Talk:Gibbs free energy

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Contents

[edit] Typo

Is this a typo:

"by showing that the heat evolved [sic] in a reaction"

which is found under section History, paragraph 5?

Shouldn't it be involved?

[edit] '04 questions

In the section that derives Gibb's free energy, an explanation of what Q is, is missing. Perhaps someone who knows exactly what Q is defined as, could edit the page with an explanation.

Q is heat transfer, and the article says so repeatedly. — Miguel 03:21, 2004 Oct 28 (UTC)
Q must be dimensionless for ln(Q) to make sense. I think it is the relative pressure (the ratio between the actual pressure and the atmospheric pressure)
--HenrikMidtiby 21:06, 16 January 2006 (UTC)
Q, if I remember correctly, is the reaction quotient. It is similar to the equilibrium constant expression; they are the same after the reaction has gone to completion. Hope that helps. Gchriss 18:24, 5 February 2006 (UTC)
heat transfer is small "q" --M1ss1ontomars2k4 18:39, 13 May 2006 (UTC)

[edit] identities

the identity relating nFE to RTlnK is incorrect (there shouldn't be a minus there)

You're right. It's been changed. --M1ss1ontomars2k4 18:43, 13 May 2006 (UTC)

[edit] Isothermal, isobaric processes

The article states "Such processes do not seem to move on a P-V diagram; they do not seem to be dynamic at all." I take issue with this, because I can name a million isothermal, isobaric processes that definitely move on a P-V diagram. Consider boiling water at atmospheric pressure and 100 degrees C... it goes from liquid to gas, and therefore the volume changes drastically. Shall we remove this statement? Ed Sanville 21:54, 10 November 2005 (UTC)

[edit] What is it?

What does the G equate to in conceptual terms? Is it for instance, the amount of thermal energy contained in a given volume? Could it be expressed as 'the amount of energy that would dissipate if the mass of given material were released to the great vacuum of space', not considering radioactive decay or chemical interactions? -- Pinbucket 00:06, 18 March 2006 (UTC)

No, basically, if you do an energy balance on constant-temperature, constant-pressure reacting system, i.e. final "total energy" = initial "total energy", you can facilitatively divide this total energy [H] released from the chemical reaction into two parts: (a) useable part = [G]; (b) un-useable part = [TS].--Sadi Carnot 21:05, 11 April 2006 (UTC)
The decrease of the Gibbs free energy equals the maximum non-volume (non-boundary) work a system can perform under isothermal, isobaric conditions. That's not quite the same as the maximum work, which is the decrease in the Helmholtz free energy. As correctly noted above, enthalpy [H] equals [G] plus [TS]. For example, a fuel cell can convert the decreased enthalpy into electrical work, the latter equal to the decrease in [G], with the remainder lost as heat. ----PotomacFever 14:24, 21 June 2006 (UTC)

[edit] What is this thing called?

I removed the following:

(sometimes also known as free enthalpy)

I've read dozens of books on thermodynamics, and I've never heard this.--Sadi Carnot 19:18, 25 April 2006 (UTC)

Er...try doing a search on Google. I'm guessing free enthalpy is not a common term where you/I live. --M1ss1ontomars2k4 18:44, 13 May 2006 (UTC)
M1ss, I checked the A to Z dictionary of Thermodynamics (Perrot), it says:
Free enthalpy – A name sometimes given to the Gibbs free energy function, G = H –TS, by people whose mother tongue is not Shakespeare’s language.
Hence, knowing personally in American engineering schools, of which Willard Gibbs was the first, that this term is not used (and only confuses the matter), I will tone down the acknowledgement of this association in the article. --Sadi Carnot 15:19, 15 May 2006 (UTC)

See also following section.

[edit] Gibbs free energy to Gibbs energy move debate

I had certainly never heard of "free enthalpy" for this parameter before, and it seems to me a poor (confusing) choice of terminology — if it is to be referred to in the text, perhaps "rarely" or "occasionally" is fitting. More importantly, the IUPAC recommendation is that this parameter be called either the Gibbs energy, or the Gibbs energy function — note, no "free"! For this reason, this article should be swapped/changed to the corresponding url/heading. (Note: I have already done this once (see history), and am waiting for Sadi to explain why it shouldn't happen, as he (she?) has reversed that change.) - DIV, 2006-05-31 (Melbourne)

My anonymous friend, first I don't see how you seem to find yourself comfortable jumping into a major article as an unknown editor and so freely making such drastic changes. Secondly, I am a chemical engineer, thermodynamic terms are my specialty, I have read near to all of Willard Gibbs books, and I specifically read about Gibbs free energy. Thirdly, reading thermodynamics books, textbooks, and articles (and physical chemistry books) in general is my hobby; I personally own over 50 such thermodynamics books. Fourthly, regardless of what justification I might or might not have as regarding experience in using this term, it would be clearly obvious from the history sections of Gibbs energy (about five edits going back to ‘05) as compared to Gibbs free energy (about 80 edits going back to ’03) that the later terminology is well preferred over the former. Also, in the future, any time you feel like making such drastic moves of entire articles please put your proposals on the talk page and let them sit for a month or two so to gather up the common opinion. Thank-you:--Sadi Carnot 17:26, 30 May 2006 (UTC)
My friend, please go back and fix all of the many changes you seem to have made in regards to terminology; I don't even know where to begin with the mess of things you have made. You have to understand that when you try to change one term in one article you disrupt the homogeneity of the entire encyclopedia and specifically the set of articles (probably about 50+) that use this term.--Sadi Carnot 17:35, 30 May 2006 (UTC)

To further clarify, please see: Free energy (disambiguation); there are over 30+ editors, not one of whom is myself, who have contributed to this page and you see, of course, what terminology results. Again, please be more careful in the future. As to a loose rank, in regards to their prevalence of use, the following is order is preferred:

  1. Gibbs free energy (most used; unambiguous; preferred in technical papers, used in themal physics book, used in biological thermodynamics books, used in chemical engineering books, used in biochemistry books, used in scientific dictionaries, etc.)
  2. Free energy (used greatly in older books, biological writings, chemistry books, used loosely, etc.)
  3. Gibbs free energy function (used in derivations)
  4. Gibbs energy (used in physical chemistry books)
  5. Thermodynamic potential at constant pressure (term used by Fermi in 1936)
  6. Gibbs energy function
  7. Gibbs function (used in some thermodynamics textbooks)
  8. Free enthalpy (used sparingly in languages other than English)
  9. Free energy function
  10. etc.

I hope this helps. If you wish, you can read an entire history of how the term has changed over the course of time in Raffa’s Drug-Receptor Thermodynamics (textbook) chapter 4: “A Brief History of Thermodynamics Terminology and Notation.” (pgs. 56-59)--Sadi Carnot 17:46, 30 May 2006 (UTC)

Hello Sadi. I respond to a few of your points.
  • I am only slightly more anonymous than you. If it helps the conversation, I am also a Chemical Engineer. From the link on your user account I would rate our education and academic achievements as comparable. Feel free to call me by my initials, DIV. The dispute is not between myself and yourself. The question is whether you feel that your qualifications are superior to the combined authority of those on the relevant IUPAC committee. I would tend to defer to IUPAC. I am also curious whether you have been elected to be an editor?
  • I am well aware that changing content in one location can potentially break many links. This is why I executed a direct swap between Gibbs energy and Gibbs free energy, making the latter the redirect instead of the former. You will notice I didn't do this with Helmholtz energy, because I don't like the trouble of having to log in with an account, so I cannot directly create (new) pages. Also, no doubt I have missed a couple of things, but my time is only finite.
You suggest two reasons for maintaining the status quo. If I quote you very liberally:
  • you note that changing the terminology will involve much work in ensuring all the reliant changes cascade through.
  • you further cite the history of the word, and make some claims about current usage patterns.
To my mind these things are entirely insufficient grounds to refuse moving the article to the IUPAC–recommended heading, and leaving a redirect at this and all other popular headings. IUPAC generally has very good reasons for making their recommendations, and it doesn't help their implementation when a "major article" such as this one uses the incorrect terminology!
There is almost always a huge resistance to change, and when Wikipedia was in its infancy and someone created the "Gibbs free energy" page using one of the very popular terms, it is not at all surprising that searchers for "Gibbs energy" found it there (eventually), and contributors added content there. Also, most users and indeed some contributors are apathetic. Whereas I dislike letting even small errors go uncorrected.
  • I take your point about leaving comments to get some feedback. I must say I was surprised to find the article under the 'wrong' listing, and may have been somewhat impatient to 'fix' it. I was of the opinion that the IUPAC reference I provided (numerous times) would be understood and accepted by any interested party. I am not of a mind to undo any of my changes. I will, however, defer reimplementing changes you have undone.
... Also, I wouldn't necessarily be so sure that your comment on 'free enthalpy' fits the definition given under the previous heading.
Regards, DIV 2006-06-01 (Melbourne)
First let me say my prejudice is towards "Gibbs Free Energy". But I totally agree that IUPAC terminology is the Wikipedia standard and we should conform to its terminology. As far as I can determine, "Gibbs Energy" is the IUPAC term for what I would normally call the Gibbs Free Energy. So the bottom line is that I support the idea of changing all references to Gibbs Free Energy to Gibbs Energy. But this must be done in a slow, coordinated manner, preferably by non-anonymous editors who are familiar with the thermo articles. I would be glad to start the process on those article that I am familiar with, once a consensus is reached. PAR 20:40, 31 May 2006 (UTC)
Hi PAR, thanks for your input.
Sadi,
I wanted to summarise two further arguments for the case of moving to "Gibbs energy" as the main listing:
  • As time passes, (unless the IUPAC recommendation changes) more and more people will come to be familiar with "Gibbs energy" rather than "Gibbs free energy". Sadi referred to a library of 'classic' texts. I contend that current and forthcoming texts will increasingly use the term "Gibbs energy". A good example is the standard work by Stan Sandler, Chemical, Biochemical, and Engineering Thermodynamics, where you will see the index makes no mention of "free energy" (although a cross-reference could have been useful, I admit). Professor Sandler, editor of the AIChE Journal, is an expert in the field (see 1, 2, 3) ...as you would expect. What I am trying to say is that the change will happen, and it is better for it to happen now.
Another example of the same usage is the latest edition of Perry's Chemical Engineers' Handbook, in the section by van Ness & Abbott.
—DIV, Melbourne (128.250.204.118 06:26, 2 June 2006 (UTC))
  • The fact that no-one made the change until now may be attributed to many causes. I have already mentioned apathy. Another is that changes can take a while to build up 'momentum' and propagate. But finally, with all due respect, a lot of the people looking at this page will emphatically _not_ be experts on thermodynamics. When I use Wikipedia, it is generally to look up things I do not know a great deal about. {I forget why exactly I viewed "Gibbs (free) energy" on this occasion, but it was related to the title of a paper I was trying to check up on (in French), which contained the phrase "chaleurs de réaction".}
Regards, DIV - Melbourne (2006-06-01)

DIV, I happen to be coincidently reading Baierlein’s 2003 Thermal Physics (textbook) and in chapter 10 “The Free Energies”, section 10.4, the topic is Gibbs free energy. Imaging that! Maybe they didn’t get that 1988 IUPAC memo? The point here is that this is an article for the English speaking world, we have to go with the most common term, i.e. the one that is most commonly used in textbooks, lectures, and in the common tongue. Maybe, in the future, things will change and the majority will start to use IUPAC standards?

Coincidently, off Amazon this last month I ordered over 30 new thermodynamic books (Sandlers I bought years ago), from virtually every branch of thermodynamics, you name it and I probably ordered it (or have it). My point is that I am going to reason that I am familiar with what is commonly used. To clarify this discussion one last time, the chapter “History of Thermodynamic Terminology and Notation”, in the book Drug-Receptor Thermodynamics, we find:

“Two conveniently defined functions are those that were originally described by using the word ‘free’ to indicate that under special conditions these were energies that were ‘free’ or available for work. In modern terms we use Gibbs energy or Gibbs function and Helmholtz energy or Helmholtz function; the descriptive ‘free’ has been banished (Mills et al. 1988), although it unfortunately continues to be used.” [(1)Mills I, Cvitas T, Homann K, et al. (1988). Quantities, Units and Symbols in Physical Chemsitry, IUPAC, Blackwell Scientific Publications, Oxford.; (2)Raffa, R.B. (2001). Drug-Receptor Thermodynamics: Introduction and Application. New York: John Wiley & Sons, Ltd.]

Strange, the descriptive 'free' was banished over 20 years ago? Maybe the people who started this article in 2003 weren't aware of the banishment? Now, here are the stats for Google hits:

for the term “Gibbs free energy”:
Results 1 - 10 of about 2,310,000 for Gibbs free energy [definition]. (0.19 seconds)
for the term “Gibbs energy”:
Results 1 - 10 of about 3,680,000 for Gibbs energy. (0.17 seconds)

As we see there is a toss-up. Yet when it is referenced in scientific encyclopedias we find a common standard. For example, here is the article as found in Eric Weissteins World of Physics: Gibbs Free Energy. The same is true for Britannica, here is a 2002 reprint of their section on free energy:

In thermodynamics, energylike property or state function of a system in thermodynamic equilibrium—it has the dimensions of energy and its value is determined by the state of the system and not by its history—expressed in two forms: the Helmholtz free energy, A, sometimes called work function, and the Gibbs free energy, G, sometimes F. If E is the internal energy of the system, PV the pressure–volume product, and TS the temperature–entropy product, then A = E - TS and G = E + PV - TS. Free energy is an extensive property; i.e., the magnitude depends on the amount of the substance present in a given thermodynamic state.
The changes in free energy, ΔA or ΔG, are useful in evaluating certain thermodynamic processes. In a reversible process, the work under constant temperature and constant volume is equal to the change in the Helmholtz free energy, ΔA, and the work under constant temperature and constant pressure is equal to the change in the Gibbs free energy, ΔG.
Changes in free energy can be used to judge whether certain transformations of state can occur spontaneously. Under certain conditions of constant temperature and volume, the transformation of state will occur spontaneously, slowly or rapidly, if the Helmholtz free energy of the final state is smaller than that of the initial state; that is, if the difference ΔA between the final and the initial state is negative. Under conditions of constant temperature and pressure, the transformation of state will occur if the change in the Gibbs free energy, ΔG, is negative.

We can go on and on but the fact remains that when people write up the entry in the encyclopedias (as the above two) exacting clarification is used along with a tendency to use the most informative and common term. In wikipedia, we have 120+ links to the Gibbs free energy page and 0 links to the Gibbs energy page. I would assume the 120 people who made these links didn’t get the 1988 IUPAC memo either? It is one thing for small committee of chemists to supposedly "ban" a term, and quite another for the world to want the term banned. As we see, we are in the middle of a 100+ year terminology evolution or transformation window, since the concept was developed by Gibbs in 1876. In time, maybe another 100 years, we will naturally (hopefully) gravitate towards a final agreement. To solidify my point, I have added 7 external links to the article (as shown below) --Sadi Carnot 02:56, 20 June 2006 (UTC)

[edit] Why is the attachment ‘free’ so important?

Answer, from Baierlein’s 2003 Thermal Physics (pg. 235), “The change in F (or G) determines the amount of energy ‘free’ for work under the given conditions. The German physicist and physiologist Hermann von Helmholtz had in mind this property when he coined the phrase ‘free energy’ for E – TS in 1882.” I will add this to the article. --Sadi Carnot 04:12, 20 June 2006 (UTC)

That's a great reference, using Baierlein, only I would differ slightly in that the statement can't be applied to Gibbs free energy without adding the qualification that it is the energy free for non-volume work. See, for example, Reiss, Methods of Thermodynamics, pp. 78-79. ----PotomacFever 14:29, 21 June 2006 (UTC)
Thanks for the input, I just added a big history section where I included your suggestion.--Sadi Carnot 05:50, 9 July 2006 (UTC)

[edit] Gibbs Free Energy, Life Processes and 'Wealth' creation

I'd like to ask a question, or so, here. First, is the relationship of Gibbs' free energy to life processes seems self evident. (Yes?) Next, life forms are highly ordered (low entropy) aggregations of matter. Their formation, therefore, I presume, occurs as another process 'externalises' these, localised, reversals of entopy increase, and of Free Energy decrease. (Is that so?) Also, have, for example, any measurements of photosynthesis, animal metabolism, etc?, ever been quantified to demontrate the fidelity of these life processes to the Gibbs'(etc) thermodynamic equations. (yes or no?) One final point, I've pondered whether the (human) 'wealth creation' processes could be described by the following word equation:

   Raw Materials + Energy --> Wealth + Pollution

Any comments on this proposition? Thanks! John Courtneidge (presently in Toronto, Canada)

Yes, many people have stabbed in this direction. The first was Herbert Spencer in his 1880 book First Principles, but he only speaks in terms ‘available energy’ and resources, dissipation, evolution, etc., not necessarily free energy as it is in the article. In 1922, Frederick Soddy applied steam engine theory to human life; he states: “life derives the whole of its physical energy or power not from anything self-contained in living matter, but solely from the inanimate world. It is dependent for all necessities of its physical continuance upon the principles of the steam engine. The principles of ethics of all human conventions must not run counter to those thermodynamics.” In 1926, in his book The Biosphere, Vladimir Vernadsky states: “Living matter, as a whole, is a unique system which accumulates chemical free energy G in the biosphere by the transformation of solar radiation.”
You might also want to check out Erwin Schrodingers 1944 book What is Life?, his book is the most referenced book in regards to free energy, entropy, negentropy, solar energy input, and evolution. Another good one is the 1998 book Thermodynamic Theory of the Evolution of Living Beings by Russian physical chemist Georgi Gladyshev. Also, on the back cover of the 2003 book Information Theory and Evolution by theoretical physicist and chemist John Avery we are told that the paradox between the complexity produced by living systems and the seeming contraction between the second law of thermodynamics has its resolution in the Gibbs free energy that enters the biosphere from outside sources. This is just quick list. I hope this helps. Adios:--Sadi Carnot 06:29, 9 July 2006 (UTC)

[edit] Conceptual understanding of Gibbs free energy

Moved here from User Talk:Sadi Carnot

Hi, I was looking in the discussion section of the Gibbs free energy page and noticed that you've read a serious amount of textbooks on thermodynamics. At the moment I'm really struggling to conceptually understanding what Gibbs free energy is. I have a couple of chemical thermodynamics textbooks (because I'm studying chemical engineering) but they seem to just define Gibbs without giving a detailed explanation of what it is. So I was wondering if you could recommend a thermo. textbook that gives a seriously detailed description of Gibbs, written in such a way that the simpleton (myself) can understand it.

I have this theory that nothing is beyond anyone, it just needs to be explained in such a way that makes it comprehensible. Is this applicable with thermodynamics or do you think that I'm wasting my time trying to understand it?

Thanks for your time, really appreciate it :)

Lochnagar (07/29/06)

[edit] Reply

Lochnagar,

Good question. Gibbs free energy is my favorite topic. As to being able to conceptually understand what Gibbs free energy is; essentially, it is a more advanced and accurate replacement for the term “affinity” used by chemists, of olden days, to describe the “force” that caused chemical reactions. The term dates back to at least the time of Albertus Magnus in 1250.

From the 1998 textbook Modern Thermodynamics by Nobelist and chemical engineering professor Ilya Prigogine’s we find: “as motion was explained by the Newtonian concept of force, chemists wanted a similar concept of ‘driving force’ for chemical change? Why do chemical reactions occur, and why do they stop at certain points? Chemists called the ‘force’ that caused chemical reactions affinity, but it lacked a clear definition.

During the entire 18th century, the dominate view in regards to heat and light was that put forward by Isaac Newton, called the “Newtonian hypothesis”, which stated that light and heat are forms of matter attracted or repelled by other forms of matter, with forces analogous to gravitation or to chemical affinity.

In the 19th century, the French chemist Marcellin Berthelot and the Danish chemist Julius Thomsen had attempted to quantify affinity using heats of reaction. In 1875, after quantifying the heats of reaction for a large number of compounds, Berthelot proposed the “principle of maximum work” in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of a system of bodies which liberate heat.

In addition to this, in 1780 Antoine Lavoisier and Pierre-Simon Laplace laid the foundations of thermochemistry by showing that the heat evolved in a reaction is equal to the heat absorbed in the reverse reaction. They also investigated the specific heat and latent heat of a number of substances, and amounts of heat evolved in combustion. Similarly, in 1840 Swiss chemist Germain Hess formulated the principle that the evolution of heat in a reaction is the same whether the process is accomplished in one-step or in a number of stages. This known as Hess's law. With the advent of the mechanical theory of heat in the early 19th century, Hess’s law came to be viewed as a consequence of the law of conservation of energy.

Based on these and other ideas, Berthelot and Danish chemist Julius Thomsen, as well as others, considered the heat evolved in the formation of a compound as a measure of the affinity, or the work done by the chemical forces. This view, however, was not entirely correct. In 1847, English physicist James Joule showed that raise the temperature of water by turning a paddle wheel in it, thus showing that heat and mechanical work were equivalent or proportion to each other, i.e. approximately, dW α dQ. This was a precursory form of the first law of thermodynamics.

By 1865, the German physicist Rudolf Clausius had showed that this equivalence principle needed amendment. That is, one can use the heat derived from a combustion reaction in a coal furnace to boil water, and use this heat to vaporize steam, and then use the enhanced high pressure energy of the vaporized steam to push a piston. Thus, we might naively reason that one can entirely convert the initial combustion heat of the chemical reaction into the work of pushing the piston. Clausius showed, however, that we need to take into account the work that the molecules of the working body, i.e. the water molecules in the cylinder, do on each other as they pass or transform from one step of or state of the engine cycle to the next, e.g. from (P1,V1) to (P2,V2). Clausius originally called this the “transformation content” of the body, and than later changed the name to entropy. Thus, the heat used to transform the working body of molecule from one state to the next cannot be used to do external work, e.g. to push the piston. Clausius defined this transformation heat as dQ = TdS.

Hence, in 1882, after the introduction of this argument by Clausius, the German scientist Hermann von Helmholtz stated, in opposition to Berthelot and Thomas’ hypothesis that chemical affinity is a measure of the heat of reaction of chemical reaction as based on the principle of maximal work, that affinity is not the heat evolved in the formation of a compound but rather it is the largest quantity of work which can be gained when the reaction is carried out in a reversible manner, e.g. electrical work in a reversible cell. The maximum work is thus regarded as the diminution of the free, or available, energy of the system (Gibbs free energy G at T = constant, P = constant or Helmholtz free energy F at V = constant, P = constant), whilst the heat evolved is usually a measure of the diminution of the total energy of the system (Internal energy). Thus, G or F is the amount of energy “free” for work under the given conditions.

Up until this point, the general view had been such that: “all chemical reactions drive the system to a state of equilibrium in which the affinities of the reactions vanish”. Over the next 60 years, the term affinity came to be replaced with the term free energy. According to chemistry historian Henry Leicester, the influential 1923 textbook Thermodynamics and the Free Energy of Chemical Reactions by Gilbert N. Lewis and Merle Randall led to the replacement of the term “affinity” by the term “free energy” in much of the English-speaking world.

I hope this helps? As to a good book, one that I'm reading this week is the 1967 textbook Nonequilibrium Thermodynamics in Biophysics published by Harvard University Press. It’s written by A. Katchalsky (Polymer Chemistry Department, Institute of Science Rehoveth, Israel) and Peter R. Curran (Biophysical Laboratory, Harvard Medical School, Boston Massachusetts). I’m about halfway through the book and it is very juicy. All the derivations are built from the ground up so you don’t miss any key pieces and they are easy to follow. It shows how the Gibbs free energy equation, in an expanded form, can be applied to very exotic situations, such as when the transport of a substance into muscle tissue causes a chemical reaction, which then does the work of stretching or contracting a muscle fiber. Very stimulating book! As to good chemical engineering thermodynamics textbooks, Smith, Van Ness and Abbott’s textbook is good as well as Sandler’s textbook. Adios: --Sadi Carnot 02:10, 30 July 2006 (UTC)

[edit] Thanks

Sadi Carnot, cool, thanks for the explanation and advice :). Rgds: User:Lochnagar (07/30/06)

[edit] Should P-V be P-T ?

In the Derivation section,

"Thus, Gibbs energy is most useful for thermochemical processes at constant temperature and pressure: both isothermal and isobaric. Such processes don't move on a P-V diagram; and therefore appear to be thermodynamically static."

if the process is isothermal and isobaric, shouldn't it say, "Such processes don't move on a P-T diagram..."?Brian Wowk 21:32, 3 August 2006 (UTC)

Yes! The Gibbs function is at constant pressure, so specifically includes pV work preformed in changing the volume of a system. Physchim62 (talk) 16:01, 4 August 2006 (UTC)

Upon reflection, I think what the original author meant was that if P and T are fixed, V will also tend to be fixed within a given region of the phase diagram. Thus he described such systems as "thermodynamically static," unless one introduces the chemical potential as an additional state variable. I edited the article to clarify this. Brian Wowk 19:44, 4 August 2006 (UTC)

[edit] Merge

Please merge Standard Gibbs free energy change of formation here to get rid of a stub which will likely remain undeveloped and which has been tagged for cleanup for over a year, if it's at all possible. Thanks. -THB 02:09, 16 October 2006 (UTC)

Done, thanks: --Sadi Carnot 23:53, 3 November 2006 (UTC)