Talk:Maxwell relations

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. --P3d0 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

${\frac {\partial }{\partial x}}\left({\frac {\partial f}{\partial y}}\right)\neq {\frac {\partial }{\partial y}}\left({\frac {\partial f}{\partial x}}\right)$

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)

Another device for remembering, assuming you know the components of the energy functions: [1] The energy functions themselves aren't hard to remember as long as you remember the conjugate variables (p,V), (T,S), and (mu,N).