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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 Thermodynamics of the universe ： ウィキペディア英語版 Thermodynamics of the universe The thermodynamics of the universe is dictated by which form of energy dominates it - relativistic particles which are referred to as radiation, or non-relativistic particles which are referred to as matter. The former are particles whose rest mass is zero or negligible compared to their energy, and therefore move at the speed of light or very close to it; the latter are particles whose kinetic energy is much lower than their rest mass and therefore move much slower than the speed of light. The intermediate case is not treated well analytically. ==Energy density in the expanding universe== If the universe is expanding adiabatically then it will satisfy the first law of thermodynamics: $0\; =\; dQ\; =\; dU\; +\; P\; dV$ where $Q$ is the total heat which is assumed to be constant, $U$ is the internal energy of the matter and radiation in the universe, $P$ is the pressure and $V$ the volume. One then finds an equation for the energy density $u\backslash equiv\; U/V$, and so $du\; =\; d\backslash left(\backslash right)=-U=-(p+u)\; =\; -3(p+u)$ where in the last equality we used the fact that the total volume of the universe is proportional to $a^3$, $a$ being the scale factor of the universe. In fact this equation can be directly obtained from the equations of motion governing the Friedmann-Lemaître-Robertson-Walker metric: by dividing the equation above with $dt$ and identifying $\backslash rho\; =\; u$ (the energy density), we get one of the FLRW equations of motions. In the comoving coordinates, $u$ is equal to the mass density $\backslash rho$. For radiation, $p=u/3$ whereas for matter For radiation $du\; =\; -4u$ thus $u$ is proportional to $a^$ For matter $du\; =\; -3u$ thus $u$ is proportional to $a^$ This can be understood as follows: For matter, the energy density is equal (in our approximation) to the rest mass density. This is inversely proportional to the volume, and is therefore proportional to $a^$. For radiation, the energy density depends on the temperature $T$ as well, and is therefore proportional to $T\; a^$. As the universe expands it cools down, so $T$ depends on $a$ as well. In fact, since the energy of a relativistic particle is inversely proportional to its wavelength, which is proportional to $a$, the energy density of the radiation must be proportional to $a^$. From this discussion it is also obvious that the temperature of radiation is inversely proportional to the scale factor $a$. 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「Thermodynamics of the universe」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.