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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Maxwell–Boltzmann statistics ： ウィキペディア英語版 Maxwell–Boltzmann statistics In statistical mechanics, Maxwell–Boltzmann statistics describes the average distribution of non-interacting material particles over various energy states in thermal equilibrium, and is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible. The expected number of particles with energy $\backslash varepsilon\_i$ for Maxwell–Boltzmann statistics is $\backslash langle\; N\_i\; \backslash rangle$ where: :$$ \langle N_i \rangle = \frac \,g_i e^ where: *$\backslash varepsilon\_i$ is the ''i''-th energy level *$\backslash langle\; N\_i\; \backslash rangle$ is the number of particles in the set of states with energy $\backslash varepsilon\_i$ *$g\_i$ is the degeneracy of energy level ''i'', that is the number of single-particle states with energy $\backslash varepsilon\_i$ *μ is the chemical potential *''k'' is Boltzmann's constant *''T'' is absolute temperature *''N'' is the total number of particles ::$N=\backslash sum\_i\; N\_i\backslash ,$ *''Z'' is the partition function ::$Z=\backslash sum\_i\; g\_i\; e^$ *e(...) is the exponential function Equivalently, the particle number is sometimes expressed as :$$ \langle N_i \rangle = \frac \,e^ where the index ''i''  now specifies a particular state rather than the set of all states with energy $\backslash varepsilon\_i$, and $Z=\backslash sum\_i\; e^$ ==Applications== Maxwell–Boltzmann statistics may be used to derive the Maxwell–Boltzmann distribution (for an ideal gas of classical particles in a three-dimensional box). However, they apply to other situations as well. Maxwell–Boltzmann statistics can be used to extend that distribution to particles with a different energy–momentum relation, such as relativistic particles (Maxwell–Jüttner distribution). In addition, hypothetical situations can be considered, such as particles in a box with different numbers of dimensions (four-dimensional, two-dimensional, etc.). 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「Maxwell–Boltzmann statistics」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.