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Two cases?

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Adiabatic expansion isn't isothermal for an ideal gas. The given equation is only true for an isothermal expansion.

For an ideal gas ( $PV=nRT$ ), adiabatic expansion / compression obeys ${\frac {P}{P_{0}}}=({\frac {\rho }{\rho _{0}}})^{\gamma }$ . This gives a temperature drop during expansion. The thermal energy is used to accelerate the atoms / molecules during the expansion. If there is no wall (i.e. free expansion), the atoms are never stopped and expansion never finishes. See Adiabatic process, ideal gas, and isothermal process SMesser (talk) 00:26, 11 February 2013 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2013-02-11T00:26:00.000Z","author":"SMesser","type":"comment","level":1,"id":"c-SMesser-2013-02-11T00:26:00.000Z-Two_cases?","replies":[]}}-->

On second thought, I'm going to back off calling this "wrong", but... there's something odd here about defining "free" expansion. The equation works if there's a wall that bounces the escaping gas back - i.e. if there's some containment. That situation conserves energy by redirecting the escape velocity back into thermal energy. I'm just not sure I'd call it free. This is probably because I've been worried lately about what happens while the gas is expanding. That expansion is both isentropic and adiabatic, but its the atoms reflecting off the walls that raises the entropy again by mixing the fast-moving atoms with the slow-moving ones. Since temperature in an ideal monatomic gas is essentially the width of the velocity distribution function, this also raises the temperature....

So maybe "free expansion" should be split into two cases? One with, and one without a wall? Or perhaps there should be some other sort of disambiguation here. SMesser (talk) 01:23, 11 February 2013 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2013-02-11T01:23:00.000Z","author":"SMesser","type":"comment","level":1,"id":"c-SMesser-2013-02-11T01:23:00.000Z-Two_cases?","replies":[]}}-->

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Should merge this into Joule expansion

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I would be willing to merge this (shorter) article into the more complete Joule expansion article. How does one initiate that process?--guyvan52 (talk) 16:51, 31 December 2013 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2013-12-31T16:51:00.000Z","author":"Guy vandegrift","type":"comment","level":1,"id":"c-Guy_vandegrift-2013-12-31T16:51:00.000Z-Should_merge_this_into_Joule_expansion","replies":["c-89.217.4.12-2015-03-14T19:25:00.000Z-Guy_vandegrift-2013-12-31T16:51:00.000Z","c-Retired_Pchem_Prof-2016-01-18T16:38:00.000Z-Guy_vandegrift-2013-12-31T16:51:00.000Z","c-Klbrain-2018-07-21T11:31:00.000Z-Guy_vandegrift-2013-12-31T16:51:00.000Z"],"displayName":"guyvan52"}}-->

I can't see any reason not to merge, except it is always enlightening (for me) to read two articles from two different perspectives. 89.217.4.12 (talk) 19:25, 14 March 2015 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2015-03-14T19:25:00.000Z","author":"89.217.4.12","type":"comment","level":2,"id":"c-89.217.4.12-2015-03-14T19:25:00.000Z-Guy_vandegrift-2013-12-31T16:51:00.000Z","replies":[]}}-->

This should definitely be merged into the Joule expansion article. That could be as simple as deleting this article (a quick glance did not reveal anything here that is not in the longer article) and redirecting "free expansion to "Joule expansion". The only problem I see is that the former name is more common than the latter. I am new here and don't know how to start the process; perhaps ask at the Teahouse? I am going to put this on my to-do list, but it might be a while before I get to it. So hopefully someone will beat me to it. @Guy vandegrift: Retired Pchem Prof (talk) 16:38, 18 January 2016 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2016-01-18T16:38:00.000Z","author":"Retired Pchem Prof","type":"comment","level":2,"id":"c-Retired_Pchem_Prof-2016-01-18T16:38:00.000Z-Guy_vandegrift-2013-12-31T16:51:00.000Z","replies":["c-Guy_vandegrift-2016-01-18T16:52:00.000Z-Retired_Pchem_Prof-2016-01-18T16:38:00.000Z"]}}-->

I am now far too busy with Wikiversity:First Journal of Science to lend anything but moral support right now. Also I don't know how merges are done on Wikipedia--Guy vandegrift (talk) 16:52, 18 January 2016 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2016-01-18T16:52:00.000Z","author":"Guy vandegrift","type":"comment","level":3,"id":"c-Guy_vandegrift-2016-01-18T16:52:00.000Z-Retired_Pchem_Prof-2016-01-18T16:38:00.000Z","replies":["c-W.carter-2016-01-18T20:19:00.000Z-Guy_vandegrift-2016-01-18T16:52:00.000Z"]}}-->

Mergeing two existing articles that both have editing history must involve an administrator because of the history merging. The editing history must be kept intact for copyright reasons. The simple cut and paste merging of the text itself can be done by an editor that is familiar with the subject. See Wikipedia:Merging. You have to ask an admin to assist you in this (Wikipedia:Requests for administrator attention). w.carter-Talk 20:19, 18 January 2016 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2016-01-18T20:19:00.000Z","author":"W.carter","type":"comment","level":4,"id":"c-W.carter-2016-01-18T20:19:00.000Z-Guy_vandegrift-2016-01-18T16:52:00.000Z","replies":["c-Klbrain-2018-06-09T09:28:00.000Z-W.carter-2016-01-18T20:19:00.000Z"]}}-->

There's no need for a history merge, nor the involvement of an administrator as the scope of the articles is identical or heavy overlapping (as everyone in this discussion seems to agree). With the usual merge edit summaries and templates on the discussion pages the former history page is maintained and there is no loss of information. History merges are necessary following an improper move, not a merge. I've also tagged the Joule expansion page for the merge; that template seems to have been missed. Klbrain (talk) 09:28, 9 June 2018 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2018-06-09T09:28:00.000Z","author":"Klbrain","type":"comment","level":5,"id":"c-Klbrain-2018-06-09T09:28:00.000Z-W.carter-2016-01-18T20:19:00.000Z","replies":[]}}-->

Merger complete. Klbrain (talk) 11:31, 21 July 2018 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2018-07-21T11:31:00.000Z","author":"Klbrain","type":"comment","level":2,"id":"c-Klbrain-2018-07-21T11:31:00.000Z-Guy_vandegrift-2013-12-31T16:51:00.000Z","replies":[]}}-->