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Massieu Function
In thermodynamics, Massieu function (sometimes called Massieu–Gibbs function, Massieu potential, or Gibbs function, or characteristic (state) function in its original terminology), symbol \Psi (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 ''r'' one may choose r variables, e.g. \big( X_1, \dots, X_i, Y_, \dots Y_r \big) \, , to define a coordinate system, where ''X'' and ''Y'' 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 (''r'' + 1)-th variable, \Psi , is then called the Massieu function.Inden, Gerhard. (2008). âIntroduction 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 eng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamics
Thermodynamics is a branch of physics that deals with heat, 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 quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System
A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, structure and purpose and 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 ''systÄma'', in turn from Greek language, Greek ''systÄma'': "whole concept made of several parts or members, system", literary "composition"."ÏÏÏÏηΌα" Henry George Liddell, Robert Scott, ''A GreekâEnglish Lexicon'', on Per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closure Operator
In mathematics, a closure operator on a set ''S'' is a function \operatorname: \mathcal(S)\rightarrow \mathcal(S) from the power set of ''S'' to itself that satisfies the following conditions for all sets X,Y\subseteq S : Closure operators are determined by their closed sets, i.e., by the sets of the form cl(''X''), since the closure cl(''X'') of a set ''X'' is the smallest closed set containing ''X''. Such families of "closed sets" are sometimes called closure systems or "Moore families", in honor of E. H. Moore who studied closure operators in his 1910 ''Introduction to a form of general analysis'', whereas the concept of the closure of a subset originated in the work of Frigyes Riesz in connection with topological spaces. Though not formalized at the time, the idea of closure originated in the late 19th century with notable contributions by Ernst Schröder, Richard Dedekind and Georg Cantor. Closure operators are also called "hull operators", which prevents confusion with the "c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensive
In grammar, an intensive word form is one which denotes stronger, more forceful, or more concentrated action relative to the root on which the intensive is built. Intensives are usually lexical formations, but there may be a regular process for forming intensives from a root. Intensive formations, for example, existed in Proto-Indo-European, and in many of the Semitic languages. Morphological devices Certain prefixes and suffixes may be used as intensifiers. English language: "preeminent" (pre+eminent) or Latin language: ''excellentissimus'' ('' excellens'' + -issimus) Grammatical categories Intensives generally function as adverbs before the word or phrase that they modify. For example, ''bloody well,'' as in "I will ''bloody well'' do it," is a commonly used intensive adverb in Great Britain. Intensives also can function as postpositive adjectives. An example in American English today is ''"the heck"'', e.g. "What ''the heck'' is going on here?" All intensives are explet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
François Massieu
François Jacques Dominique Massieu (4 August 1832 â 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). âNotice of the Life and Work of Mr. Massieu Inspector General of Minesâ (French â 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 â April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous inductive 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 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 invented modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period). In 1863, Yale awarded Gibbs the first American doctorate in engineering. After a three-year sojourn in Europe, Gibbs spent the rest of his ... [...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 VorgÀnge.''" Together they form the foundation of chemical thermodynamics as well as a large part of physical chemistry. Gibbs's ''Equilibrium'' 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 others, which form the basis for modern physical chemistry. American writer Bill Bryson describes Gibbs's ''Equilibrium'' 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy
In physics, energy (from Ancient Greek: áŒÎœÎÏγΔÎčα, ''enĂ©rgeia'', âactivityâ) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantityâthe law of conservation of energy states that energy can be 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). Common 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 field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, and the internal energy contained within a thermodynamic system. All living organisms constantly take in and release energy. Due to massâenergy equivalence, any object that has mass whe ... [...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 or 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, yielding an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
