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Response Reactions
The theory of response reactions (RERs) or response equilibria was elaborated for the thermodynamic systems in which more than one equilibrium is established simultaneously. It is based on detailed analysis of the Hessian determinant. The theory derives the sensitivity coefficient as the sum of the contributions of individual RERs. Thus all phenomena which are in apparent contradiction to the Le Chatelier principle Le Chatelier's principle (pronounced or ), also called Chatelier's principle (or the Equilibrium Law), is a principle of chemistry used to predict the effect of a change in conditions on chemical equilibria. The principle is named after French ... could be interpreted. With the help of RERs the equilibrium coupling was defined. RERs could be derived based either on the species, or on the stoichiometrically independent reactions of a parallel system. The set of RERs is unambiguous in a given system; and the number of them (M) is S \choose C+1, where S denotes the num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic
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 co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Determinant
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named after him. Hesse originally used the term "functional determinants". Definitions and properties Suppose f : \R^n \to \R is a function taking as input a vector \mathbf \in \R^n and outputting a scalar f(\mathbf) \in \R. If all second-order partial derivatives of f exist, then the Hessian matrix \mathbf of f is a square n \times n matrix, usually defined and arranged as follows: \mathbf H_f= \begin \dfrac & \dfrac & \cdots & \dfrac \\ .2ex \dfrac & \dfrac & \cdots & \dfrac \\ .2ex \vdots & \vdots & \ddots & \vdots \\ .2ex \dfrac & \dfrac & \cdots & \dfrac \end, or, by stating an equation for the coefficients using indices i and j, (\mathbf H_f)_ = \fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Le Chatelier Principle
Le Chatelier's principle (pronounced or ), also called Chatelier's principle (or the Equilibrium Law), is a principle of chemistry used to predict the effect of a change in conditions on chemical equilibria. The principle is named after French chemist Henry Louis Le Chatelier, and sometimes also credited to Karl Ferdinand Braun, who discovered it independently. It can be stated as: Phenomena in apparent contradiction to Le Chatelier's principle can also arise in systems of simultaneous equilibrium (see response reactions). Le Chatelier's principle is sometimes alluded to in discussions of topics other than thermodynamics. Thermodynamic statement The Le Chatelier–Braun principle analyzes the qualitative behaviour of a thermodynamic system when a designated one of its externally controlled state variables, say L, changes by an amount \Delta L, the 'driving change', causing a change \delta_ M, the 'response of prime interest', in its conjugate state variable M, all other ext ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Footnotes
A note is a string of text placed at the bottom of a page in a book or document or at the end of a chapter, volume, or the whole text. The note can provide an author's comments on the main text or citations of a reference work in support of the text. Footnotes are notes at the foot of the page while endnotes are collected under a separate heading at the end of a chapter, volume, or entire work. Unlike footnotes, endnotes have the advantage of not affecting the layout of the main text, but may cause inconvenience to readers who have to move back and forth between the main text and the endnotes. In some editions of the Bible, notes are placed in a narrow column in the middle of each page between two columns of biblical text. Numbering and symbols In English, a footnote or endnote is normally flagged by a superscripted number immediately following that portion of the text the note references, each such footnote being numbered sequentially. Occasionally, a number between brack ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
