翻訳と辞書 Words near each other ・ Root system ・ Root system of a semi-simple Lie algebra ・ Root test ・ Root Township, Adams County, Indiana ・ Root trainer ・ Root wall ・ Root window ・ Root zone ・ Root! ・ Root, New York ・ Root, Switzerland ・ Root-finding algorithm ・ Root-knot nematode ・ Root-mean-square deviation ・ Root-mean-square deviation of atomic positions ・ Root-mean-square speed ・ Root-raised-cosine filter ・ Root-Tilden Scholarship ・ Rootabaga Stories ・ Rootare ・ Rootare–Prenzlow equation ・ Rootdown ・ Rooted (film) ・ Rooted graph ・ Rooted in Community ・ Rooted product of graphs ・ Rooter ・ Rooterberg ・ Rootes ・ Rootes Arrow 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 Root-mean-square speed ： ウィキペディア英語版 Root-mean-square speed Root-mean-square speed is the measure of the speed of particles in a gas that is most convenient for problem solving within the kinetic theory of gases. It is defined as the square root of the average velocity-squared of the molecules in a gas. It is given by the formula〔 〕 :$v\_\backslash mathrm\; =\; \backslash sqrt$ where ''v''rms is the root mean square of the speed in meters per second, ''Mm'' is the molar mass of the gas in kilograms per mole, ''R'' is the molar gas constant, and ''T'' is the temperature in kelvin. Although the molecules in a sample of gas have an average kinetic energy (and therefore an average speed) the individual molecules move at various speeds and they stop and change direction according to the law of density measurements and isolation, i.e. they exhibit a distribution of speeds. Some move fast, others relatively slowly. Collisions change individual molecular speeds but the distribution of speeds remains the same. This equation is derived from kinetic theory of gases using Maxwell–Boltzmann distribution function. The higher the temperature, the greater the mean velocity will be. This works well for both nearly ideal, atomic gases like helium and for molecular gases like diatomic oxygen. This is because despite the larger internal energy in many molecules (compared to that for an atom), 3''RT''/2 is still the mean translational kinetic energy. This can also be written in terms of the Boltzmann constant (''k'') as :$v\_\backslash mathrm\; =\; \backslash sqrt$ where ''m'' is the mass of one molecule of the gas. This can be derived with energy methods: :$E\_\backslash mathrm\; =\; nRT\; =\; \backslash fracNkT$ where ''E''k is the kinetic energy and ''N'' is the number of gas molecules. :$E\_\backslash mathrm\; =\; mv^2$ Given that ''v''2 ignores direction, it is logical to assume that the formula can be extended to the entire sample, replacing ''m'' with the entire sample's mass, equal to the molar mass times the number of moles ''n'' yielding :$nMv^2\; =\; E\_\backslash mathrm$ Therefore :$v\_\backslash mathrm\; =\; \backslash sqrt\; \backslash over\}$ which is equivalent. The same result is obtained by solving the Gaussian integral containing the Maxwell speed distribution, ''p''(''v''): :$v\_\backslash mathrm\; =\; \backslash sqrt\; v^2\backslash \; p(v)dv\}\backslash ,\backslash !$ ::$=\; \backslash sqrt\; 4\; \backslash pi\; \backslash left\; (\backslash frac\; \backslash right\; )^\backslash frac\; v^4\backslash \; e^\}dv\}\backslash ,\backslash !$ ::$=\; \backslash sqrt\; \backslash right\; )^\backslash frac\; \backslash frac\; \backslash pi^\}\; \backslash left(\; \backslash frac\backslash right)^\}\}\backslash ,\backslash !$ ::$=\; \backslash sqrt\}$ ==References== 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「Root-mean-square speed」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.