Talk:Gibbs' phase rule
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Is not Celsius the correct name for what used to be called Centigrade? ---
[ Should "Gibbs' phase rule" be "Gibbs's Phase Rule" ? Geologist 18:07, 27 March 2007 (UTC) ]
--- And, what happened to the nice exposition on the homology to Euler's polyhedron, or the question about Poincarre? I hope this stuff is coming back, this is what is interesting to (*) non-chemists. Since Gibbs based his rule on Euler it's hardly controversial. On the question of thermodynamic implications of polyhedral holes, I think there is comment by Cliff Joslyn on this. Just something I vaguely remember.
- I beg to disagree here - adding these quasi-mathematical detours makes the article much _less_ useful. There should be a clear division between material that a competent natural scientist needs to know, and 'explanations' however beautifal that appeal to pure mathematicians. This article desperately needs a rewrite to apply properly to multi-component systems, which is where its non-trivial content lies - the rule physically is about multiple applications of the equation ΔG = 0 - see any physical chemistry textbook.(eg Moore's Physical Chemistry p101)
- I must agree with the spirit of the above remark. Gibbs's phase rule was of very great importance in physics & chemistry, and it still is in the natural & more applied sciences. Though its similarity to Euler's theorem on polyhedra was, at one time, intriguing; and philosophers took an interest in Poincaré's remark, the theorem's great value deserves a strong presentation of its effect on phase diagrams, and the theorem and diagrams' profound effect on most every science. Igneous and metamorphic petrology, for example, were both founded by this theorem. Geologist 18:42, 27 March 2007 (UTC)
This page should be merged with Gibbs phase rule -- till we *) 01:42, Aug 26, 2003 (UTC) ___
The relation of the universal gas law to the Gibbs' phase rule looks to be a bit tenous to me - can the gas laws be related to the thermodynamics of the Iron-carbon phase diagram??? Of course, if you want to talk fugacity in perfect systems that might be difference, but _this_ is about degrees of freedom, I think. Linuxlad 19:25, 20 Feb 2005 (UTC)
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[edit] Degrees of freedom..
I would like some clarification on the term 'degrees of freedom'. Following the links doesn't really give a satisfactory explaination as to what this means in relation to the phase rule. As simple as possible would be good.. my concept of physics is limited...
[edit] Degrees of Freedom
One rarely sees the phase rule written so the independent variables (thermodynamic flexibility, f) is ( c+2) - p, the variables minus independent relations among them. Another is f = (s - r) + 2, species minus independent reactions among them, plus 2 (T & p). Multicomponent mixtures provide wonderful applications for students of elementary linear algebra. Geologist 19:09, 27 March 2007 (UTC)
[edit] Vandalism?
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)
[edit] Alternative derivation
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
[edit] Alternative derivation
The one depicted here is the more logical. Gibbs never proved his phase rule, did he?--this despite elementary texts' using his suggestive argument as a proof. More advanced texts, such as Denbigh's, use proofs such as yours. There are at least two proofs in the primary literature; the one more commonly used is Wind's. There was also a claim by Helm that the 1st law was necessary & sufficient to prove the phase rule. 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)
[edit] Suggestions
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.
When the system exhibits three phases in equilibrium (triple point) you get no degrees of freedom by Gibbs phase rule (C=1, P=2). Meaning: the temperature and pressure of this triple point is determined by the thermophysical properties of the system (see triple point of water, for instance) and, in no manner, by the will of the observer. Yet, you may well change extensive and specific properties of the system at the triple point. For instance you may change the volume of the system, or energy, or enthalpy... just by changing the amount of liquid, solid and vapour present at the triple point thus leading to a line of triple point if volume (or energy, or entropy ...) is pictured. But, notice all these lines, states, collapses on a single value of the intensive parameters ---pressure and temperature---
2. The example pV=nRT is poorly presented since V is not an intensive property and can not be accounted for the number of degrees of freedom. Three intensive variable set would be pressure, temperature and chemical potential. Just two are freely choosen, the third being determined by the Gibbs-Duhem relation
3. Nothing gets complex at the critical point. That paragraph should be erased.
Etaoin Shdrlu 13:11, 28 March 2007 (UTC)
