翻訳と辞書 Words near each other ・ Gibbs' inequality ・ Gibbs, Missouri ・ Gibbs, Tennessee ・ Gibbsboro Air Force Station ・ Gibbsboro School District ・ Gibbsboro, New Jersey ・ GibbsCAM ・ Gibbsia ・ Gibbsite ・ Gibbston, New Zealand ・ Gibbstown, New Jersey ・ Gibbsville ・ Gibbsville (TV series) ・ Gibbsville, Wisconsin ・ Gibbs–Donnan effect ・ Gibbs–Duhem equation ・ Gibbs–Helmholtz equation ・ Gibbs–Thomson equation ・ Gibbula ・ Gibbula adansonii ・ Gibbula adriatica ・ Gibbula albida ・ Gibbula ardens ・ Gibbula beckeri ・ Gibbula benzi ・ Gibbula buchi ・ Gibbula candei ・ Gibbula capensis ・ Gibbula cicer ・ Gibbula cineraria Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gibbs–Duhem equation ： ウィキペディア英語版 Gibbs–Duhem equation In thermodynamics, the Gibbs–Duhem equation describes the relationship between changes in chemical potential for components in a thermodynamical system:〔''A to Z of Thermodynamics'' Pierre Perrot ISBN 0-19-856556-9〕 :$\backslash sum\_^I\; N\_i\backslash ,\backslash mathrm\backslash mu\_i\; =\; -\; S\backslash ,\backslash mathrmT\; +\; V\backslash ,\backslash mathrmp\; \backslash ,$ where $N\_i\backslash ,$ is the number of moles of component $i\backslash ,$, $\backslash mathrm\backslash mu\_i\backslash ,$ the infinitesimal increase in chemical potential for this component, $S\backslash ,$ the entropy, $T\backslash ,$ the absolute temperature, $V\backslash ,$ volume and $p\backslash ,$ the pressure. It shows that in thermodynamics intensive properties are not independent but related, making it a mathematical statement of the state postulate. When pressure and temperature are variable, only $I-1\backslash ,$ of $I\backslash ,$ components have independent values for chemical potential and Gibbs' phase rule follows. The law is named after Josiah Willard Gibbs and Pierre Duhem. The Gibbs−Duhem equation cannot be used for small thermodynamic systems due to the influence of surface effects and other microscopic phenomena. ==Derivation== Deriving the Gibbs–Duhem equation from the fundamental thermodynamic equation is straightforward.〔''Fundamentals of Engineering Thermodynamics, 3rd Edition'' Michael J. Moran and Howard N. Shapiro, p. 538 ISBN 0-471-07681-3〕 The total differential of the Gibbs free energy $G\backslash ,$ in terms of its natural variables is :$\backslash mathrmG$ =\left. \frac\right | _\,\mathrmp +\left. \frac\right | _\,\mathrmT +\sum_^I \left. \frac\right | _N_i \,. Since the Gibbs free energy is the Legendre transformation of the internal energy, the derivatives can be replaced by its definitions transforming the above equation into: :$\backslash mathrmG$ =V \,\mathrmp-S \,\mathrmT +\sum_^I \mu_i \, \mathrmN_i \, As shown in the Gibbs free energy article, the chemical potential is simply another name for the partial molar (or just partial, depending on the units of N) Gibbs free energy, thus the gibbs free energy of a system can be calculated by collecting moles together carefully at a specified T, P and at a constant molar ratio composition (so that the chemical potential doesn't change as the moles are added together), i.e. :$G\; =\; \backslash sum\_^I\; \backslash mu\_i\; N\_i\; \backslash ,$. The total differential of this expression is〔 :$\backslash mathrmG\; =\; \backslash sum\_^I\; \backslash mu\_i\; \backslash ,\; \backslash mathrmN\_i\; +\; \backslash sum\_^I\; N\_i\; \backslash ,\backslash mathrm\backslash mu\_i\; \backslash ,$ By subtracting the two expressions for the total differential of the Gibbs free energy gives the Gibbs–Duhem relation:〔 :$\backslash sum\_^I\; N\_i\backslash ,\backslash mathrm\backslash mu\_i\; =\; -\; S\backslash ,\backslash mathrmT\; +\; V\backslash ,\backslash mathrmp\; \backslash ,$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gibbs–Duhem equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.