Talk:Phase rule

message: *Question asked in 'Comments about the Ratings'. (Click the 'Show' on the blue bar above, which reveals:-
'There is something not explained in the gibbs'  equation ... the equation is F=C-P+2 when the pressure OR temperature is constant but this formula is not valid when there is a change in both temperature and pressure the formula will change to F=C-P+1 please revise and reply...thank you for your effort'.
:Gibbs's phase rule relates natural objects: the 'number of phases, P' and the 'number of intensive variables, C+2'. I'm not clear the phase rule ever changes, unless one adds new forms of work. When p=0, some rewrite it F=C-P+1; but a clearer statement is F=C+2-P, with dp=0 (which reduces the number of intensive variables by one). If one substitutes a natural, univariant curve for the pressure axis (which one always can): it's not so clear that the phase rule 'becomes' F=C-P+1 at a state of constant pressure. This confusion may also arise because we don't normally change scientific formulas: we change the values of its variables.
:The phase rule F=C+2-P is valid at all equilibrium states (described by, at most, C+2 intensities) in open or closed systems. The rule F=C+2-P is valid when all intensities are kept constant (at an equilibrium, invariant state, illustrated by the triple point of water), when all but one are kept constant (along, for example, an equilibrium, univariant path), ..., or none is kept constant (along a C+2-dimensional family of equilibrium paths within a graphical region), where change is so slow that the system continuously equilibrates with its environment). Enrico Fermi offered a paragraph opining the existence of the last, which geologists see frequently.
:By modifying the environment at one's will, equilibrium states can be moved or stopped at one's will. These equilibrium states will always be either stable or indifferent equilibrium states (discussed in treatises by Pierre Duhem and a thesis by Paul Saurel), not reversible ones (which are not realized in nature). At all these states, the phase rule F=C+2-P is satisfied.
:I'm unclear about the confusion being asked about, but I'm hoping these remarks might help. Geologist (talk) 00:43, 28 October 2008 (UTC)
thread_title: Basic Issues

message: 'Intensity' is a handy term, little used today, that is one class of thermodynamic variable. Specific equations, such as Clapeyron's, can be easily generalized by substituting any intensity & conjugate density. Other generalizations are (generalized) densities, extensities, and energies (characteristic potentials). One can find some use of these in the late 19th Century thermodynamic literature, and in Bryan's admirable little attempt to generalize thermodynamics using geometry and (unfortunately) Energetics.
Note, however, the phase rule applies to intensive variables (intensities & densities), variables that don't change their values when the system is replicated. (Using the Gibbs-Duhem equation & conservative chemical reactions to calculate the values of accessible directions on an intensity diagram is a wonderful application for students of elementary linear algebra, and appears in an early paper by Gibbs.
Geologist (talk) 10:51, 21 March 2008 (UTC)
thread_title: From intensities to intensive variables

message: There is a substantial drop in quality in the Examples section, between the 10 March 2006 and 17 March 2006 revisions. I don't know whether to add a cleanup tag or revert to the 10 March 2006 version (implying deliberate vandalism). Comments and help please? Sentinel75 06:14, 11 May 2006 (UTC)
thread_title: Vandalism?

message: In our thermodynamics class, we saw a different, more elaborate derivation of the Gibbs phase rule. It is this:
A system with C components in P phases, can be specified using the following intensive variables:
* Temperature and pressure for each phase
* Mole fraction of each component, for all phases.
* In total: 2*P + C*P
The relations you can come up with, are the following (letters standing for components, numbers for phases):
* in equilibrium:
** T1 = T2 = ... (P-1) relations
** p1 = p2 = ...
** x1_a = x2_a = ...
** x1_b = x2_b = ...
** ...
** + -----------------
** (P-1) * (C+2) relations
* always:
** x1_a + x1_b + ... = 1
** ...
** + ---------------------
** P relations
This gives us ( 2*P + C*P ) - (  (P-1)(C+2) + P ) = C - P + 2 degrees of freedom. I don't know which derivation is most logical; the one depicted here or the one currently in the article. Please comment
=== Alternative derivation ===
The proof depicted here is the more logical, if one uses the variables used in texts today, xi. Gibbs, I believe, used the Gibbs-Duhem equation to derive, but not to prove, the phase rule. He chose not to prove it, though his argument is always cited as proof. (Similarly, his description of a phase (planar sides, &c) is not the definition he used: his definition was a region homogeneous in densities. Gibbs was a mathematician, and his is the only treatment I've read that clearly states both the necessary & sufficient conditions, not just sufficient, for a statement to be true. He argues for a phase rule, using intensities only, such dp, dT, & dμi. However, he states that the equation f = (c+2) - p applies to generalized densities as well (all intensive variables). His equation is local, appying within the neighborhood of a point on a surface. 
More advanced texts, such as Denbigh's, use proofs such as yours - using global variables. Each intensive variable T, (-p), & xi is presumably a curve over a domain. (Some people prefer to use scalar stresses, such as dT, because 'relative values have absolute significance' -P. Bridgman.) There are at least two proofs in the primary literature; yours comes, I believe, from an early German paper by Wind. There was also a claim by Helm that the 1st law was necessary & sufficient to prove the phase rule. Other names associated with early papers on the phase rule are Natanson, Riecke, Duhem, de Donder, Planck, Saurel, Wind, Meyerhoffer, Nerst, Perrin, Raveau, and Trevor. H.W. Bakhuis-Roozeboom wrote a nice, qualitative thirty page article on the phase rule as a preface to his famous treatises on phase diagrams. 
It would be nice to finally clarify all this, for I've never seen a review of proofs. Geologist 17:58, 27 March 2007
(UTC)
====Two possible 1901 proofs found====
Google's Books has a review of the 1901 physics literature, Die Fortschritte der Physik im Jahre 1901, that reviews two significant papers. One reviewer claims Paul Saurel (in 1901, 'On the Phase Rule'.J. Phys. Chemistry, v.5, p. 401-3) has extended Gibbs's phase rule from intensities to intensive variables: 'Temperatur, Druck, und Concentration der Phasen'. Saurel's works are flawless, so let's hope 'Concentration der Phasen' means independently variable concentrations within the phases.
The same abstracting journal reviews a paper by C.H. Wind in 1901, 'Sur la règle des phases de Gibbs'. Arch. Néed. v. 4, p.323-31. The review of this paper contains an equation that very closely resembles Gibbs's phase rule as developed by de Donder, but for a wrong sign. I have Saurel's paper, I know, but I don't believe I have Wind's original paper at hand. If I have misread the German reviewer's definitions of Wind's variables, these two 1901 papers may contain the first proofs of the two expressions of Gibbs's phase rule described under 'Degrees of Freedom'. Geologist (talk) 13:48, 24 March 2008 (UTC)
thread_title:  Alternative derivation 

message: The proof depicted here is the more logical, if one uses the variables used in texts today, xi. Gibbs, I believe, used the Gibbs-Duhem equation to derive, but not to prove, the phase rule. He chose not to prove it, though his argument is always cited as proof. (Similarly, his description of a phase (planar sides, &c) is not the definition he used: his definition was a region homogeneous in densities. Gibbs was a mathematician, and his is the only treatment I've read that clearly states both the necessary & sufficient conditions, not just sufficient, for a statement to be true. He argues for a phase rule, using intensities only, such dp, dT, & dμi. However, he states that the equation f = (c+2) - p applies to generalized densities as well (all intensive variables). His equation is local, appying within the neighborhood of a point on a surface. 
More advanced texts, such as Denbigh's, use proofs such as yours - using global variables. Each intensive variable T, (-p), & xi is presumably a curve over a domain. (Some people prefer to use scalar stresses, such as dT, because 'relative values have absolute significance' -P. Bridgman.) There are at least two proofs in the primary literature; yours comes, I believe, from an early German paper by Wind. There was also a claim by Helm that the 1st law was necessary & sufficient to prove the phase rule. Other names associated with early papers on the phase rule are Natanson, Riecke, Duhem, de Donder, Planck, Saurel, Wind, Meyerhoffer, Nerst, Perrin, Raveau, and Trevor. H.W. Bakhuis-Roozeboom wrote a nice, qualitative thirty page article on the phase rule as a preface to his famous treatises on phase diagrams. 
It would be nice to finally clarify all this, for I've never seen a review of proofs. Geologist 17:58, 27 March 2007
(UTC)
====Two possible 1901 proofs found====
Google's Books has a review of the 1901 physics literature, Die Fortschritte der Physik im Jahre 1901, that reviews two significant papers. One reviewer claims Paul Saurel (in 1901, 'On the Phase Rule'.J. Phys. Chemistry, v.5, p. 401-3) has extended Gibbs's phase rule from intensities to intensive variables: 'Temperatur, Druck, und Concentration der Phasen'. Saurel's works are flawless, so let's hope 'Concentration der Phasen' means independently variable concentrations within the phases.
The same abstracting journal reviews a paper by C.H. Wind in 1901, 'Sur la règle des phases de Gibbs'. Arch. Néed. v. 4, p.323-31. The review of this paper contains an equation that very closely resembles Gibbs's phase rule as developed by de Donder, but for a wrong sign. I have Saurel's paper, I know, but I don't believe I have Wind's original paper at hand. If I have misread the German reviewer's definitions of Wind's variables, these two 1901 papers may contain the first proofs of the two expressions of Gibbs's phase rule described under 'Degrees of Freedom'. Geologist (talk) 13:48, 24 March 2008 (UTC)
thread_title:  Alternative derivation 

message: Google's Books has a review of the 1901 physics literature, Die Fortschritte der Physik im Jahre 1901, that reviews two significant papers. One reviewer claims Paul Saurel (in 1901, 'On the Phase Rule'.J. Phys. Chemistry, v.5, p. 401-3) has extended Gibbs's phase rule from intensities to intensive variables: 'Temperatur, Druck, und Concentration der Phasen'. Saurel's works are flawless, so let's hope 'Concentration der Phasen' means independently variable concentrations within the phases.
The same abstracting journal reviews a paper by C.H. Wind in 1901, 'Sur la règle des phases de Gibbs'. Arch. Néed. v. 4, p.323-31. The review of this paper contains an equation that very closely resembles Gibbs's phase rule as developed by de Donder, but for a wrong sign. I have Saurel's paper, I know, but I don't believe I have Wind's original paper at hand. If I have misread the German reviewer's definitions of Wind's variables, these two 1901 papers may contain the first proofs of the two expressions of Gibbs's phase rule described under 'Degrees of Freedom'. Geologist (talk) 13:48, 24 March 2008 (UTC)
thread_title: Two possible 1901 proofs found

message: 1. A definition of 'degrees of freedom'. 
In thermodynamics 'degrees of freedom' points to the number of intensive properties that may be freely set.
On simple monophasic hydrostatic systems (C=1, P=1) this number is two. Usually temperature and pressure, for the sake of simplicity.
When the system exhibits two phases in equilibrium (for instance water boiling at 100 celsius and standard pressure)
the number of degrees of freedom reduces to one by Gibbs phase rule (C=1, P=1). This means you may freely change
the temperature (for instance) of this system while preserving phase equilibrium. But, pressure will change accordingly
in a way which is not due to the observer but to the thermophysical properties of water, Ie: through the coexistence line of vapour and liquid.
*You meant to write P=2 here, I think. Geologist (talk) 11:13, 21 March 2008 (UTC)
thread_title:  Suggestions 

message: Does anyone have an early reference to Gibbs work or writings on the phase rule.  I cannot find any. I am looking at Max Plank "Treatise on Thermodynamics," 1945 unabridged republication of 6th/7th edition ca. 1926 (original preface dated 1897).  Planck does not go into degrees of freedom or variability and doesn't invoke Gibbs Duhem however he uses Eurler relation to collapse the equilibrium expressed by (T,P) and [S - (U + pv)/T].  Perhaps this is actually Gibbs Duhem.
*That would be interesting, for the derivation of the Gibbs-Duhem equation using Euler's relation is not in Gibbs, and the equation itself is not in either of Duhem's celebrated treatises. (So many mathematical relations in chemical thermodynamics were derived in Gibbs's treatise below that one needs to distinguish them: attaching the name of someone who later derived it independently or developed its implications is almost a necessity. In the preface to Duhem's Thermodynamique et chemie, one can read of his great enthusiasm for Gibbs's work. Though Duhem's work differs (he says) in containing more mathematics than typical works of the time on the phase rule, I can't find the Gibbs-Duhem equation in it.) The equation is very clearly derived in Gibbs, however. What is not derived in Gibbs is the phase rule. Gibbs uses his equation 97 (the Gibbs-Duhem equation) to quickly argue its likelihood, but never changes his variables from intensities (the same in each phase) to concentrations (different in each phase). This was left to someone else - Wind, I think, though Natanson comes to mind as well - in the early German literature. Here, I think, is a Google reference to Gibbs's phase rule (a term he never uses):
Gibbs's Original Derivation of his Phase Rule
*There is also a forgotten work published in 1900 by H.W. Bakhuis-Roozeboom that serves as a very long preface to his many volumed work on the applications of the phase rule. I don't have a reference, but I'm sure it's also in Google Books (somewhere).
*Planck's unappreciated work was never too attractive to me (it was originally a doctoral dissertation), because I never knew when approximate gas equations were mixed into his relations. He doesn't refer to Euler's derivation of anything in his early versions (in German), but his equation 151 is reminiscent to the Gibbs-Duhem equation. If so, he passes it over without a second thought. Oh, yes; unless I'm mistaken, Max Planck refers in his earlier copies of his treatise to 'phases', but he never mentions the name 'Gibbs'. :-) Geologist (talk) 14:01, 18 January 2008 (UTC)
thread_title:  Possible improvement 

message: I found the page in a sad state and did an extensive rewrite.  I tried to not only correct the errors, but to put the rule in context.  When you look at the basis, you can see why there is a different rule for condensed phases.
It should be clear that the rule is of no help in predicting when mulitple phases will form and does not give equations of state.  That you get no phase transition above the critical point relates to phase diagrams, but is not relevant on this page.  There are all kinds of different phase behavior and the rule only tells you what to do after you have figured out the number of phases by some other means.  The reference to Euler's formula was apochryphal, but somehow persisted from the first draft until I nixed it.  The talk about degrees of freedom was confusing and I suspect came out of someone editting the page without quite understanding the rule or being able to articulate their understanding. 
I should have mentioned the assumption of no chemical reactions.  My source assumes no chemical reactions, but there is a comment above about this and I suspect the only chemical reactions that would matter would be ones that change the number of species.
A derivation of the rule would be nice, but I am going to leave that to someone else.  I think I see a good one in the talk above: assumptions that T, P, and xi specify each phase corresponds to my Duhem's Rule applied separately to each phase.  Add in phase equilibrium and the derivation is just a few steps.Paul V. Keller (talk) 06:30, 15 November 2008 (UTC)
thread_title: November 2008 Rewrite

message: I am glad to see that Petergans and Paul Keller are converging on a useful set of examples (or "consequences"). I would like to suggest that the examples would be clearer if each (or most) specified the explicit calculation of F using the phase rule. Sample format: for the liquid-vapour equilibrium of a pure substance, C=1, P=2, F = 1-2+2 = 1 so that T and p cannot vary independently.  Dirac66 (talk) 16:19, 24 November 2008 (UTC)
thread_title: Examples should include calculation of F = C-P+2

message: After the edits by PVKeller yesterday, the material on pure systems is much improved. The material on binary systems has been removed for the moment, since it implied incorrectly that the phase rule is responsible for the existence of features such as azeotropes and eutectics. I think the next step is to rewrite more correct material for binary systems, possibly based on a physical chemistry text or texts. Dirac66 (talk) 02:36, 9 December 2008 (UTC)
thread_title:  Pure systems much improved, binary systems to redo. 

message: There are several 'lever rules': one in which only the mass of the phase is known, one in which the composition of the phase is known, and one in which ... well, nothing fixed is known. The first is nice in that one need not know compositions, and can specify a phase as 'halite'. The second is used in petrology; and it is necessary when crystals precipitate (or bits or rock are added). OK, I won't complain about the third; though association & dissociation vary with temperature, and the 'lever' seems a bit unnecessary. This mimics the Lewis-Bancroft split mentioned above; and is likely illustrates the split between chemists and natural scientists:-) Geologist (talk) 12:40, 26 July 2009 (UTC)
thread_title:  Lever Rules 

message: I do have a comment on this line. 'If four phases of a pure substance were in equilibrium, the phase rule would give F = -1 which is impossible. This means that four phases of a pure substance (such as ice I, ice III, liquid water and water vapour) can never be in equilibrium at any temperature and pressure.'
This is what Gibbs wrote: 'It does not seem probable that P can ever exceed C+2.' -Gibbs, p.97
 
The article might benefit from a proof; but, because the phase rule can't be proved, that is asking too much. We cannot prove, to my knowledge, that there should not someday be found a relation among the temperature, pressure, & chemical potentials of components in a phase other than the Gibbs-Duhem equation. Gibbs was certainly aware of this, and never proved the phase rule. Wind & Duhem, I believe, both draw upon the equality of chemical potentials (which I'm glad was removed).
The derivation given by me at the top of the page is Wind's, I believe; and Duhem was first to use Euler's theorem to derive the Gibbs-Duhem equation. Here is Gibbs's derivation:
'If a homogeneous body has C independently variable components, the phase of the body is evidently capable of C+1 independent variations. A system of P coexistent phases, each of which has the same C independently variable components, is capable of C+2-P variations of phase.' -Gibbs, p.96.
Notice that the above derivation just counts phases, employing 'intensities', not all intensive variables (which include 'generalized densities'). Geologist (talk) 12:40, 26 July 2009 (UTC)
thread_title:  Proofs 

message: I think that Geologist's points about Proofs are generally valid, but that it is necessary to bring the argument down to a suitable level for the article. An encyclopedia article is intended as an introduction for those unfamiliar with a subject who have seen the term and want some explanations. For the phase rule perhaps the typical reader would be a student with one year of physical chemistry and one year of calculus.
I agree that there is no rigorous proof of the phase rule, since the usual justification/derivation/argument does not exclude the possibility of linear dependence. But to introduce the subject I think it would be useful first to explain why the rule generally (= “almost always”)  works for equilibrium systems, and then mention the possibility of exceptions due to linear dependence or non-equilibrium.
In order to make the learning curve as simple as possible for typical 2009 students, I think it should be based on contemporary textbooks and use chemical potentials, even if Gibbs etc. used other functions which are now less familiar. To simplify the discussion even further, we can start as now with the special cases C=1, P=2 and C=1, P=3 but I propose to add a mention of the chemical potential equations, at the level of high school algebra: two equations can be solved to find two unknowns T and p. This would be analogous to what is already in the discussion of binary systems. The argument for the general case (any C) could be added too, but we have given a reference to a leading textbook. 
Finally the case of C=1, P=4 (i.e. “F=-1”) does need revision, but I will leave that for next week.
Dirac66 (talk) 21:44, 4 August 2009 (UTC)
thread_title: Justification for use in article

message: Gibbs's original statement, motivated by an example, seems a simple & intuitive derivation. Note that he wrote his rule F = C+2 - p. (I'm not sure the new casting clarifies it any.) Linear algebra wasn't invented in Gibbs's time: Gibbs's treatise used determinant theory. In the 19th Century, this was taught to American secondary school students. (American education has changed.) If you wish to also use a more general derivation containing the equality of chemical potential functions, mole fractions, and reactions, may I suggest the derivation in Prigogine & Defay?
One can safely pull 'escaping tendency' functions out of the air, for this is what Gibbs did. Calling them 'escaping tendencies' makes their equalities intuitive, avoiding the deadly MIT derivation. Chemical engineering texts from MIT inherited Gibbs's derivation of equalities of escaping tendencies for closed systems and consequently derive a phase rule limited to closed systems.
Picture of Gibbs's Rule
Gibbs always illustrated his analytical equations geometrically. Each phase can be represented by a surface in the space p, T, mu(H2O). Three surfaces intersect at a point. The univariant curve liquid-vapor can even terminate when the corresponding surfaces rotate and become a single, fluid sheet. Projected along the mu(H2O) axis, the objects trace the p,T-diagram for H2O already shown. There must be a simple diagram like this somewhere. Geologist (talk) 18:14, 6 August 2009 (UTC)
thread_title: Perhaps two rules?

message: Sorry, thought I should clarify why I thought Gibbs believed the phase rule isn't a theorem (for he covers most linear dependencies in the paragraph that derives the Gibbs-Konovalow Theorem): he chose to believe the critical point of water to be a phase, so the phase rule consequently fails at the critical point. Denbigh has other ideas; but note this:
'For as every stable phase which has a coexistent phase lies upon the limit which separates stable from unstable phases, the same must be true of any stable critical phase.' Gibbs, p. 131.
In other words (this is like interpreting Scripture), the two phases liquid water and water vapor occupy a curvilinear region on a P,T-diagram that stops suddenly, where there is a tie-line of zero length :-) joining that region with the critical point, occupied by the critical phase: one component, one phase, zero degrees of freedom. The phase rule fails. Two more relations are needed, to stabilize the critical phase.
Gibbs states that the curvature of the characteristic function (the spinodal) is zero there - providing the needed relation (which, by itself, stops any metastable extensions into the fluid region). This choice of a critical phase led to the study of critical points of various orders (the Curie point, superconductive transitions, &c).
A third relation is needed to limit the critical region to a point. Having examined the characteristic function of the critical phase, Gibbs found the tangent zero and the curvature zero. The third derivative, the flatness, must be less than zero (convex - Gibbs chose the entropy function, which was concave). Some greater derivative must be non-zero or the critical phase could not be stable. Now one has three phases imparting one relation each to create a point, and one critical phase imparting three relations to create a point. Gibbs is really simple. :-)
One could claim that the critical phase H2O is not within the domain of classical thermodynamics; but this murky phase we can clearly see in a test tube. This choice of phase creates a clear failure of the phase rule, which Gibbs had to have seen very clearly. Geologist (talk) 00:18, 6 August 2009 (UTC)
thread_title: Failure of Phase Rule

message: Equalities of chemical potentials, used in most popular dervations, appear earlier in Gibbs, who didn't use them when deriving the phase rule; for a good reason, I think: they follow from the assumption of a closed system. Gibbs's derivation is valid for open systems; it is a local proof (making independence the linear independence of tangent vectors at a point), and his proposition becomes one describing a phenomenon (a change). Geologists have applied the phase rule (and equilibrium calculations of temperatures at which metamorphism stopped) for many decades to rocks undergoing changes in bulk composition without any problems. Geologist (talk) 12:40, 26 July 2009 (UTC)
thread_title: The Phase rule is Valid for Open Systems (though few agree)

message: Geologists have been confused about the appearance of three 1-component, densely crystalline polymorphs (andalusite, sillimanite, and kyanite) coexisting in certain geological regions. Sorry, but you can't see the triple point if you discard pressure from the P,T-diagram. (Cough.) (A study of extensities rather than intensities explains this phenomenon, I believe.)
Two possibilities of dealing with the unmeasurable effect of pressure might be to discard the d(-p) term, or set the changes in V to zero if it cannot be measured using today's instruments, or if its effects cannot be observed. Geologists never have use of such a 'rule', and either of the last choices would be an operationally correct way of dealing with the situation.
It would be bad if a geology student recognized the phases as condensed and applied F = C + 1 - P.
Geologist (talk) 16:10, 26 July 2009 (UTC)
thread_title: The Condensed Phase Rule Again

message: Truly, I hate to nag. 'Liquid-vapour phase diagrams for other systems may have azeotropes (maxima or minima) in the composition curves, but the application of the phase rule is unchanged. The only difference is that the compositions of the two phases are equal exactly at the azeotropic composition. The same is true for liquid-solid phase diagrams which have minima known as eutectics.'
It must have been late. :-) Eutectic points are points of minimal-temperature liquids, but only when the phases differ in composition. Azeotropes are points where curves intersect, and phases become the same composition. The Gibbs-Konovalow theorem assures they are extreme points (minima or maxima).
The phase rule is applicable to an open or closed assemblage of phases in stable or indifferent equilibrium, unaffected by energy fields (external energy).  
Geologist (talk) 16:10, 26 July 2009 (UTC)
thread_title: Azeotropes & Eutectics

message: Were I to recommend a single book and an online reference for thermodynamics in general (and the phase rule in particular), they follow. (Active scientists may wish to add to these and consider adding some to the article. Because I have no access to a research library, I don't contribute to articles.)
de Heer, J, 1986. Phenomenological Thermodynamics. Englewood Cliffs, NJ: Prentice-Hall.
The above discusses the relation between the 'Wind' and 'Gibbs' form of the phase rule.
Geologist (talk) 02:47, 28 July 2009 (UTC)
thread_title: References

message: Why does a search for newlink redirect here? I was looking for a company called newlink and instead get redirected to a page with no mention of newlink or new link. Clearly this is not helpful. --Shadebug (talk) 16:08, 29 December 2008 (UTC)
replies: text: That was just a glitch; it was created a few years ago by mistake. I've deleted it. DS (talk) 03:39, 31 December 2008 (UTC)
thread_title:  Newlink 

message: Today 221.232.151.68 added the words "There exists an error in the phase diagram.The superheated vapour region and gaseous phase should be replaced mutually", which Ddcampayo reverted with the edit summary "I think the diagram is fine the way it is."
I believe that 221.232.151.68 is mostly correct here. A vapour is defined as a gas which is below its critical temperature. So the region T > Tc cannot be described as a vapour and should simply be labelled "gas". The low-T region can be described as "vapour", though "vapour (gas)" would probably be better, since the vapour phase is physically a gas. For the purpose of this article on the phase rule, vapour and gas are equivalent.
As for "superheated", this term is used mostly for steam (water), for which superheated steam is steam above the normal boiling point. Not really a useful term to explain phase diagrams.
So this diagram which appears in several articles should be redrawn. For now I will restore a mention that vapour should be in the low-T region, in the paragraph which refers to the Figure. Dirac66 (talk) 15:44, 27 January 2010 (UTC)
replies: text: The diagrams being discussed seem to have little to do with the phase rule, whose value lies in its description of a heterogeneous phase assemblage at one intensive state. The p,T-diagram of H2O benefits very little from the phase rule; and what is being discussed here has nothing at all to do with the phase rule, but with arbitrary nomenclature. The distinction of gas and vapor, superheated steam and vapor, &c is irrelevant to the article. It might be better to use only the words 'crystal', 'liquid', 'gas', and 'fluid' (near but beyond the critical state). The fluid resembles more a liquid on one side of the slightly extrapolated melting curve, a gas on the other. There is no clear distinction by a meniscus, however. Geologist (talk) 20:57, 2 February 2010 (UTC)

text: It might be clearer to erase all the dotted and dashed lines, and use a substance other than H2O if you don't like its curve. Only the 2-phase curves, 3-phase triple point, and 1-phase critical point (with critical opalescence) are natural. (I prefer 'vapor, but 'gas' is spelled the same in Britain and the United States.) Other objects, and your distinctions among them, are as artificial as the axes 'pressure' and 'temperature'. (These are artificial axes of convenience.) The term superheated steam is a layman's term for hot, 1-phase water vapor in stable equilibrium (ie. points in the gas region above 100 degrees Celsius): 'saturated steam' is hot, 2-phase steam in stable equilibrium (ie. points on the boiling curve above 100 degrees Celsius). Geologist (talk) 20:57, 2 February 2010 (UTC)

text: Because the phase rule is a theoretical relation among natural objects, the relation F = C + 2 - P was originally presented by Gibbs as an existence theorem for natural objects (the boiling curve, triple point), objects that are independent of the coordinate axes. As coordinate directions, one may choose the directions of any two phase reactions at a triple point. The phase rule is still valid. Temperature isn't necessary to derive the phase rule, but it is necessary to delineate, here, 'gas' from 'vapor'. Geologist (talk) 20:57, 2 February 2010 (UTC)
replies: text: I agree that the present diagram is far too cluttered with terms which are irrelevant to the article, as well as extra lines and curves. On reading your comments I remembered that in many chemistry texts the first minimal phase diagram is for CO2, so I checked the carbon dioxide article. The first diagram there seems a suitable replacement, as it is simpler with less extraneous terms (as well as more colorful!). I will tweak the text a little to define very briefly the triple and critical points, but I don't want to tweak the actual diagram myself as I am not up to redrawing it.  Dirac66 (talk) 22:51, 3 February 2010 (UTC)

text: OK, I have inserted the CO2 diagram which seems the most appropriate existing diagram I could find, and also modified the text according to the new diagram. Thanks to Geologist for his useful suggestions. Dirac66 (talk) 02:23, 4 February 2010 (UTC)

text: 'Vapour vs gas' contains an excellent lexicographical distinction by 221.232.151.68 and Dirac66 that I wasn't aware of. In geology, I distinguish classes that are 'natural' from 'artificial' by the nature of the separation: if discontinuous, the class of objects is natural; if continuous, the classification is artificial. Geologist (talk) 18:27, 26 March 2010 (UTC)

text: The CO2 diagram should thus have two natural objects labeled 'liquid' & 'vapour', and an artificial one labeled 'fluid'. (The straight boundaries should be erased.) However, draw a horizontal isobar in the 'vapour' region. Because a liquid's volume decreases little with pressure, one can move a liquid on the melting curve to the right until it touches the boiling curve. At this pressure and temperature, the fugacity of CO2 can be estimated: one can, in similar ways, estimate thermodynamic properties of liquids, and calculate those of vapours. This illustrates a nice use of 'artificial' classification. Geologist (talk) 18:27, 26 March 2010 (UTC)

text: Below the critical point, a meniscus separates liquid from vapor; just beyond it, there is a continuous change from liquid-like fluid to vapor-like fluid. Farther from the critical point, these properties converge to 'just fluid'. If one used a very light blue for the vapor, one could darken this continuously during a rotation about the critical point from the horizontal to vertical artificial lines. Solid, liquid, & vapor could even be colored yellow, green, & blue: the fluid would be a gradient of hues. (Next, one might visualize densities with hues: a scientific visualization of an artificial class of thermodynamic states. (Sadly, I'm bad with the GIMP.) Geologist (talk) 18:27, 26 March 2010 (UTC)
thread_title:  Vapour vs gas 

message: 'In practice, however, the coexistence of more phases than the phase rule allows normally means that the phases are not all in equilibrium, i.e. that one or more is metastable.'
Perhaps 'not stable' would do? ('Unstable' won't.) Metastable is stable: after all, we can't afford to wait around forever. Most curves on petrologic phase diagrams are probably metastable, though one tries for stability. Metastable states can sometimes exist near one or both sides of, in this case, a univariant curve. They can displace a curve or point, but they can't increase their numbers. Geologist (talk) 01:55, 26 March 2010 (UTC)
replies: text: I have now removed "metastable" which perhaps doesn't mean what I thought. The article on metastable seems unhelpful also. Rather than get into "not stable" vs "unstable", I have simply said that the phases are not all in true (i.e. not apparent) equilibrium.  Dirac66 (talk) 20:13, 26 March 2010 (UTC)
replies: text: Even better! Geologist (talk) 01:56, 27 March 2010 (UTC)
thread_title: Metastability

message: Gibbs wrote the variance F as C + 2 - P (with a change in notation). Only in the last paragraph of 'On Coexistent Phases of Matter' in his treatise 'On the Equilibrium of Heterogeneous Substances' is Gibbs's phase rule offered: 'Hence, if P = C + 2, no variation in the phases (remaining coexistant) is possible. It does not seem probable that P can ever exceed C + 2.'
This statement follows from the homogeneity of densities defining a phase, and the homogeneity of intensities defining its intrinsic stable equilibrium. If all phases are homogeneous in intensities, the P phases display a heterogeneous stable equilibrium. The general, trivial solution to this square array of linear, Gibbs-Duhem equations is d(-p), dT, dmu(1), ..., dmu(i) = 0.
The solution equates differentials to zeros of intensities, not intensive variables. This more generalized phase rule is owed to people other than Gibbs, such as Wind and Duhem.
One should not suppose newer literature is better than older. The only two phase diagrams in Modell & Reid's 1983 postgraduate text for classical thermodynamics at M.I.T. are incorrectly drawn; whereas beautiful diagrams, flawlessly drawn according to theory, can be found in Bakhuis-Roozeboom's 1904 Book 2, Part 1 of 'Die Heterogenen Gleichgewichte vom Standpunkte der Phasenlehre'. It would be nice to see the simplicity, clarity, and precision of the earlier literature (which I have little access to).
One needs to ask who the audience is. One can first sketch the subject using everyday language for everyone, then clarify it mathematically for more advanced readers. Geologist (talk) 10:38, 26 March 2010 (UTC)
thread_title: Gibbs's Phase Rule

message: I think your last paragraph suggests a way forward. The audience is surprisingly large - on the revision history page one can click on Page view statistics - this article had 3832 viewers in February 2010 and 3975 from March 1-26! I would guess that all these viewers would have many different levels of prior knowledge about the subject. So I agree that we should have a simple presentation first, followed by more advanced material.
By initial simple presentation I mean essentially what we have now, which corresponds to undergraduate physical chemistry texts. For this topic I do believe that new texts are better than older, since I understand Gibbs was not a very clear writer whereas modern textbook writers have spent several decades simplifying the subject to be clearer to students. Also new texts tend to be more accessible in (university) libraries for readers who wish to go further. I don't worry about the fact that the presentation is not that of Gibbs - the article is a modern presentation of the phase rule originally due to Gibbs. Just as the article on Newton's laws of motion uses vector notation introduced long after Isaac Newton.
As more advanced material to follow, I suggest two new sections. The first could perhaps be called "Historical development of the phase rule", and explain what Gibbs did and what others did, with mathematical clarification as needed. The second might be "The phase rule in geology", where the systems (or minerals) are more complex than the chemists' homogeneous phases of known composition. 
However I do not feel competent to start writing either of these two sections. Perhaps a certain geologist who appears to know a lot about these two subjects could now come off the talk page and edit some first versions. Dirac66 (talk) 16:51, 27 March 2010 (UTC)
thread_title: Suggestions for new sections

message: I have been reading the Article and Discussion (long time after my first reading) and found it really improved.
Yet, I want to add some points for your consideration concerning proof, foundations and signficance of the rule.
Gibb's rule is proved (see any thermodynamic textbook, for instance those by HB Callen) under a very simple, clear assumption: that the description of the thermodynamic potential of a substance is an homogeneous function of the extensive variables. The thermodynamic potential expresses a full knowledge of the system and it is usually taken as S(U,V,N). The knowledge of this function provides you specific heat, compresibility, thermal expansion coeficients and, in turn, any thermodynamic property of the system, including, theoretically, phase transitions.
That S(U,V,N) be an homogeneous function degree one of extensive propirties means S(aU,aV,aN)=aS(U,V,N). That is, to my knowledge, the Gibbs hypothesis for homogeneity.
After that hypothesis, and including standard considerations on equilibrium conditions, Gibbs' phase rule can be found for a multicomponent system with C components and P phases.
You may recognize that, speaking of pure substance, there are 3 independent extensive properties in the description S(U,V,N). While the degrees of freedom (number of independent intensive properties) ---and here, when I say intensive property I mean properties providing equilibrium conditions and thus excluding specific properties--- is, at most, two. 
Extensive properties are aditive properties and, in turn, sizeable properties. They account for the size of the system.
Intensive properties on the contrary are non-aditive, non-sizeble properties. Gibbs's phase rule is saying that the number of independent intensive properties is less than the number of independent extensive properties. Meaning, you should always keep at least one extensive property on your description. That extensive property will ultimately account for the size of the system.
For instance, from U(S,V,N) (a valid representation and also an homogeneous function under Gibbs' hypotheiss) you may perform Legendre transformation and arrive to G(T,P,N). Where N will still account for the size of the system. But never to R(T,p,mu) because that 'potential' will be zero due to Gibbs' hypothesis or Gibbs-Duhem equation (the former being a consequence of the latter).
Incidentally, the Gibbs hypothesis of homogeneity provides a grounding for specific properties. Since the homogenous relation is valid for any a, it is also valid for a=1/N and so U(S/N,V/N,N/N)=U(S,V,N)/N so that U(S,V,N)= N U(s,v,1) where s=S/N, v=V/N are specific entropy and volume. Being U(s,v,1)=u(s,v) the specific energy (energy per one N) we find U=Nu. Less than trivial, the hypothesis provides a scientific background for the intuitive utility of specific properties: we find the behaviour for N=1, we know the behaviour for any N.
Last and not least. The very experimental fact that you never ever observe P=4 on a pure substance shouldn't be related to whether F=-1 is meaningless or not. That very experimental fact is of huge significance since, in turn, it validate the Gibbs hypothesis. As long as we have never ever observed a P=4 point we are pretty sure that S(U,V,N) is an homogeneous function degree 1 of U,V,N which is a fundamental condition for the whole building so-called thermodynamics (dealing with entropy, chemical potentials, specifice properties and so). Meaning, we are pretty pretty sure, none will ever found a P=4 point on a pure substance. You might also want to say that the inexistence fo P=4-point is an 'experimental proof' of the Gibbs phase rule (meaning, the existence of the 4-point would have removed the rule).
An article for the Gibb's hypothesis of homogeneity should be considered.
217.216.118.109 (talk) 10:45, 1 November 2010 (UTC)
replies: text: This one of the cases when a rule, in this case the convention regarding common names can be ignored, as the statement Gibbs' phase rule is a theorem is obvious/straightforward (like water is a liquid) and doesn't require to be sourced.--79.119.209.111 (talk) 18:50, 10 January 2011 (UTC)
thread_title:  Proof, foundations and meaning 

message: Since it's proved, the article should be called Gibb's phase theorem like any other proved statements.--79.116.89.242 (talk) 21:00, 3 January 2011 (UTC)
replies: text: This one of the cases when a rule, in this case the convention regarding common names can be ignored, as the statement Gibbs' phase rule is a theorem is obvious/straightforward (like water is a liquid) and doesn't require to be sourced.--79.119.209.111 (talk) 18:50, 10 January 2011 (UTC)
thread_title: Theorem

message: Following the discussion above, it is proposed to move (rename) this article to Phase rule, i.e. to remove Gibbs's name from the article title. The opening line of the article would of course continue to specify that it was Gibbs who proposed the phase rule. Also a search for the old title Gibbs' phase rule would be redirected to the article with the new title.
Further comments are invited here. If there are no major objections, I propose to rename the article in one week. Dirac66 (talk) 00:51, 24 November 2013 (UTC)
thread_title: PROPOSED NEW ARTICLE TITLE

message: The intro to this article now has two conflicting meanings for the symbol N. The first paragraph defines N as an alternative symbol for the number of components, usually denoted C. But the second paragraph defines N (since an edit yesterday) as an alternative symbol for the number of non-compositional variables such as temperature and pressure. 
This contradiction is confusing and could lead some non-expert readers to think that the number of components is equal or somehow related to the number of non-compositional variables. So at least one usage should be eliminated from the article. My own preference would be eliminate all the alternative symbols and only mention the usual symbol (F, C, P) for each number in the phase rule. What do others think? Dirac66 (talk) 01:14, 29 April 2016 (UTC)
replies: text: No reply after 2 months, so I have gone ahead and deleted the alternative symbols including both meanings for N. Dirac66 (talk) 20:42, 6 July 2016 (UTC)
thread_title:  Conflicting meanings for N 

message: Substituted at 18:32, 17 July 2016 (UTC)
thread_title: Assessment comment

message: The number of independent parameters should not be described in terms of what a controller of the system can or can not do. This is about defining other parameters by the F number of independent intensive ones, no matter how the system arrived to those values. 
In fact, pressure ALWAYS changes with the change of tempetature. You can arrive to a different set of T and p by changing T and p in weird patterns. But YOU CAN arrive to any set of T and p within the gas space on the diagram. That's the point. Its not about what you can do with control. But if you observe a system with 2 phases, and T is such, then p is such (one parameter defies this state). Vesta1212 (talk) 02:58, 10 April 2024 (UTC)
thread_title:  Its not independent control of variables