平衡状態

関: equilibrium

WordNet

express in words; "He said that he wanted to marry her"; "tell me what is bothering you"; "state your opinion"; "state your name" (同)say, tell
a state of depression or agitation; "he was in such a state you just couldnt reason with him"
the way something is with respect to its main attributes; "the current state of knowledge"; "his state of health"; "in a weak financial state"
a politically organized body of people under a single government; "the state has elected a new president"; "African nations"; "students who had come to the nations capitol"; "the countrys largest manufacturer"; "an industrialized land" (同)nation, country, land, commonwealth, res publica, body_politic
the territory occupied by one of the constituent administrative districts of a nation; "his state is in the deep south" (同)province
the group of people comprising the government of a sovereign state; "the state has lowered its income tax"
a stable situation in which forces cancel one another
a sensory system located in structures of the inner ear that registers the orientation of the head (同)labyrinthine sense, vestibular sense, sense of balance, sense_of_equilibrium

PrepTutorEJDIC

〈C〉(人・物事の)『状態』,ありさま,様子 / 〈C〉《a ~》《話》極度の緊張状態,異常な精神状態 / 〈U〉地位,階級,身分 / 〈C〉〈U〉《しばしばS-》『国家』,国,政府 / 〈C〉《時にS-》(アメリカ・オーストラリアなどの)『州』 / 《the States》《話》『米国』 / 〈U〉威厳;公式;堂々とした様子 / 国家の,国事に関する / 《しばしばS-》《米》州の,州立の / 公式の,儀式用の
…‘を'『はっきり述べる』,公式に申し立てる / 〈当局が〉…‘を'指定する,決める
(力・勢力・作用などの)釣り合い,均衡;(心の)平静
決まった,規定の;定期の / はっきり述べられた,明言された;公認された

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2012/10/14 10:31:38」(JST)

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In thermodynamics, a thermodynamic system is in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. Equilibrium means a state of balance. In a state of thermodynamic equilibrium, there are no net flows of matter or of energy, no phase changes, and no unbalanced potentials (or driving forces), within the system. A system that is in thermodynamic equilibrium experiences no changes when it is isolated from its surroundings.

In non-equilibrium systems there are net flows of matter or energy, or phase changes are occurring; if such changes can be triggered to occur in a system in which they are not already occurring, it is said to be in a metastable equilibrium.

Overview

Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:

A = U – TS.

Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:

G = U – TS + PV.

where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.

Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.

Conditions for thermodynamic equilibrium

For a completely isolated system, S is maximum at thermodynamic equilibrium.
For a system with controlled constant temperature and volume, A is minimum at thermodynamic equilibrium.
For a system with controlled constant temperature and pressure, G is minimum at thermodynamic equilibrium.

The various types of equilibriums are achieved as follows:

Two systems are in thermal equilibrium when their temperatures are the same.
Two systems are in mechanical equilibrium when their pressures are the same.
Two systems are in diffusive equilibrium when their chemical potentials are the same.
All forces are balanced.

Local and global equilibrium

It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.

If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature breaks down, and the temperature becomes undefined.

It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas need not be in thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.

As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell-Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell-Boltzmann distribution for another temperature.

Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell-Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally stably stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Transport phenomena are processes that lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.^[1]

Types of equilibrium

Thermal equilibrium

Main article: Thermal equilibrium

Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.^[2]

Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell-Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. Thermal equilibrium of a system does not imply absolute uniformity within a system; for example, a river system can be in thermal equilibrium when the macroscopic temperature distribution is stable and not changing in time, even though the spatial temperature distribution reflects thermal pollution inputs.

Quasistatic equilibrium

Main article: Quasistatic equilibrium

Quasistatic equilibrium is the quasi-balanced state of a thermodynamic system near to thermodynamic equilibrium, in some sense. In a quasistatic or equilibrium process, a sufficiently slow transition of a thermodynamic system from one equilibrium state to another occurs such that at every moment in time the state of the system is close to an equilibrium state. During a quasistatic process, the system reaches equilibrium much faster, almost instantaneously, than its physical parameters vary.

Non-equilibrium

Main article: Non-equilibrium thermodynamics

Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.

General references

Cesare Barbieri (2007) Fundamentals of Astronomy. First Edition (QB43.3.B37 2006) CRC Press ISBN 0-7503-0886-9, ISBN 978-0-7503-0886-1
Hans R. Griem (2005) Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics), Cambridge University Press, New York ISBN 0-521-61941-6
C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases, Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington DC [1]
F. Mandl (1988) Statistical Physics, Second Edition, John Wiley & Sons

Footnotes

^ H.R. Griem, 2005
^ R. K. Pathria, 1996

External links

Breakdown of Local Thermodynamic Equilibrium George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15
Thermodynamic Equilibrium, Local and otherwise lecture by Michael Richmond
Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres Paper by R. E. Samueison quantifying the effects due to non-LTE in a atmosphere
Local Thermodynamic Equilibrium
Xchanger Inc, webpage Calculator for thermodynamic equilibrium of pneumatic conveying air and conveyed product.

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Pyridine N-oxide/trichloroacetic acid complex in acetonitrile: FTIR spectra, anharmonic calculations and computations of 1-3D potential surfaces of O-H vibrations.

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FTIR spectra of pyridine N-oxide and trichloroacetic acid H-bonded complex in acetonitrile were studied at 20 and 50°C. The calculations of equilibrium configurations of the complex and their IR spectra in harmonic- and anharmonic approximations were carried out at the level of B3LYP/cc-pVTZ/PCM. H
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Japanese Journal

Structural fluctuation observed in Z-DNA d(CGCGCG)2 in the absence of divalent metal cations and polyamines.

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The macroeconomic effects of the wage gap between regular and non-regular employment and of minimum wages

Sasaki Hiroaki,Matsuyama Jun,Sako Kazumitsu
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