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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 fundamental thermodynamic relation ： ウィキペディア英語版 fundamental thermodynamic relation In thermodynamics, the fundamental thermodynamic relation is generally expressed as an infinitesimal change in internal energy in terms of infinitesimal changes in entropy, and volume for a closed system in thermal equilibrium in the following way. :$\backslash mathrmU=\; T\backslash ,\backslash mathrmS\; -\; P\backslash ,\backslash mathrmV\backslash ,$ Here, ''U'' is internal energy, ''T'' is absolute temperature, ''S'' is entropy, ''P'' is pressure, and ''V'' is volume. This is only one expression of the fundamental thermodynamic relation. It may be expressed in other ways, using different variables (e.g. using thermodynamic potentials). For example, the fundamental relation may be expressed in terms of the Helmholtz free energy (''F'') as: :$\backslash mathrmF=\; -S\backslash ,\backslash mathrmT\; -\; P\backslash ,\backslash mathrmV\backslash ,$ and in terms of the enthalpy as :$dH\; =\; VdP\; +\; TdS\; \backslash ;\; .$ == Derivation from the first and second laws of thermodynamics== The first law of thermodynamics states that: :$\backslash mathrmU\; =\; \backslash delta\; Q\; -\; \backslash delta\; W\backslash ,$ where $\backslash delta\; Q$ and $\backslash delta\; W$ are infinitesimal amounts of heat supplied to the system by its surroundings and work done by the system on its surroundings, respectively. According to the second law of thermodynamics we have for a reversible process: :$\backslash mathrmS\; =\; \backslash frac\backslash ,$ Hence: :$\backslash delta\; Q\; =\; T\backslash ,\backslash mathrmS\backslash ,$ By substituting this into the first law, we have: :$\backslash mathrmU\; =\; T\backslash ,\backslash mathrmS\; -\; \backslash delta\; W\backslash ,$ Letting dW be reversible pressure-volume work, we have: :$\backslash mathrmU\; =\; T\backslash ,\backslash mathrmS\; -\; P\backslash ,\backslash mathrmV\backslash ,$ This equation has been derived in the case of reversible changes. However, since $U$, $S$, and $V$ are thermodynamic functions of state, the above relation holds also for non-reversible changes. If the system has more external parameters than just the volume that can change and if the numbers of particles in the system can also change, the fundamental thermodynamic relation generalizes to: :$\backslash mathrmU\; =\; T\backslash ,\backslash mathrmS\; -\; \backslash sum\_X\_\backslash ,\backslash mathrmx\_\; +\; \backslash sum\_\backslash mu\_\backslash ,\backslash mathrmN\_\backslash ,$ Here the $X\_$ are the generalized forces corresponding to the external parameters $x\_$. The $\backslash mu\_$ are the chemical potentials corresponding to particles of type $j$. 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「fundamental thermodynamic relation」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.