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Joule expansion : ウィキペディア英語版
Joule expansion

The Joule expansion is an irreversible process in thermodynamics in which a volume of gas is kept in one side of a thermally isolated container (via a small partition), with the other side of the container being evacuated. The partition between the two parts of the container is then opened, and the gas fills the whole container.
The Joule expansion is also called ''free expansion''. The process is a useful exercise in classical thermodynamics, as it is easy to work out the resulting increase in entropy in an ideal gas, the so-called entropy production. If the gas is not ideal, the process is more complex and is called the ''Joule–Thomson effect''.〔(【引用サイトリンク】url=http://www.britannica.com/EBchecked/topic/306635/Joule-Thomson-effect )〕〔(【引用サイトリンク】url=http://www.chm.wright.edu/grossie/CHM3510L/joule_thomson.pdf )
This type of expansion is named after James Prescott Joule who used this expansion, in 1845, in his study for the mechanical equivalent of heat, but this expansion was known long before Joule e.g. by John Leslie, in the beginning of the 19th century, and studied by Joseph-Louis Gay-Lussac in 1807 with similar results as obtained by Joule.〔D.S.L. Cardwell, From Watt to Clausius, Heinemann, London (1957)〕〔M.J. Klein, Principles of the theory of heat, D. Reidel Pub.Cy., Dordrecht (1986)〕
==Description==
We consider an ideal gas under some pressure, ''P''i at temperature ''T''i, confined to one half of a thermally isolated container (see drawing). The gas occupies a volume ''V''i = ''V''0, mechanically separated from the other half of the container, which has an equal volume ''V''0, and is under lower or zero pressure. The tap (solid line) between the two halves of the container is then suddenly opened, and the gas expands to fill the entire container, which has a total volume of ''V''f = 2''V''0. Both the previous and new temperature and pressure (''T''f, ''P''f) follow the Ideal Gas Law, so that initially we have ''P''i''V''i = ''nRT''i and then, when the tap is opened, we have ''P''f''V''f = ''nRT''f (where ''R'' is the molar ideal gas constant).
Because this ideal system is thermally isolated, it cannot exchange heat with its surroundings. Also, since the system's volume is kept constant, the system cannot perform work on its surroundings.〔Note that the fact that the gas expands in a vacuum and thus against zero pressure is irrelevant. The work done by the system would also be zero if the right hand side of the chamber were not evacuated, but is instead filled with a gas at a lower pressure. While the expanding gas would then do work against the gas in the right-hand side of the container, the whole system doesn't do any work against the environment.〕 As a result, the change in internal energy Δ''U'' = 0, and because ''U'' is strictly a function of temperature for the ideal gas, we know that ''T''i = ''T''f (the temperature of the gas does not change). This implies that ''P''i''V''0 = ''P''f(2''V''0), and thus the pressure halves; i.e. ''P''f = ½''P''i.

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