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Massieu Function
In thermodynamics, the Massieu function (sometimes called Massieu–Gibbs function, Massieu potential, or Gibbs function, or characteristic (state) function in its original terminology), symbol ( Psi), is defined by the following relation: : \Psi = \Psi \big( X_1, \dots, X_i, Y_, \dots Y_r \big) \, where for every system with degree of freedom one may choose variables, e.g. \big( X_1, \dots, X_i, Y_, \dots Y_r \big) , to define a coordinate system, where and are extensive and intensive variables, respectively, and where at least one extensive variable must be within this set in order to define the size of the system. The -th variable, , is then called the Massieu function.Inden, Gerhard. (2008). �Introduction to Thermodynamics��, ''Materials Issues for Generation IV Systems'', pgs. 73–112. Springer The Massieu function was introduced in the 1869 paper "On the Characteristic Functions of Various Fluids" by French engineer François Massieu (1832-1896). The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamics
Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics, which convey a quantitative description using measurable macroscopic physical quantity, physical quantities but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to various topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering, and mechanical engineering, as well as other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the thermodynamic efficiency, efficiency of early steam engines, particularly through the work of French physicist Nicolas Léonard Sadi Carnot, Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psi (Greek)
Psi (uppercase , lowercase or ; ''psi'' ) is the twenty-third and penultimate letter of the Greek alphabet and is associated with a numeric value of 700. In both Classical and Modern Greek, the letter indicates the combination (as in English word " lapse"). For Greek loanwords in Latin and modern languages with Latin alphabets, psi is usually transliterated as "ps". The letter's origin is uncertain. It may or may not derive from the Phoenician alphabet. It appears in the 7th century BC, expressing in the Eastern alphabets, but in the Western alphabets (the sound expressed by Χ in the Eastern alphabets). In writing, the early letter appears in an angular shape (). There were early graphical variants that omitted the stem ("chickenfoot-shaped psi" as: or ). The Western letter (expressing , later ) was adopted into the Old Italic alphabets, and its shape is also continued into the Algiz rune of the Elder Futhark. Psi, or its Arcadian variant or was adopted in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, structure and purpose and is expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity. Etymology The term ''system'' comes from the Latin word ''systēma'', in turn from Greek language, Greek ''systēma'': "whole concept made of several parts or members, system", literary "composition"."σύστημα" , Henry George Liddell, Robert Scott, ''A Greek–English Lexicon'', on Pers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degree Of Freedom
In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinitesimal object on the plane might have additional degrees of freedoms related to its orientation. In mathematics, this notion is formalized as the dimension of a manifold or an algebraic variety. When ''degrees of freedom'' is used instead of ''dimension'', this usually means that the manifold or variety that models the system is only implicitly defined. See: * Degrees of freedom (mechanics), number of independent motions that are allowed to the body or, in case of a mechanism made of several bodies, number of possible independent relative motions between the pieces of the mechanism * Degrees of freedom (physics and chemistry), a term used in explaining dependence on parameters, or the dimensions of a phase space * Degrees of freedom (statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate System
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are not interchangeable; they are commonly distinguished by their position in an ordered tuple, or by a label, such as in "the ''x''-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of analytic geometry. Common coordinate systems Number line The simplest example of a coordinate system is the identification of points on a line with real numbers using the '' number line''. In this system, an arbitrary point ''O'' (the ''origin'') is chosen on a given line. The coordinate o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensive And Extensive Properties
Physical or chemical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. The terms "intensive and extensive quantities" were introduced into physics by German mathematician Georg Helm in 1898, and by American physicist and chemist Richard C. Tolman in 1917. According to International Union of Pure and Applied Chemistry (IUPAC), an intensive property or intensive quantity is one whose magnitude is independent of the size of the system. An intensive property is not necessarily homogeneously distributed in space; it can vary from place to place in a body of matter and radiation. Examples of intensive properties include temperature, ''T''; refractive index, ''n''; density, ''ρ''; and hardness, ''η''. By contrast, an extensive property or extensive quantity is one whose magnitude is additive for subsystems. Examples include mass, volume and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
François Massieu
François Jacques Dominique Massieu (4 August 1832 – 5 February 1896) was a French thermodynamics engineer noted for his two 1869 characteristic functions, each of which known as a Massieu function (the first of which sometimes called free entropy), as cited by American engineer Willard Gibbs in his 1876 ''On the Equilibrium of Heterogeneous Substances In the history of thermodynamics, "On the Equilibrium of Heterogeneous Substances" is a 300-page paper written by American chemical physicist Willard Gibbs. It is one of the founding papers in thermodynamics, along with German physicist Hermann ...''. References External links *Nivoit, E. (1897). �Notice of the Life and Work of Mr. Massieu Inspector General of Mines” (French → English), Annales des Mines, 9th Series, Vol. 11. {{DEFAULTSORT:Massieu, Francois 1832 births 1896 deaths Thermodynamicists ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Willard Gibbs
Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American mechanical engineer and scientist who made fundamental theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous deductive science. Together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of Statistical ensemble (mathematical physics), ensembles of the possible states of a physical system composed of many particles. Gibbs also worked on the application of Maxwell's equations to problems in physical optics. As a mathematician, he created modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period) and described the Gibbs phenomenon in the theory of Fourier analysis. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
On The Equilibrium Of Heterogeneous Substances
In the history of thermodynamics, "On the Equilibrium of Heterogeneous Substances" is a 300-page paper written by American chemical physicist Willard Gibbs. It is one of the founding papers in thermodynamics, along with German physicist Hermann von Helmholtz's 1882 paper "'' Thermodynamik chemischer Vorgänge''." Together they form the foundation of chemical thermodynamics as well as a large part of physical chemistry. Gibbs's paper marked the beginning of chemical thermodynamics by integrating chemical, physical, electrical, and electromagnetic phenomena into a coherent system. It introduced concepts such as chemical potential, phase rule, and more, which form the basis for modern physical chemistry. American writer Bill Bryson describes Gibbs's paper as "the '' Principia'' of thermodynamics". "On the Equilibrium of Heterogeneous Substances", was originally published in a relatively obscure American journal, the '' Transactions of the Connecticut Academy of Arts and Sciences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy
Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and light. Energy is a Conservation law, conserved quantity—the law of conservation of energy states that energy can be Energy transformation, converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J). Forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a Classical field theory, field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, the internal energy contained within a thermodynamic system, and rest energy associated with an object's rest mass. These are not mutual ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjugate Variables (thermodynamics)
In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature and entropy, pressure and volume, or chemical potential and particle number. In fact, all thermodynamic potentials are expressed in terms of conjugate pairs. The product of two quantities that are conjugate has units of energy or sometimes power. For a mechanical system, a small increment of energy is the product of a force times a small displacement. A similar situation exists in thermodynamics. An increment in the energy of a thermodynamic system can be expressed as the sum of the products of certain generalized "forces" that, when unbalanced, cause certain generalized "displacements", and the product of the two is the energy transferred as a result. These forces and their associated displacements are called ''conjugate variables''. The thermodynamic force is always an intensive variable and the displacement is always an extensive variable, yiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
