while +2 is found in carbon monoxide and transition metal carbonyl complexes. The largest sources of carbon are limestones, dolomites and carbon dioxide, but significant quantities occur in organic deposits of coal, peat, oil. For this reason, carbon has often referred to as the king of the elements. The allotropes of carbon graphite, one of the softest known substances, and diamond. It bonds readily with other small atoms including other carbon atoms, Carbon is known to form almost ten million different compounds, a large majority of all chemical compounds. Carbon also has the highest sublimation point of all elements, although thermodynamically prone to oxidation, carbon resists oxidation more effectively than elements such as iron and copper that are weaker reducing agents at room temperature. Carbon is the element, with a ground-state electron configuration of 1s22s22p2. Its first four ionisation energies,1086.5,2352.6,4620.5 and 6222.7 kJ/mol, are higher than those of the heavier group 14 elements. Carbons covalent radii are normally taken as 77.2 pm,66.7 pm and 60.3 pm, although these may vary depending on coordination number, in general, covalent radius decreases with lower coordination number and higher bond order. Carbon compounds form the basis of all life on Earth
35.
Debye model
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In thermodynamics and solid state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat in a solid. It treats the vibrations of the lattice as phonons in a box, in contrast to the Einstein model. The Debye model correctly predicts the low temperature dependence of the heat capacity, just like the Einstein model, it also recovers the Dulong–Petit law at high temperatures. But due to simplifying assumptions, its accuracy suffers at intermediate temperatures, see M. Shubin and T. Sunada for a rigorous treatment of the Debye model. The Debye model is an equivalent of Plancks law of black body radiation. The Debye model treats atomic vibrations as phonons in a box, most of the calculation steps are identical. Consider a cube of side L, from the particle in a box article, the resonating modes of the sonic disturbances inside the box have wavelengths given by λ n =2 L n, where n is an integer. The energy of a phonon is E n = h ν n, in three dimensions we will use, E n 2 = p n 2 c s 2 =2, in which p n is the magnitude of the three-dimensional momentum of the phonon. Lets now compute the energy in the box, E = ∑ n E n N ¯. In other words, the energy is equal to the sum of energy multiplied by the number of phonons with that energy. In 3 dimensions we have, U = ∑ n x ∑ n y ∑ n z E n N ¯, now, this is where Debye model and Plancks law of black body radiation differ. Unlike electromagnetic radiation in a box, there is a number of phonon energy states because a phonon cannot have infinite frequency. Its frequency is bound by the medium of its propagation—the atomic lattice of the solid, consider an illustration of a transverse phonon below. It is reasonable to assume that the wavelength of a phonon is twice the atom separation. There are N atoms in a solid and our solid is a cube, which means there are N3 atoms per edge. Atom separation is then given by L / N3, and this is the upper limit of the triple energy sum U = ∑ n x N3 ∑ n y N3 ∑ n z N3 E n N ¯. For slowly varying, well-behaved functions, a sum can be replaced with an integral U ≈ ∫0 N3 ∫0 N3 ∫0 N3 E N ¯ d n x d n y d n z. So far, there has no mention of N ¯
36.
Heat capacity
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Heat capacity or thermal capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change. The unit of capacity is joule per kelvin J K. Specific heat is the amount of heat needed to raise the temperature of one kilogram of mass by 1 kelvin, Heat capacity is an extensive property of matter, meaning it is proportional to the size of the system. The molar heat capacity is the capacity per unit amount of a pure substance. In some engineering contexts, the heat capacity is used. Other contributions can come from magnetic and electronic degrees of freedom in solids, for quantum mechanical reasons, at any given temperature, some of these degrees of freedom may be unavailable, or only partially available, to store thermal energy. In such cases, the capacity is a fraction of the maximum. As the temperature approaches zero, the heat capacity of a system approaches zero. Quantum theory can be used to predict the heat capacity of simple systems. In a previous theory of common in the early modern period, heat was thought to be a measurement of an invisible fluid. Bodies were capable of holding an amount of this fluid, hence the term heat capacity, named. Heat is no longer considered a fluid, but rather a transfer of disordered energy, nevertheless, at least in English, the term heat capacity survives. In some other languages, the thermal capacity is preferred. In the International System of Units, heat capacity has the unit joules per kelvin, if the temperature change is sufficiently small the heat capacity may be assumed to be constant, C = Q Δ T. Heat capacity is a property, meaning it depends on the extent or size of the physical system studied. A sample containing twice the amount of substance as another sample requires the transfer of twice the amount of heat to achieve the change in temperature. For many purposes it is convenient to report heat capacity as an intensive property. In practice, this is most often an expression of the property in relation to a unit of mass, in science and engineering, International standards now recommend that specific heat capacity always refer to division by mass
37.
Einstein solid
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In the Einstein model, each atom oscillates independently. The original theory proposed by Einstein in 1907 has great historical relevance, the heat capacity of solids as predicted by the empirical Dulong-Petit law was required by classical mechanics, the specific heat of solids should be independent of temperature. But experiments at low temperatures showed that the heat capacity changes, as the temperature goes up, the specific heat goes up until it approaches the Dulong and Petit prediction at high temperature. By employing Plancks quantization assumption, Einsteins theory accounted for the experimental trend for the first time. Together with the effect, this became one of the most important pieces of evidence for the need of quantization. Einstein used the levels of the mechanical oscillator many years before the advent of modern quantum mechanics. Einstein’s Theory of Specific Heats In Einsteins model, the specific heat approaches zero exponentially fast at low temperatures and this is because all the oscillations have one common frequency. The correct behavior is found by quantizing the normal modes of the solid in the way that Einstein suggested. Then the frequencies of the waves are not all the same, and the specific heat goes to zero as a T3 power law and this modification is called the Debye Model, which appeared in 1912. When Walther Nernst learned of Einsteins 1907 paper on specific heat, he was so excited that he traveled all the way from Berlin to Zürich to meet with him. The heat capacity of an object at constant volume V is defined through the internal energy U as C V = V. T, to find the entropy consider a solid made of N atoms, each of which has 3 degrees of freedom. So there are 3 N quantum harmonic oscillators, next, we must compute the multiplicity of the system. That is, compute the number of ways to distribute q quanta of energy among N ′ SHOs, the number of arrangements of n objects is n. So the number of arrangements of q pebbles and N ′ −1 partitions is. However, if partition #3 and partition #5 trade places, no one would notice, the same argument goes for quanta. To obtain the number of possible distinguishable arrangements one has to divide the number of arrangements by the number of indistinguishable arrangements. There are q. identical quanta arrangements, and, therefore, multiplicity of the system is given by Ω =. Q. which, as mentioned before, is the number of ways to deposit q quanta of energy into N ′ oscillators, entropy of the system has the form S / k = ln Ω = ln
38.
Thermal expansion
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Thermal expansion is the tendency of matter to change in shape, area, and volume in response to a change in temperature. Temperature is a function of the average molecular kinetic energy of a substance. When a substance is heated, the energy of its molecules increases. Thus, the molecules begin vibrating/moving more and usually maintain an average separation. Materials which contract with increasing temperature are unusual, this effect is limited in size, the degree of expansion divided by the change in temperature is called the materials coefficient of thermal expansion and generally varies with temperature. If an equation of state is available, it can be used to predict the values of the expansion at all the required temperatures and pressures. A number of contract on heating within certain temperature ranges. For example, the coefficient of expansion of water drops to zero as it is cooled to 3. Also, fairly pure silicon has a coefficient of thermal expansion for temperatures between about 18 and 120 Kelvin. Unlike gases or liquids, solid materials tend to keep their shape when undergoing thermal expansion, in general, liquids expand slightly more than solids. The thermal expansion of glasses is higher compared to that of crystals, at the glass transition temperature, rearrangements that occur in an amorphous material lead to characteristic discontinuities of coefficient of thermal expansion and specific heat. These discontinuities allow detection of the transition temperature where a supercooled liquid transforms to a glass. Absorption or desorption of water can change the size of common materials. Common plastics exposed to water can, in the long term, the coefficient of thermal expansion describes how the size of an object changes with a change in temperature. Specifically, it measures the change in size per degree change in temperature at a constant pressure. Several types of coefficients have been developed, volumetric, area, which is used depends on the particular application and which dimensions are considered important. For solids, one might only be concerned with the change along a length, the volumetric thermal expansion coefficient is the most basic thermal expansion coefficient, and the most relevant for fluids. In general, substances expand or contract when their temperature changes, substances that expand at the same rate in every direction are called isotropic
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Maxwell relations
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Maxwells relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. These relations are named for the nineteenth-century physicist James Clerk Maxwell, the structure of Maxwell relations is a statement of equality among the second derivatives for continuous functions. It follows directly from the fact that the order of differentiation of a function of two variables is irrelevant. It is seen that for every thermodynamic potential there are n/2 possible Maxwell relations where n is the number of variables for that potential. The thermodynamic square can be used as a mnemonic to recall, the usefulness of these relations lies in their quantifying entropy changes, which are not directly measurable, in terms of measurable quantities like temperature, volume, and pressure. Maxwell relations are based on simple partial differentiation rules, in particular the differential of a function. This leads to the identity d P d V = d T d S. The physical meaning of identity can be seen by noting that the two sides are the equivalent ways of writing the work done in an infinitesimal Carnot cycle. An equivalent way of writing the identity is ∂ ∂ =1, the Maxwell relations now follow directly. For example, T = ∂ ∂ = ∂ ∂ = V, the critical step is the penultimate one. The other Maxwell relations follow in similar fashion, for example, S = ∂ ∂ = ∂ ∂ = − V. The above are not the only Maxwell relationships, for example, if we have a single-component gas, then the number of particles N is also a natural variable of the above four thermodynamic potentials. The Maxwell relationship for the enthalpy with respect to pressure and particle number would then be, in addition, there are other thermodynamic potentials besides the four that are commonly used, and each of these potentials will yield a set of Maxwell relations. Each equation can be re-expressed using the relationship z =1 / z which are also known as Maxwell relations. Table of thermodynamic equations Thermodynamic equations
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Phenomenon
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A phenomenon is any thing which manifests itself. Phenomena are often, but not always, understood as things that appear or experiences for a sentient being, the term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon. In contrast to a phenomenon, a noumenon can not be directly observed, Kant was heavily influenced by Gottfried Wilhelm Leibniz in this part of his philosophy, in which phenomenon and noumenon serve as interrelated technical terms. In modern philosophical use, the phenomena has come to mean what is experienced is the basis of reality. He wrote that humans could infer only as much as their senses allowed, thus, the term phenomenon refers to any incident deserving of inquiry and investigation, especially events that are particularly unusual or of distinctive importance. According to The Columbia Encyclopedia, Modern philosophers have used phenomenon to designate what is apprehended before judgment is applied and this may not be possible if observation is theory laden. In scientific usage, a phenomenon is any event that is observable, however common it might be, even if it requires the use of instrumentation to observe, record, another example of scientific phenomena can be found in the experience of phantom limb sensations. This occurrence, the sensation of feeling in amputated limbs, is reported by over 70% of amputees, although the limb is no longer present, they report still experiencing sensations. This is an event that defies typical logic and has been a source of much curiosity within the medical and physiological fields. A mechanical phenomenon is a phenomenon associated with the equilibrium or motion of objects. Some examples are Newtons cradle, engines, and double pendulums, in gemology, a phenomenon is an unusual optical effect that is displayed by a gem. Play-of-color, labradorescence, iridescence, adularescence, chatoyancy, asterism, aventurescence, lustre, group phenomena concern the behavior of a particular group of individual entities, usually organisms and most especially people. The behavior of individuals often changes in a setting in various ways. Social phenomena apply especially to organisms and people in that states are implicit in the term. Attitudes and events particular to a group may have effects beyond the group, in popular usage, a phenomenon often refers to an extraordinary event. The term is most commonly used to refer to occurrences that at first defy explanation or baffle the observer
41.
Gibbs free energy
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Just as in mechanics, where the decrease in potential energy is defined as maximum useful work that can be performed, similarly different potentials have different meanings. The Gibbs energy is also the potential that is minimized when a system reaches chemical equilibrium at constant pressure and temperature. Its derivative with respect to the coordinate of the system vanishes at the equilibrium point. As such, a reduction in G is a condition for the spontaneity of processes at constant pressure and temperature. The Gibbs free energy, originally called available energy, was developed in the 1870s by the American scientist Josiah Willard Gibbs. The initial state of the body, according to Gibbs, is supposed to be such that the body can be made to pass from it to states of dissipated energy by reversible processes. In his 1876 magnum opus On the Equilibrium of Heterogeneous Substances, according to the second law of thermodynamics, for systems reacting at STP, there is a general natural tendency to achieve a minimum of the Gibbs free energy. A quantitative measure of the favorability of a reaction at constant temperature and pressure is the change ΔG in Gibbs free energy that is caused by the reaction. As a necessary condition for the reaction to occur at constant temperature and pressure, ΔG must be smaller than the non-PV work, ΔG equals the maximum amount of non-PV work that can be performed as a result of the chemical reaction for the case of reversible process. The equation can be seen from the perspective of the system taken together with its surroundings. First assume that the reaction at constant temperature and pressure is the only one that is occurring. Then the entropy released or absorbed by the system equals the entropy that the environment must absorb or release, the reaction will only be allowed if the total entropy change of the universe is zero or positive. This is reflected in a negative ΔG, and the reaction is called exergonic, if we couple reactions, then an otherwise endergonic chemical reaction can be made to happen. In traditional use, the term free was included in Gibbs free energy to mean available in the form of useful work, the characterization becomes more precise if we add the qualification that it is the energy available for non-volume work. However, a number of books and journal articles do not include the attachment free. This is the result of a 1988 IUPAC meeting to set unified terminologies for the scientific community. This standard, however, has not yet been universally adopted. Further, Gibbs stated, In this description, as used by Gibbs, ε refers to the energy of the body, η refers to the entropy of the body
42.
Chemical reaction
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A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Nuclear chemistry is a sub-discipline of chemistry that involves the reactions of unstable. The substance initially involved in a reaction are called reactants or reagents. Chemical reactions are characterized by a chemical change, and they yield one or more products. Reactions often consist of a sequence of individual sub-steps, the elementary reactions. Chemical reactions are described with chemical equations, which present the starting materials, end products. Chemical reactions happen at a characteristic reaction rate at a given temperature, typically, reaction rates increase with increasing temperature because there is more thermal energy available to reach the activation energy necessary for breaking bonds between atoms. Reactions may proceed in the forward or reverse direction until they go to completion or reach equilibrium, Reactions that proceed in the forward direction to approach equilibrium are often described as spontaneous, requiring no input of free energy to go forward. Non-spontaneous reactions require input of energy to go forward. Different chemical reactions are used in combinations during chemical synthesis in order to obtain a desired product, in biochemistry, a consecutive series of chemical reactions form metabolic pathways. These reactions are catalyzed by protein enzymes. Chemical reactions such as combustion in fire, fermentation and the reduction of ores to metals were known since antiquity, in the Middle Ages, chemical transformations were studied by Alchemists. They attempted, in particular, to lead into gold, for which purpose they used reactions of lead. The process involved heating of sulfate and nitrate minerals such as sulfate, alum. In the 17th century, Johann Rudolph Glauber produced hydrochloric acid and sodium sulfate by reacting sulfuric acid, further optimization of sulfuric acid technology resulted in the contact process in the 1880s, and the Haber process was developed in 1909–1910 for ammonia synthesis. From the 16th century, researchers including Jan Baptist van Helmont, Robert Boyle, the phlogiston theory was proposed in 1667 by Johann Joachim Becher. It postulated the existence of an element called phlogiston, which was contained within combustible bodies. This proved to be false in 1785 by Antoine Lavoisier who found the explanation of the combustion as reaction with oxygen from the air
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