Talk:Maxwell relations

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Failed to parse(unknown function '\begin') — Preceding unsigned comment added by 2601:7:F00:CF0:9942:D5E4:777:C5F9 (talk) 18:41, 9 February 2014 (UTC)

Hello, in the last line of "Derivation of the Maxwell relations", it is said all other relations can be derived from similar method discussed in Gibbs equation. I think the example given here is of H? Liuxunchen (talk) 01:19, 25 February 2008 (UTC)

Note: Moved content from User:Talk to this discussion page. Thorwald 01:42, 25 Jan 2005 (UTC)

Thorwald: Hello - I want to make some massive changes in the Maxwell relations page but I want to run it by you first, since you have worked on that page a lot. The Maxwell relationships are just the four equations numbered 1-4 that are now in the page. The other differential equations are not. I would like to rewrite the page to include just those four. The other differential equations deserve a separate page, that we could call perhaps "Thermodynamic equations". Paul Reiser 02:44, 24 Jan 2005 (UTC)
 * Paul: Hello. Thank you for the questions and your interest in this article. When I took Physical Chemistry, my professor taught us that there were six Maxwell relationships. We even had to prove each of them as a homework problem (I have provided two of these proofs). I am completely open to any changes. However, I would like to keep the proofs in the article. We could put the other differential equations under a new article. Thorwald 05:25, 24 Jan 2005 (UTC)
 * Thorwald:According to my tome "Thermodynamics" by Randall and Lewis, Maxwells relations are derived from the differential definitions of thermodynamic potentials of which there are four main ones. (see thermodynamic potentials.) There may be others that could be defined, (see http://web.mit.edu/chemistry/alberty/part6.html) which would give rise to more Maxwell type relations, but the two proofs that you have are definitely not of this type. I really think that, since they are not Maxwell relations, they should be included in the new page, rather than the Maxwell relation page. Paul Reiser 12:06, 24 Jan 2005 (UTC)

What are G, F, U, and H?
The article doesn't define what G, F, U, and H are in the mnemonic device. --Doradus 15:13, August 5, 2005 (UTC)

This is not a mnemonic device for the Maxwell relations. Its a mnemonic device for something else, perhaps in the Thermodynamic potentials article. Please read the article before inserting this. Be sure it coincides with what is written in the article. PAR 02:33, 6 August 2005 (UTC)

Problem in the introduction
The introduction states that "the order of differentiation in a second derivative is irrelevant" but this is not true for many equations. With some functions the second derivatives do depend on the order in which the differentiation is done. I think internal energy just happens to be one of the staight forward ones where the the order doesn't matter.


 * What would be an example where the order mattered? PAR 15:19, 5 March 2007 (UTC)


 * The order doesn't matter, as shown in Mixed Derivatives, because all U, H, F and G are continuous because they are made up of reversible changes. Furious.baz 20:22, 5 March 2007 (UTC)


 * The sentance "They follow directly from the fact that the order of differentiation in a second derivative is irrelevant" implys that the order of differentiation never matters for any mathmatical function. In fact thereare many mathmatical functions for with the order of differentiation does matter.  I think this sentance should be re-worded to avoid confusion.  It should be made clear that though the order of differentiation doesn't matter for the thermodynamic potentials the same cannot always be said for other quantitys 81.137.148.225 15:41, 8 March 2007 (UTC) Melissa


 * I just curious - what is an example of a function where the order matters? PAR 06:21, 9 March 2007 (UTC)


 * Example The order matters here because the partials are not continuous for all x and y, i.e. at (0,0), and I think the partials of the state functions are continuous because they can only go through equilibrium states (i.e. reversible) for them to be state functions.  So, yeah, maybe there aught to be some sort of clarification here. Furious.baz 14:14, 9 March 2007 (UTC)


 * I'm thinking that if a function is discontinuous, its derivative is not defined. So if you have a case where the order matters, the functions must be continuous. And I cannot think of a case where the order matters. What is an example of f(x,y) where

\frac{\partial}{\partial x}\left(\frac{\partial f}{\partial y}\right) \ne \frac{\partial}{\partial y}\left(\frac{\partial f}{\partial x}\right) $$
 * PAR 22:33, 10 March 2007 (UTC)

Mnemonic Device
There is a mnemonic device for remembering the 4 relations, it is -S, p, T and V arranged anticlockwise in a diamond, with -S at the top, and can be remembered (as taught us by our proffessor) Society for the prevention of Teaching of Vectors. To obtain the relations from this, start at, for example, T and move clockwise, collecting terms, i.e. dT/dp with S constant. We then move anticlockwise from the unused term, V in this case, giving dV/dS with p constant. Passing the "-" gives makes each expression negative, so when they are equated, the signs cancel. Does anyone know if this is the same mnemonic that was deleted before? Furious.baz 20:42, 5 March 2007 (UTC)


 * one of them is easy: the letters in one line almost spell PoSiTiVe with negative sign!


 * ∂P/∂S =  - ∂T/∂V


 * The other relation with a negative sign is PoSiTiVe upside down (∂S/∂P = - ∂V/∂T)
 * Then you might have oVerSTeP ∂V/∂S =  ∂T/∂P  and its inversion ∂S/∂V  =  ∂P/∂T  Acorrector (talk) 23:10, 3 November 2021 (UTC)

Another device for remembering, assuming you know the components of the energy functions:  The energy functions themselves aren't hard to remember as long as you remember the conjugate variables (p,V), (T,S), and (mu,N). —Preceding unsigned comment added by 76.251.12.179 (talk) 00:18, 1 March 2009 (UTC)

Roadmap to the thermodynamic web
I just uploaded a "map" I created of thermodynamic equations. I wanted to convert it to SVD (e.g., using Inkscape), however, I am not really good at graphic design. If anyone has the time and know-how, please feel free to convert it to SVG. Also, I am not sure if this article is the best place for it. I am only including this comment on this article, as this "map" helped me a lot as an undergrad whilst learning thermodynamics, etc. --Thorwald (talk) 00:51, 7 December 2013 (UTC)


 * Hi Thorwald, as promised I'll create an SVG version. Are you sure you want volume to be a lower case "v" and not uppercase "V"? Uppercase seems more common. Thanks, M&and;Ŝc2ħεИτlk 11:18, 3 January 2014 (UTC)




 * Here it is:


 * The (minor) changes are:
 * made the colours brighter and less dull,
 * lower case s and v -> uppercase S and V for entropy and volume respectively.
 * left out the names for coefficient of thermal expansion and the thermal compressibility, since the the caption should define all the symbols,
 * left out the words for the cyclic relations "relations without P, T, S, V)" since it is clear the relations do not involve those quantities,
 * Let me know if you want anything original reinstated, or for any other corrections or suggestions. Your original is a great diagram, so thanks again for uploading it! ^_^
 * Unfortunately, during the upload, the name " file:Thermodynamic map.svg " was disallowed with the message "there is another file with this name", despite the fact there was not. On commons I have requested the page be moved from " file:Thermodynamic map 2.svg " to the file name " file:Thermodynamic map.svg ".
 * Best regards, M&and;Ŝc2ħεИτlk 12:42, 3 January 2014 (UTC)
 * Awesome! Nice job and I like your changes. I say we add this to the main article somewhere. Thank you for doing that! --Thorwald (talk) 15:58, 3 January 2014 (UTC)


 * Cool! In the caption, all the symbols will be defined. M&and;Ŝc2ħεИτlk 16:12, 3 January 2014 (UTC)


 * Should also say: the move has been done by user:Marcus Cyron, so the name of the file is now indeed " File:Thermodynamic map.svg ". Thanks to him too. M&and;Ŝc2ħεИτlk 16:17, 3 January 2014 (UTC)


 * First, great map, thank you. I use it very often. I am afraid, though, that the following derivatives are not quite right.
 * [last row] (dP/dV)T = 1/(κV), should be: (dP/dV)T = -1/(κV)
 * [last row] -(dT/dP)V = κ/α, should be: -(dT/dP)V = -κ/α
 * [one row before last] (dP/dT)V = -α/κ, should be: (dP/dT)V = α/κ

Henriquew (talk) 16:00, 28 February 2016 (UTC)


 * Thanks for posting here, will check and later update the image if needed. 'M'&and;Ŝc2ħεИτlk 16:31, 28 February 2016 (UTC)


 * You are correct. ^_^ I will fix. 'M'&and;Ŝc2ħεИτlk 22:55, 28 February 2016 (UTC)


 * Glad to help :) Henriquew (talk) 23:57, 28 February 2016 (UTC)

Sound Speed
I love the mnemonic device. Notice that the top derivative (dP/dV at const S) is the sound speed. I believe sound speed should be incorporated into the bigger picture, making it just as important as thermal expansion, compressibility, and the heat capacities. — Preceding unsigned comment added by 130.221.224.7 (talk) 14:08, 23 November 2015 (UTC)