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Clausius–Clapeyron Relation
The Clausius–Clapeyron relation, in chemical thermodynamics, specifies the temperature dependence of pressure, most importantly vapor pressure, at a discontinuous phase transition between two phases of matter of a single constituent. It is named after Rudolf Clausius and Benoît Paul Émile Clapeyron. However, this relation was in fact originally derived by Sadi Carnot in his '' Reflections on the Motive Power of Fire'', which was published in 1824 but largely ignored until it was rediscovered by Clausius, Clapeyron, and Lord Kelvin decades later. Kelvin said of Carnot's argument that "nothing in the whole range of Natural Philosophy is more remarkable than the establishment of general laws by such a process of reasoning." Kelvin and his brother James Thomson confirmed the relation experimentally in 1849–50, and it was historically important as a very early successful application of theoretical thermodynamics. Its relevance to meteorology and climatology is the increase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Thermodynamics
Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the ''spontaneity'' of processes. The structure of chemical thermodynamics is based on the first two laws of thermodynamics. Starting from the first and second laws of thermodynamics, four equations called the "fundamental equations of Gibbs" can be derived. From these four, a multitude of equations, relating the thermodynamic properties of the thermodynamic system can be derived using relatively simple mathematics. This outlines the mathematical framework of chemical thermodynamics. History In 1865, the German physicist Rudolf Clausius, in his ''Mechanical Theory of Heat'', suggested that the principles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molar Entropy
{{disambig, geo ...
Molar may refer to: *Molar (tooth), a kind of tooth found in mammals * Molar (grape), another name for the Spanish wine grape Listan Negro *Molar (unit), a unit of concentration equal to 1 mole per litre * Molar quantities, such as molar mass, molar volume, etc. * El Molar, Tarragona, a village in the comarca (county) of Priorat, province of Tarragona in the autonomous region of Catalonia, Spain * El Molar, Madrid, a town in the north of the Community of Madrid in the road to Burgos, after San Agustín de Guadalix See also * Moler, a power-pop band from Australia * Moler (surname) * Molaro (other) * Molar tooth sign, a characteristic of the genetic disorder Joubert syndrome Joubert syndrome is a rare autosomal recessive genetic disorder that affects the cerebellum, an area of the Human brain, brain that controls balance and coordination. Joubert syndrome is one of the many genetic syndromes associated with syndromic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. the other being Derivative, differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given Function (mathematics), function between two points in the real line. Conventionally, areas above the horizontal Coordinate axis, axis of the plane are positive while areas below are n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorization
In mathematics, factorization (or factorisation, see American and British English spelling differences#-ise, -ize (-isation, -ization), English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several ''Factor (arithmetic), factors'', usually smaller or simpler objects of the same kind. For example, is an ''integer factorization'' of , and is a ''polynomial factorization'' of . Factorization is not usually considered meaningful within number systems possessing division ring, division, such as the real number, real or complex numbers, since any x can be trivially written as (xy)\times(1/y) whenever y is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by Greek mathematics, ancient Greek mathematicians in the case of integers. They proved the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Derivative
In mathematics, the total derivative of a function at a point is the best linear approximation near this point of the function with respect to its arguments. Unlike partial derivatives, the total derivative approximates the function with respect to all of its arguments, not just a single one. In many situations, this is the same as considering all partial derivatives simultaneously. The term "total derivative" is primarily used when is a function of several variables, because when is a function of a single variable, the total derivative is the same as the ordinary derivative of the function. The total derivative as a linear map Let U \subseteq \R^n be an open subset. Then a function f:U \to \R^m is said to be (totally) differentiable at a point a\in U if there exists a linear transformation df_a:\R^n \to \R^m such that :\lim_ \frac=0. The linear map df_a is called the (total) derivative or (total) differential of f at a. Other notations for the total derivative inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f(x, y, \dots) with respect to the variable x is variously denoted by It can be thought of as the rate of change of the function in the x-direction. Sometimes, for the partial derivative of z with respect to x is denoted as \tfrac. Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: f'_x(x, y, \ldots), \frac (x, y, \ldots). The symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical Engineering
Mechanical engineering is the study of physical machines and mechanism (engineering), mechanisms that may involve force and movement. It is an engineering branch that combines engineering physics and engineering mathematics, mathematics principles with materials science, to design, analyze, manufacture, and maintain mechanical systems. It is one of the oldest and broadest of the List of engineering branches, engineering branches. Mechanical engineering requires an understanding of core areas including mechanics, Analytical dynamics, dynamics, thermodynamics, materials science, design, structural analysis, and electricity. In addition to these core principles, mechanical engineers use tools such as computer-aided design (CAD), computer-aided manufacturing (CAM), computer-aided engineering (CAE), and product lifecycle management to design and analyze manufacturing plants, industrial equipment and industrial machinery, machinery, HVAC, heating and cooling systems, transport systems, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell Relation
file:Thermodynamic map.svg, 400px, Flow chart showing the paths between the Maxwell relations. P is pressure, T temperature, V volume, S entropy, \alpha coefficient of thermal expansion, \kappa compressibility, C_V heat capacity at constant volume, C_P heat capacity at constant pressure. Maxwell's 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. Equations 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 an analytic function of two variables is irrelevant ( Schwarz theorem). In the case of Maxwell relations the function considered is a thermodynamic potential and x_i and x_j are two different natural variables for that potential, we have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed System
A closed system is a natural physical system that does not allow transfer of matter in or out of the system, althoughin the contexts of physics, chemistry, engineering, etc.the transfer of energy (e.g. as work or heat) is allowed. Physics In classical mechanics In nonrelativistic classical mechanics, a closed system is a physical system that does not exchange any matter with its surroundings, and is not subject to any net force whose source is external to the system. A closed system in classical mechanics would be equivalent to an isolated system in thermodynamics. Closed systems are often used to limit the factors that can affect the results of a specific problem or experiment. In thermodynamics In thermodynamics, a closed system can exchange energy (as heat or work) but not matter, with its surroundings. An isolated system cannot exchange any heat, work, or matter with the surroundings, while an open system can exchange energy and matter. (This scheme of definition of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Transition
In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic State of matter, states of matter: solid, liquid, and gas, and in rare cases, plasma (physics), plasma. A phase of a thermodynamic system and the states of matter have uniform physical property, physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. Types of phase transition States of matter Phase transitions commonly refer to when a substance tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous
Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, income, disease, temperature, radioactivity, architectural design, etc.); one that is heterogeneous is distinctly nonuniform in at least one of these qualities. Etymology and spelling The words ''homogeneous'' and ''heterogeneous'' come from Medieval Latin ''homogeneus'' and ''heterogeneus'', from Ancient Greek ὁμογενής (''homogenēs'') and ἑτερογενής (''heterogenēs''), from ὁμός (''homos'', "same") and ἕτερος (''heteros'', "other, another, different") respectively, followed by γένος (''genos'', "kind"); -ous is an adjectival suffix. Alternate spellings omitting the last ''-e-'' (and the associated pronunciations) are common, but mistaken: ''homogenous'' is strictly a biological/pathological term whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Postulate
The state postulate is a term used in thermodynamics that defines the given number of properties to a thermodynamic system in a state of equilibrium. It is also sometimes referred to as the state principle. The state postulate allows a finite number of properties to be specified in order to fully describe a state of thermodynamic equilibrium. Once the state postulate is given the other unspecified properties must assume certain values. The state postulate says: A more general statement of the state postulate says: ''the state of a simple system is completely specified by r+1 independent, intensive properties where r is the number of significant work interactions.'' A system is considered to be a simple compressible one in the absence of certain effects which are uncommon in many engineering applications. These are electromagnetic and gravitational fields, surface tension, and motion. For such a system, only two independent intensive variables are sufficient to derive all the ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
