The Fahrenheit scale is a temperature scale based on one proposed in 1724 by Dutch–German–Polish physicist Daniel Gabriel Fahrenheit. It uses the degree Fahrenheit as the unit. Several accounts of how he defined his scale exist; the lower defining point, 0 °F, was established as the freezing temperature of a solution of brine made from equal parts of ice and salt. Further limits were established as the melting point of ice and his best estimate of the average human body temperature; the scale is now defined by two fixed points: the temperature at which water freezes into ice is defined as 32 °F, the boiling point of water is defined to be 212 °F, a 180 °F separation, as defined at sea level and standard atmospheric pressure. At the end of the 2010s, Fahrenheit was used as the official temperature scale only in the United States, its associated states in the Western Pacific, the Bahamas, the Cayman Islands and Liberia. Antigua and Barbuda and other islands which use the same meteorological service, such as Anguilla, the British Virgin Islands and Saint Kitts and Nevis, as well as Bermuda and the Turks and Caicos Islands, use Fahrenheit and Celsius.
All other countries in the world now use the Celsius scale, named after Swedish astronomer Anders Celsius. On the Fahrenheit scale, the freezing point of water is 32 degrees Fahrenheit and the boiling point is 212 °F; this puts the freezing points of water 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. The Rankine temperature scale uses degree intervals of the same size as those of the Fahrenheit scale, except that absolute zero is 0 °R — the same way that the Kelvin temperature scale matches the Celsius scale, except that absolute zero is 0 K; the Fahrenheit scale uses the symbol ° to denote a point on the temperature scale and the letter F to indicate the use of the Fahrenheit scale, as well as to denote a difference between temperatures or an uncertainty in temperature.
For an exact conversion, the following formulas can be applied. Here, f is the value in Fahrenheit and c the value in Celsius: f °Fahrenheit to c °Celsius: °F × 5°C/9°F = /1.8 °C = c °C c °Celsius to f °Fahrenheit: + 32 °F = °F + 32 °F = f °FThis is an exact conversion making use of the identity −40 °F = −40 °C. Again, f is the value in Fahrenheit and c the value in Celsius: f °Fahrenheit to c °Celsius: − 40 = c. C °Celsius to f °Fahrenheit: − 40 = f. Fahrenheit proposed his temperature scale in 1724, basing it on two reference points of temperature. In his initial scale, the zero point was determined by placing the thermometer in a mixture "of ice, of water, of ammonium chloride or of sea salt"; this combination forms a eutectic system which stabilizes its temperature automatically: 0 °F was defined to be that stable temperature. The second point, 96 degrees, was the human body's temperature. According to a story in Germany, Fahrenheit chose the lowest air temperature measured in his hometown Danzig in winter 1708/09 as 0 °F, only had the need to be able to make this value reproducible using brine.
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 Rømer's scale, brine freezes at zero, water freezes and melts at 7.5 degrees, body temperature is 22.5, water boils at 60 degrees. Fahrenheit multiplied each value by four in order to eliminate fractions and make the scale more fine-grained, he re-calibrated his scale using the melting point of ice and normal human body temperature. Fahrenheit soon after observed; the use of the freezing and boiling points of water as thermometer fixed reference points became popular following the work of Anders Celsius and these fixed points were adopted by a committee of the Royal Society led by Henry Cavendish in 1776. Under this system, the Fahrenheit scale is redefined so that the freezing point of water is 32 °F, the boiling point is 212 °F or 180 degrees higher, it is for this reason that normal human body temperature is 98° on the revised scale. In the present-day Fahrenheit scale, 0 °F no longer corresponds to the eutectic temperature of ammonium chloride brine as described above.
Instead, that eutectic is at 4 °F on the final Fahrenheit scale. The Rankine temperature s
In physics, the electronvolt is a unit of energy equal to 1.6×10−19 joules in SI units. The electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences, because a particle with electric charge q has an energy E = qV after passing through the potential V. Like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 J/C √2hα / μ0c0, it is a common unit of energy within physics used in solid state, atomic and particle physics. It is used with the metric prefixes milli-, kilo-, mega-, giga-, tera-, peta- or exa-. In some older documents, in the name Bevatron, the symbol BeV is used, which stands for billion electronvolts. An electronvolt is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. Hence, it has a value of one volt, 1 J/C, multiplied by the electron's elementary charge e, 1.6021766208×10−19 C.
Therefore, one electronvolt is equal to 1.6021766208×10−19 J. The electronvolt, as opposed to volt, is not an SI unit, its derivation is empirical, which means its value in SI units must be obtained by experiment and is therefore not known unlike the litre, the light-year and such other non-SI units. Electronvolt is a unit of energy; the SI unit for energy is joule. 1 eV is equal to 1.6021766208×10−19 J. By mass–energy equivalence, the electronvolt is a unit of mass, it is common in particle physics, where units of mass and energy are interchanged, to express mass in units of eV/c2, where c is the speed of light in vacuum. It is common to express mass in terms of "eV" as a unit of mass using a system of natural units with c set to 1; the mass equivalent of 1 eV/c2 is 1 eV / c 2 = ⋅ 1 V 2 = 1.783 × 10 − 36 kg. For example, an electron and a positron, each with a mass of 0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy. The proton has a mass of 0.938 GeV/c2. In general, the masses of all hadrons are of the order of 1 GeV/c2, which makes the GeV a convenient unit of mass for particle physics: 1 GeV/c2 = 1.783×10−27 kg.
The unified atomic mass unit, 1 gram divided by Avogadro's number, is the mass of a hydrogen atom, the mass of the proton. To convert to megaelectronvolts, use the formula: 1 u = 931.4941 MeV/c2 = 0.9314941 GeV/c2. In high-energy physics, the electronvolt is used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy; this gives rise to usage of eV as units of momentum, for the energy supplied results in acceleration of the particle. The dimensions of momentum units are LMT−1; the dimensions of energy units are L2MT−2. Dividing the units of energy by a fundamental constant that has units of velocity, facilitates the required conversion of using energy units to describe momentum. In the field of high-energy particle physics, the fundamental velocity unit is the speed of light in vacuum c. By dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/c; the fundamental velocity constant c is dropped from the units of momentum by way of defining units of length such that the value of c is unity.
For example, if the momentum p of an electron is said to be 1 GeV the conversion to MKS can be achieved by: p = 1 GeV / c = ⋅ ⋅ = 5.344286 × 10 − 19 kg ⋅ m / s. In particle physics, a system of "natural units" in which the speed of light in vacuum c and the reduced Planck constant ħ are dimensionless and equal to unity is used: c = ħ = 1. In these units, both distances and times are expressed in inverse energy units (while energy and mass are expressed in the same units, see mas
A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei, can be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur; the substance involved in a chemical reaction are called reactants or reagents. Chemical reactions are characterized by a chemical change, they yield one or more products, which have properties different from the reactants. Reactions consist of a sequence of individual sub-steps, the so-called elementary reactions, the information on the precise course of action is part of the reaction mechanism. Chemical reactions are described with chemical equations, which symbolically present the starting materials, end products, sometimes intermediate products and reaction conditions.
Chemical reactions happen at a characteristic reaction rate at a given temperature and chemical concentration. 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 described as spontaneous, requiring no input of free energy to go forward. Non-spontaneous reactions require input of free 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. Enzymes increase the rates of biochemical reactions, so that metabolic syntheses and decompositions impossible under ordinary conditions can occur at the temperatures and concentrations present within a cell.
The general concept of a chemical reaction has been extended to reactions between entities smaller than atoms, including nuclear reactions, radioactive decays, reactions between elementary particles, as described by quantum field theory. Chemical reactions such as combustion in fire and the reduction of ores to metals were known since antiquity. Initial theories of transformation of materials were developed by Greek philosophers, such as the Four-Element Theory of Empedocles stating that any substance is composed of the four basic elements – fire, water and earth. In the Middle Ages, chemical transformations were studied by Alchemists, they attempted, in particular, to convert lead into gold, for which purpose they used reactions of lead and lead-copper alloys with sulfur. The production of chemical substances that do not occur in nature has long been tried, such as the synthesis of sulfuric and nitric acids attributed to the controversial alchemist Jābir ibn Hayyān; the process involved heating of sulfate and nitrate minerals such as copper sulfate and saltpeter.
In the 17th century, Johann Rudolph Glauber produced hydrochloric acid and sodium sulfate by reacting sulfuric acid and sodium chloride. With the development of the lead chamber process in 1746 and the Leblanc process, allowing large-scale production of sulfuric acid and sodium carbonate chemical reactions became implemented into the industry. Further optimization of sulfuric acid technology resulted in the contact process in the 1880s, the Haber process was developed in 1909–1910 for ammonia synthesis. From the 16th century, researchers including Jan Baptist van Helmont, Robert Boyle, Isaac Newton tried to establish theories of the experimentally observed chemical transformations; the phlogiston theory was proposed in 1667 by Johann Joachim Becher. It postulated the existence of a fire-like element called "phlogiston", contained within combustible bodies and released during combustion; this proved to be false in 1785 by Antoine Lavoisier who found the correct explanation of the combustion as reaction with oxygen from the air.
Joseph Louis Gay-Lussac recognized in 1808 that gases always react in a certain relationship with each other. Based on this idea and the atomic theory of John Dalton, Joseph Proust had developed the law of definite proportions, which resulted in the concepts of stoichiometry and chemical equations. Regarding the organic chemistry, it was long believed that compounds obtained from living organisms were too complex to be obtained synthetically. According to the concept of vitalism, organic matter was endowed with a "vital force" and distinguished from inorganic materials; this separation was ended however by the synthesis of urea from inorganic precursors by Friedrich Wöhler in 1828. Other chemists who brought major contributions to organic chemistry include Alexander William Williamson with his synthesis of ethers and Christopher Kelk Ingold, among many discoveries, established the mechanisms of substitution reactions. Chemical equations are used to graphically illustrate chemical reactions, they consist of chemical or structural formulas of the reactants on the left and those of the products on the right.
They are separated by an arrow which indicates the type of the reaction.
Standardization or standardisation is the process of implementing and developing technical standards based on the consensus of different parties that include firms, interest groups, standards organizations and governments Standardization can help to maximize compatibility, safety, repeatability, or quality. It can facilitate commoditization of custom processes. In social sciences, including economics, the idea of standardization is close to the solution for a coordination problem, a situation in which all parties can realize mutual gains, but only by making mutually consistent decisions; this view includes the case of "spontaneous standardization processes", to produce de facto standards. Standard weights and measures were developed by the Indus Valley Civilization; the centralized weight and measure system served the commercial interest of Indus merchants as smaller weight measures were used to measure luxury goods while larger weights were employed for buying bulkier items, such as food grains etc.
Weights existed in categories. Technical standardisation enabled gauging devices to be used in angular measurement and measurement for construction. Uniform units of length were used in the planning of towns such as Lothal, Kalibangan, Dolavira and Mohenjo-daro; the weights and measures of the Indus civilization reached Persia and Central Asia, where they were further modified. Shigeo Iwata describes the excavated weights unearthed from the Indus civilization: A total of 558 weights were excavated from Mohenjodaro and Chanhu-daro, not including defective weights, they did not find statistically significant differences between weights that were excavated from five different layers, each measuring about 1.5 m in depth. This was evidence; the 13.7-g weight seems to be one of the units used in the Indus valley. The notation was based on decimal systems. 83% of the weights which were excavated from the above three cities were cubic, 68% were made of chert. The implementation of standards in industry and commerce became important with the onset of the Industrial Revolution and the need for high-precision machine tools and interchangeable parts.
Henry Maudslay developed the first industrially practical screw-cutting lathe in 1800. This allowed for the standardisation of screw thread sizes for the first time and paved the way for the practical application of interchangeability to nuts and bolts. Before this, screw threads were made by chipping and filing. Nuts were rare. Metal bolts passing through wood framing to a metal fastening on the other side were fastened in non-threaded ways. Maudslay standardized the screw threads used in his workshop and produced sets of taps and dies that would make nuts and bolts to those standards, so that any bolt of the appropriate size would fit any nut of the same size; this was a major advance in workshop technology. Maudslay's work, as well as the contributions of other engineers, accomplished a modest amount of industry standardization. Joseph Whitworth's screw thread measurements were adopted as the first national standard by companies around the country in 1841, it came to be known as the British Standard Whitworth, was adopted in other countries.
This new standard specified a 55° thread angle and a thread depth of 0.640327p and a radius of 0.137329p, where p is the pitch. The thread pitch increased with diameter in steps specified on a chart. An example of the use of the Whitworth thread is the Royal Navy's Crimean War gunboats; these were the first instance of "mass-production" techniques being applied to marine engineering. With the adoption of BSW by British railway lines, many of which had used their own standard both for threads and for bolt head and nut profiles, improving manufacturing techniques, it came to dominate British manufacturing. American Unified Coarse was based on the same imperial fractions; the Unified thread angle has flattened crests. Thread pitch is the same in both systems except that the thread pitch for the 1⁄2 in bolt is 12 threads per inch in BSW versus 13 tpi in the UNC. By the end of the 19th century, differences in standards between companies, was making trade difficult and strained. For instance, an iron and steel dealer recorded his displeasure in The Times: "Architects and engineers specify such unnecessarily diverse types of sectional material or given work that anything like economical and continuous manufacture becomes impossible.
In this country no two professional men are agreed upon the size and weight of a girder to employ for given work." The Engineering Standards Committee was established in London in 1901 as the world's first national standards body. It subsequently extended its standardization work and became the British Engineering Standards Association in 1918, adopting the name British Standards Institution in 1931 after receiving its Royal Charter in 1929; the national standards were adopted universally throughout the country, enabled the markets to act more rationally and efficiently, with an increased level of cooperation. After the First World War, similar national bodies were established in other countries; the Deutsches Institut für Normung was set up in Germany in 1917, followed by its counterparts, the American National Standard Institute and the French Commissi
The Celsius scale known as the centigrade scale, is a temperature scale used by the International System of Units. As an SI derived unit, it is used by all countries except the United States, the Bahamas, the Cayman Islands and Liberia, it is named after the Swedish astronomer Anders Celsius. The degree Celsius can refer to a specific temperature on the Celsius scale or a unit to indicate a difference between two temperatures or an uncertainty. Before being renamed to honor Anders Celsius in 1948, the unit was called centigrade, from the Latin centum, which means 100, gradus, which means steps. From 1743, the Celsius scale is based on 0 °C for the freezing point of water and 100 °C for the boiling point of water at 1 atm pressure. Prior to 1743, the scale was based on the boiling and melting points of water, but the values were reversed; the 1743 scale reversal was proposed by Jean-Pierre Christin. By international agreement, since 1954 the unit degree Celsius and the Celsius scale are defined by absolute zero and the triple point of Vienna Standard Mean Ocean Water, a specially purified water.
This definition precisely relates the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature with symbol K. Absolute zero, the lowest temperature possible, is defined as being 0 K and −273.15 °C. The temperature of the triple point of water is defined as 273.16 K. This means that a temperature difference of one degree Celsius and that of one kelvin are the same. On 20 May 2019, the kelvin, along with it the degree Celsius, will be redefined so that its value will be determined by definition of the Boltzmann constant. In 1742, Swedish astronomer Anders Celsius created a temperature scale, the reverse of the scale now known as "Celsius": 0 represented the boiling point of water, while 100 represented the freezing point of water. In his paper Observations of two persistent degrees on a thermometer, he recounted his experiments showing that the melting point of ice is unaffected by pressure, he determined with remarkable precision how the boiling point of water varied as a function of atmospheric pressure.
He proposed that the zero point of his temperature scale, being the boiling point, would be calibrated at the mean barometric pressure at mean sea level. This pressure is known as one standard atmosphere; the BIPM's 10th General Conference on Weights and Measures defined one standard atmosphere to equal 1,013,250 dynes per square centimetre. In 1743, the Lyonnais physicist Jean-Pierre Christin, permanent secretary of the Académie des sciences, belles-lettres et arts de LyonAcadémie des sciences, belles-lettres et arts de Lyon, working independently of Celsius, developed a scale where zero represented the freezing point of water and 100 represented the boiling point of water. On 19 May 1743 he published the design of a mercury thermometer, the "Thermometer of Lyon" built by the craftsman Pierre Casati that used this scale. In 1744, coincident with the death of Anders Celsius, the Swedish botanist Carl Linnaeus reversed Celsius's scale, his custom-made "linnaeus-thermometer", for use in his greenhouses, was made by Daniel Ekström, Sweden's leading maker of scientific instruments at the time, whose workshop was located in the basement of the Stockholm observatory.
As happened in this age before modern communications, numerous physicists and instrument makers are credited with having independently developed this same scale. The first known Swedish document reporting temperatures in this modern "forward" Celsius scale is the paper Hortus Upsaliensis dated 16 December 1745 that Linnaeus wrote to a student of his, Samuel Nauclér. In it, Linnaeus recounted the temperatures inside the orangery at the University of Uppsala Botanical Garden:...since the caldarium by the angle of the windows from the rays of the sun, obtains such heat that the thermometer reaches 30 degrees, although the keen gardener takes care not to let it rise to more than 20 to 25 degrees, in winter not under 15 degrees... Since the 19th century, the scientific and thermometry communities worldwide have used the phrase "centigrade scale". Temperatures on the centigrade scale were reported as degrees or, when greater specificity was desired, as degrees centigrade; because the term centigrade was the Spanish and French language name for a unit of angular measurement and had a similar connotation in other languages, the term centesimal degree was used when precise, unambiguous language was required by international standards bodies such as the BIPM.
More properly, what was defined as "centigrade" would now be "hectograde". To eliminate any confusion, the 9th CGPM and the CIPM formally adopted "degree Celsius" in 1948, formally keeping the recognized degree symbol, rather than adopting the gradian/centesimal degree symbol. For scientific use, "Celsius" is the term used, with "centigrade" remaining in common but decreasing use in informal contexts in English-speaking countries, it was not until February 1985 that the weather forecasts issued by
Gibbs free energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum of reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system; when a system transforms reversibly from an initial state to a final state, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces. The Gibbs energy is the thermodynamic potential, minimized when a system reaches chemical equilibrium at constant pressure and temperature, its derivative with respect to the reaction coordinate of the system vanishes at the equilibrium point. As such, a reduction in G is a necessary condition for the spontaneity of processes at constant pressure and temperature; the Gibbs free energy called available energy, was developed in the 1870s by the American scientist Josiah Willard Gibbs.
In 1873, Gibbs described this "available energy" as the greatest amount of mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total volume or allowing heat to pass to or from external bodies, except such as at the close of the processes are left in their initial condition. 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, a graphical analysis of multi-phase chemical systems, he engaged his thoughts on chemical free energy in full. 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 given reaction at constant temperature and pressure is the change ΔG in Gibbs free energy, 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, equal to zero. 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. If the analysis indicated a positive ΔG for the reaction energy — in the form of electrical or other non-PV work — would have to be added to the reacting system for ΔG to be smaller than the non-PV work and make it possible for the reaction to occur. We can think of ∆G as the amount of "free" or "useful" energy available to do work; the equation can be seen from the perspective of the system taken together with its surroundings. First, assume that the given reaction at constant temperature and pressure is the only one, occurring; the entropy released or absorbed by the system equals the entropy that the environment must absorb or release, respectively. The reaction will only be allowed if the total entropy change of the universe is positive.
This is reflected in a negative ΔG, the reaction is called exergonic. If we couple reactions an otherwise endergonic chemical reaction can be made to happen; the input of heat into an inherently endergonic reaction, such as the elimination of cyclohexanol to cyclohexene, can be seen as coupling an unfavourable reaction to a favourable one such that the total entropy change of the universe is greater than or equal to zero, making the total Gibbs free energy difference of the coupled reactions negative. 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, an increasing number of books and journal articles do not include the attachment "free", referring to G as "Gibbs energy"; this is the result of a 1988 IUPAC meeting to set unified terminologies for the international scientific community, in which the adjective "free" was banished.
This standard, has not yet been universally adopted. The quantity called "free energy" is a more advanced and accurate replacement for the outdated term affinity, used by chemists in the earlier years of physical chemistry to describe the force that caused chemical reactions. In 1873, Willard Gibbs published A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces, in which he sketched the principles of his new equation, able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. By studying the interactions of homogeneous substances in contact, i.e. bodies composed of part solid, part liquid, part vapor, by using a three-dimensional volume-entropy-internal energy graph, Gibbs was able to determine three states of equilibrium, i.e. "necessarily stable", "neutral", "unstable", whether or not changes woul
The term phase transition is most used to describe transitions between solid and gaseous states of matter, as well as plasma in rare cases. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change discontinuously, as a result of the change of external conditions, such as temperature, pressure, or others. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume; the measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions occur in nature and are used today in many technologies. Examples of phase transitions include: The transitions between the solid and gaseous phases of a single component, due to the effects of temperature and/or pressure: A eutectic transformation, in which a two component single phase liquid is cooled and transforms into two solid phases.
The same process, but beginning with a solid instead of a liquid is called a eutectoid transformation. A peritectic transformation, in which a two component single phase solid is heated and transforms into a solid phase and a liquid phase. A spinodal decomposition, in which a single phase is cooled and separates into two different compositions of that same phase. Transition to a mesophase between solid and liquid, such as one of the "liquid crystal" phases; the transition between the ferromagnetic and paramagnetic phases of magnetic materials at the Curie point. The transition between differently ordered, commensurate or incommensurate, magnetic structures, such as in cerium antimonide; the martensitic transformation which occurs as one of the many phase transformations in carbon steel and stands as a model for displacive phase transformations. Changes in the crystallographic structure such as between ferrite and austenite of iron. Order-disorder transitions such as in alpha-titanium aluminides.
The dependence of the adsorption geometry on coverage and temperature, such as for hydrogen on iron. The emergence of superconductivity in certain metals and ceramics when cooled below a critical temperature; the transition between different molecular structures of solids, such as between an amorphous structure and a crystal structure, between two different crystal structures, or between two amorphous structures. Quantum condensation of bosonic fluids; the superfluid transition in liquid helium is an example of this. The breaking of symmetries in the laws of physics during the early history of the universe as its temperature cooled. Isotope fractionation occurs during a phase transition, the ratio of light to heavy isotopes in the involved molecules changes; when water vapor condenses, the heavier water isotopes become enriched in the liquid phase while the lighter isotopes tend toward the vapor phase. Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables.
This condition stems from the interactions of a large number of particles in a system, does not appear in systems that are too small. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, where temperature is not a parameter. Examples include: quantum phase transitions, dynamic phase transitions, topological phase transitions. In these types of systems other parameters take the place of temperature. For instance, connection probability replaces temperature for percolating networks. At the phase transition point the two phases of a substance and vapor, have identical free energies and therefore are likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the gaseous form is preferred, it is sometimes possible to change the state of a system diabatically in such a way that it can be brought past a phase transition point without undergoing a phase transition. The resulting state is metastable, i.e. less stable than the phase to which the transition would have occurred, but not unstable either.
This occurs in superheating and supersaturation, for example. Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free energy as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the free energy, discontinuous at the transition. First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable; the various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, the first derivative of the free energy with respect to pressure. Second-order phase transitions are continuous in the first derivative but exhibit discontinuity in a second derivative of the free energy; these include the ferromagnetic phase transition in materials such as iron, where the magnetization, the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the Curie temperature.
The magnetic susceptibility, the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification sche