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Talk:Chemical potential

About chemical potential of a system of electron
Here is a quote from Solid State Physics, Ashcroft and Mermin(1976),Chapter 2, p.43 eq.(2.53): "[...]for metals the chemical potential remains equal to the Fermi energy to a high degree of precision, all the way up to room temperature. As a result, people frequently fail to make any distinction between the two when dealing with metals. This, however, can be dangerously misleading. In precise calculations it is essential to keep track of the extent to which μ, the chemical potential, differs from its zero temperature value, εF[the Fermi energy]". This would be a precision of "The chemical potential of a system of electrons is also called the Fermi level" from the article. —Preceding unsigned comment added by 216.144.116.202 (talk) 21:11, 30 January 2011 (UTC)

 * The article text "The chemical potential of a system of electrons is also called the Fermi level" is exactly correct. "Fermi level" as used in semiconductor physics is not the same as "Fermi energy" as used by some solid-state physicists. "Fermi level" in semiconductor physics is an exact synonym of "chemical potential". The "Fermi level" (as the term is used in semiconductor physics) does vary with temperature, sometimes substantially, and its temperature-dependence is common knowledge and it is discussed frequently and openly as an important topic. It is not defined as a zero-temperature limit! This confused claim comes up so often that I made a little webpage about it,.

 * Perhaps the article text could be clarified, "In semiconductor physics, the chemical potential of a system of electrons is called the Fermi level." --Steve (talk) 21:39, 30 January 2011 (UTC)

I think this statement is plainly wrong. The chemical potential is only equal to the Fermi energy at zero kelvin. The fact that a lot of people are confused and that in several cases the chemical potential has a very small temperature dependence does not change this. I would suggest the following statement:

In physics the chemical potential for a system at 0 Kelvin is known as the Fermi level. — Preceding unsigned comment added by 92.224.192.89 (talk) 19:34, 7 September 2013 (UTC)

on the simplified introductory sentence
Chemical potentials are not a per-system phenomenon. One system can have multiple chemical potentials. For instance, in a non-equilibrium system, at any location, the chemical potentials of different species are not guaranteed to be the same. Furthermore, even in an equilibrium system (such as one in a steady state steady flow condition), the chemical potential would be different at different locations. Finally, the change in energy is not just a change in Gibbs free energy, it is a change in all the energy potentials of the system including internal energy (excepting energy potentials that are not functions of the chemical potential). ChrisChiasson (talk) 03:35, 20 November 2007 (UTC)
 * OK, I over-simplified. Under the "precise definition" section (Chemical_potential) it does state that "the chemical potential is the partial derivative of the Gibbs free energy with respect to number of particles" "under conditions of constant temperature and pressure" (typical laboratory conditions). I do think that a simpler introductory sentence would be helpful for general readers than the existing introduction -- without compromising accuracy. --Ben Best (talk) 07:40, 20 November 2007 (UTC)
 * Hi. I find the introductory section to be rather poorly worded. I, for one, did not understand it. Perhaps we should update it Paskari (talk) 13:42, 7 October 2009 (UTC).
 * I concur with Paskari. The introduction should begin with a definition, not a history.  --BBUCommander (talk) 21:40, 6 February 2012 (UTC)
 * I've moved the cited definition into the first sentence. It's still not the best definition, but it's better than just stating the origin of the term, I think.Forbes72 (talk) 01:44, 28 February 2012 (UTC)

Random comments
1) Chemical Potential is a noun, it should not be described as a verb, such as "change". Velocity is a noun and defined as the change in position with time. ...... So the article is fine.

2) Constituent: an artifact that is one of the individual parts of which a composite entity is made up; especially a part that can be separated from or attached to a system

A particle is added to a group of particles. The energy required defines the chemical potential. I ommited the word "constituent particle" because the additional particle need not be "one of the individual [particles] of which the [group of particles]" is added to. A chemical potential is still defined if I take a particle that is not a member of the group of particles and add it to the group of particles.

3) Point 1) above is not right. Change can be a noun as well as a verb. E.g., if I change (v.) x to x+1, then the change (n.) in x is 1.

4) The fundamental concept of the chemical potential (1st sentence of the article) as being the change in energy on adding a particle, is often (in many books and papers) taken literally to mean a finite difference F(N+1)-F(N), where N=number of particles and F is either the internal energy or the Helmholtz free energy (the difference is taken at constant entropy and volume in the former case, at constant temperature and volume for the latter). That this can be essentially incorrect for finite systems (even for some very large finite systems) has been discussed recently (see The Chemical Potential, by T. A. Kaplan, J. Stat. Phys. 122, 1237 (2006)).--Tomkaplan 19:16, 3 January 2007 (UTC)

5) Appreciation of unity in physics where it exists is clearly desirable. Making a distinction between `thermodynamic chemical potential' and `electronic chemical potential' seems to introduce a fundamental distinction where it, in fact, does not exist: the electronic version introduced in the main page of this subject is actually the zero-temperature limit of the thermodynamic chemical potential. For this see J. P. Perdew in Density-functional methods in Physics}, edited by R. M. Dreizler and J. da Providencia, Plenum, New York, 1985, and T. A. Kaplan, J. Stat. Phys. 122,1237 (2006). Thus the distinction, as presented in the fundamental definitions section of the article on the chemical potential, is highly undesirable.--Tomkaplan 19:16, 3 January 2007 (UTC)

The article states: "In the case of photons, photons are bosons and can very easily and rapidly appear or disappear. Therefore, at thermodynamic equilibrium, the chemical potential of photons is always and everywhere zero. The reason is, if the chemical potential somewhere was higher than zero, photons would spontaneously disappear from that area until the chemical potential went back to zero; likewise, if the chemical potential somewhere was less than zero, photons would spontaneously appear until the chemical potential went back to zero. Since this process occurs extremely rapidly (at least, it occurs rapidly in the presence of dense charged matter), it is safe to assume that the photon chemical potential is never different from zero."

It should be made clearer that the photons do not 'disappear'... photons are persistent perturbations in the ambient EM field. Raise the energy density of that ambient EM field, and the photons are 'subsumed' in the ambient EM field, no longer persistent. Remember, photons are energy... energy cannot just 'disappear'. — Preceding unsigned comment added by 71.135.41.65 (talk) 02:08, 28 January 2021 (UTC)

Other Contexts
Chemical potential plays a huge role in the theories of chemical equilibria. But it also plays a role in chemical species diffusion, bose-einstein condensation, etc.. There's a lot of room to expand.

Should this article be split?
I believe this article should eventually be split into 2 articles and then have a disambiguation page. Theoretical chemists use the term "chemical potential" to refer to the electronic chemical potential. All other chemists use the term "chemical potential" to refer to the thermodynamic chemical potential. It seems totally obvious to me, but this confuses nearly all chemists (because the electronic chemical potential is rarely discussed in undergraduate course work - and even in graduate course work).

For the time being, what is written might suffice; however, if/when more content is added to describe the electronic chemical potential more accurately and completely (including the principle of chemical potential equalization arising from density functional theory - here refering to the electronic chemical potential), the amount of content and the mixing of the terminology on the same page may prove far too confusing. --anon

 * I broke it up into sections and added a description of the electronic chemical potential. It seems to work fine, in my opinion.  I don't think splitting it up into several pages is necessary. I need to include some references, but I am awfully tired right now. --anon 06:00, 2 December 2005 (UTC)

 * I think its a bad idea to split up the article. In physics, more precisely statistical physics, the chemical potential is usually defined as a rather abstract lagrange multiplier connected to the avarage number of particles. Thermodynamic and electronic chemical potentials, used in chemistry, are rather special cases of the more general concept of chemical potential! —Preceding unsigned comment added by 82.211.200.170 (talk) 20:32, 15 January 2009 (UTC)

 * As seen in this article, the physicist's definition of chemical potential is applicable to the interaction of any system of particles. It is so general it is being applied to nucleus physics and I suspect we will soon hear of the chemical potential of a galaxie. The article is on chemical potential. The article should focus on all the definitions of chemical potential that are used to calculate, measure, or predict chemical reactions (and the physical changes of phase, etc. which influence the course of chemical reactions.) Of course the article should include any underlying physical principles and especially clarifying examples thereof, but they should be put in subsidiary sections, not in the principal section. BTW, I give the idea of electronic chemical potential to my Advanced Organic Chemistry students (undergraduates also) because it is so tied in with the concepts of electronegativity, HOMO, LUMO, etc. that they use to describe the potential for an organic reaction to take place. I also use chemical potential in my course on organic photovoltaics, with much more physical theory. I also told both not to spend too much time wading this article (as of this date). There are much clearer sources. But, bravo to those who are trying to make this article clearer. Laburke (talk) 16:52, 13 September 2011 (UTC)

 * The term chemical potential is used in chemistry with a very specialized definition. In physics, the exact same term is used for a more general idea which can be specialized into the chemist's definition.  While I agree it would be preferable for chemical to refer to chemistry, the current usage in the literature suggests it does not.  Since this is an encyclopedia, the current usage should be used.  Thus splitting the article would be akin to original research as it would imply an attempt to adopt a new language not commonly used.  My suggestion for resolving this dilemma is to mention in the introductory paragraph that chemical potential is used in both a broad and specific sense.  The initial definition should use the broad sense, and then the specific use in chemistry should be given to introduce the specific sense.  That way any point of confusion is headed off immediately, especially for readers new to the subject who are likely to run into this dual-usage fairly quickly.  Thoughts? --BBUCommander (talk) 19:34, 5 February 2013 (UTC)

Relativistic chemical potential?
I think that the section titled relativistic chemical potential should either be clarified by an expert or removed. It is totally unclear to me what the relativistic chemical potential is. It is stated as being related to symmetries and charges, but some sort of definition (preferably an equation) seems necessary (I mean, there's all sorts of things related to symmetries and charges, so it is quite a vague description).

I don't do any relativistic-stuff, but I am fairly well-versed in atomic physics, in general, and if it's not clear to me I highly doubt it's clear to anyone other than the original author. I'm going let it sit for a day-or-so, and then just remove it unless there is any discussion or changes. DrF 03:43, 24 May 2006 (UTC)

 * Added Expert request tag. I'll let this section sit a little while longer before I delete it.  DrF 04:20, 26 May 2006 (UTC)

 * This reads about right I clean it a bit and add a ref link for those who want to read more.--Sadi Carnot 15:12, 25 July 2006 (UTC)

Suggestions
A curve would be a clearer illustration than the 2D plot. Chemical formulæ are not all correctly subscripted. Refers to non-existent "web-links". —DIV (128.250.80.15 (talk) 04:36, 1 April 2008 (UTC))

The example figure
I think the example figure needs to be expanded( such as how the particles flow downhill, in more detail). Or it is too dry to give any useful information. At this stage it does not help people to understand the concept of chemical potential. —Preceding unsigned comment added by 128.61.29.249 (talk) 18:20, 27 September 2008 (UTC)

Two items

 * 1) The opening paragraph has a Gibbs quotation prominently displayed.  If it's a direct quotation then it needs a reference.  My temptation is to remove that quotation until a citation can be added to show that it really comes from Gibbs.  It should be possible to track the quotation down.
 * 2) The example figure is, well, I'm not sure what it is.  The x and y axes appear to refer to chemical potential with, I assume, typical units of something like energy per mole.  However, the text says "Particles will tend to move from regions of ..." and I'm not sure what that movement means at all with reference to the figure's axes and units.  Again my tendency is just to delete the figure completely.  A previous entry on this page suggested that a curve might be clearer.  I agree, particularly since this will be the first example the reader meets.

I'm not a regular contributor to this article, and don't have time right now to become one. I trust that my comments will be taken in the helpful spirit in which they are intended. - Astrochemist (talk) 23:54, 17 December 2008 (UTC)

False distinction?
I think the article is misleading when it separates "electronic chemical potential" from "thermodynamic chemical potential". Any mobile species in local equilibrium has a chemical potential. When the species is, say, a hydrogen ion or a water molecule, the article calls it a "thermodynamic chemical potential". When the species is an electron, the article calls it an "electronic chemical potential", as if that was totally different. It's not different at all, it's the exact same definition, just electrons instead of protons, neutrons, or whatever. Would anyone object to me rewriting on that basis? :-) --Steve (talk) 07:49, 29 March 2009 (UTC)

Units
The units used for chemical potential should be discussed in the article. This seems like an important missing detail. Thanks! David Hollman (Talk) 21:40, 1 September 2010 (UTC)
 * Done. PAR (talk) 23:24, 2 September 2010 (UTC)
 * Wow, awesome, cheers! David Hollman (Talk) 11:58, 3 September 2010 (UTC)

Split the article
I concur with the previous suggestion that the article should be split, etc. There is no scientific connection between thermodynamic and electronic potentials, only the use of the same words. The first is about chemical reactions, the second is physics. I can do the chemistry. Can anyone help with the physics? Petergans (talk) 07:54, 26 April 2012 (UTC)

 * I disagree. Not only is there a scientific connection, it's the exact same concept: Change in free energy upon removing (object) from (system). I don't even think it should be called "electronic chemical potential", I think it should be called "chemical potential of electrons".
 * The electron section was obviously written by someone who had learned how, mathematically, to calculate the chemical potential of electrons using density functional theory, but basically had no conceptual idea what they were calculating. So they presented the mathematical calculation technique as being the same as the conceptual definition.
 * I want to make the exact opposite change: Rewrite the electron section (and the intro) to emphasize that electrons have a chemical potential in the exact same way (and with the exact same definition) as how sodium ions have a chemical potential. --Steve (talk) 12:30, 26 April 2012 (UTC)
 * You make a good point, but I'm looking at it as if I were a chemistry student. Such a person would have no idea what the chemical potential of an electron is. For chemists, the chemical potential is a property of a molecular species, its partial molar, or molal, free energy. This is important in understanding the free energy change in a chemical reaction. Chemical potential is a function of the activity (concentration) of the species in a mixture. What is the concentration of an electron?

 * If you don't want the article to be split, I suggest that the two aspects be completely separated apart from an explanation of the relationship somewhere near the beginning. I particularly don't like the lead-in: the first sentence is waffle and won't mean anything at all to a chemist. Petergans (talk) 09:48, 27 April 2012 (UTC)

 * The concentration of electrons is the number of electrons per volume! Isn't that obvious?...
 * No, it isn't obvious. There are no free electrons in solution. I assume the electron in question is attached to an atom, ion or molecule. Petergans (talk) 09:42, 28 April 2012 (UTC)
 * I shall do some rewriting and let's see how it turns out :-P --Steve (talk) 13:47, 27 April 2012 (UTC)
 * Done. I deleted the density functional theory part among other things. I have advertised at Talk:Density functional theory and elsewhere for that text to be found a new home in another article, because (for all I know) it was well-written and correct. --Steve (talk) 15:34, 27 April 2012 (UTC)

I'm very unhappy about this article in its present form. I came to it because of a link in equilibrium constant, which was mostly written by me. In that context this article is not helpful at all and for that reason I had not originally linked it. Now another editor has made the link. In a chemical equilibrium the sum of chemical potentials of reactants and products is equal to zero, that is, there is no tendency for the reaction to proceed in either forward or backward direction because no energy would be released in the process.

Here's my (thermodynamic) definition: the chemical potential of a chemical species in a chemical mixture is the partial molar free energy of that species. It is the partial derivative (slope) of the free energy with respect to the number of moles of the species, that is, the infinitesimal amount by which the free energy changes divided by the infinitesimal change in the amount of that species. In this definition the amounts of the other chemical substances in the mixture are assumed to be constant, hence it is a partial derivative. Temperature is also assumed to be constant. At constant pressure it related to Gibbs free energy, at constant volume it related to Helmholtz free energy. If you can, I suggest you look at Atkins, Physical chemistry, section 5.1, "Partial molar quantities", for a full explanation of the significance of chemical potential in thermodynamics. None of that material appears in the present article; it should!

Also In Atkins, Physical Chemistry, the term chemical potential is related to the Fermi level in molecular orbital bands (section 20.9(b), p 725 in the 8th edition). Petergans (talk) 09:42, 28 April 2012 (UTC)

 * Again, the exact words you say are a wonderful description of how the chemical potential of an electron in a solid is defined. (Besides the trivial exception that for electrons in solids, it's usually expressed in eV rather than kcal/mol.) The chemical potential is the partial derivative of the free energy with respect to the number of electrons in the solid. In fact I wrote in wording just like that at the start of the "electrons in solids" section.

 * Your main complaint now seems to be the introduction, not the two physics sections that I just rewrote. I did not write the introduction and I don't like it any more than you do. I hope you rewrite it, or else maybe I will when I get a chance. (I did, however, write the "overview" section.) :-) --Steve (talk) 20:04, 28 April 2012 (UTC)
 * OK, I'll give it a try. At the same time I'll put things in a different order, hopefully to clarify the presentation. I'll do it in my sandbox and will let you know when it is ready. One final point: I don't think that the bit on particle physics belong here. Sub-atomic particles don't have properties of relevance to chemistry so applying the term "chemical potential" to them seems like a misnomer to me. I understand the concept of a partial derivative of energy with respect to quantity can apply in a plasma etc., but what energy is involved here?Petergans (talk) 08:51, 29 April 2012 (UTC)
 * I've just clocked the fact that there are two sections called "Overview". Yours is the first and gives good examples of phase equilibria, but it is not linked in the index, so I didn't see it when I clicked on overview! I'll add another exmple for chemical equilibria and merge in the second, where possible. Petergans (talk) 09:05, 29 April 2012 (UTC)

 * Please don't split the article. The broad application of the concept is useful for its understanding. Everyone who claims to have understood it in one field but is annoyed by application to other fields has yet to climb to a higher level of abstraction. --Rainald62 (talk) 23:24, 3 May 2012 (UTC)
 * I agree with the preceding comment. The notion of chemical potential is universal for all physical systems in thermodynamic equilibrium.Xxanthippe (talk) 21:42, 4 March 2018 (UTC).

Explanation

 * I would like to have an explanation for the (approximate) logarithmic dependence of the intrinsic chemical potential on concentration. Is it only for the Boltzman distribution of particle energies? --Rainald62 (talk) 23:24, 3 May 2012 (UTC)
 * See E.T.Jaynes, 1957. --Rainald62 (talk) 21:30, 4 March 2018 (UTC)

Ashcroft/Mermin and the (electro)chemical potential
As far as I understand them Ashcroft/Mermin don't say that the "electrochemical potential" is the internal chemical potential (the article says they do). Instead they call the external chemical potential the "electrochemical potential" (p. 257). Imho they use the terms exactly like Kittel/Kroemer do, but please feel free to correct me if I'm wrong. Anybody mind me correcting this in the article?

They - as well as many others - sometimes add for clarification: "a voltmeter measures [...] the electrochemical potential". Anybody mind me incorporating this into the article? --Mest (talk) 14:25, 4 May 2012 (UTC)
 * This is outside my area of expertise, so go ahead. However, I have rewritten the article, draft is in User:Petergans/sandbox so we need to be careful about synchronizing versions. Petergans (talk) 15:14, 4 May 2012 (UTC)

 * I put that in but maybe I was misreading the book. Or maybe you have a different version than me and they corrected the "mistake"? I will check it ASAP. (I don't have the book on-hand right now.)
 * I hope you're right, that would make everything much simpler!!
 * I definitely agree that "a voltmeter measures the electrochemical potential of electrons". --Steve (talk) 15:18, 4 May 2012 (UTC)
 * I have that book (and I love it), so I could double check what exactly it says. Headbomb {talk / contribs / physics / books} 15:28, 4 May 2012 (UTC)

Ashcroft and Mermin write... (p.256–257) When a temperature gradient is maintained in a metal and no electric current is allowed to flow, there will be a steady-state electrostatic potential difference between the high- and low-temperature region of the specimen. Measuring this potential drop is not completely straightforward for several reasons: The thermoelectric power (or thermopower) of a metal, Q, is defined as the proportionality constant between the contribution of the metal to the reading of such a voltmeter, and the temperature change: $$-\int \mathbf{\mathcal{E}} \cdot d\mathbf{\ell} = Q ~ \Delta T$$ or $$\mathbf{\mathcal{E}}= Q ~ \nabla T$$. Headbomb {talk / contribs / physics / books} 16:03, 4 May 2012 (UTC)
 * 1) To measure voltages accurately enough to detect a thermoelectric voltage, it is essential that the voltmeter connects points of the specimen at the same temperature. Otherwise, since the leads to the meter are in thermal equilibrium with the specimen at the contact point, there would be a temperature gradient within the circuitry of the meter itself, accompanied by an additational thermoelectric voltage. Since no thermoelectric voltage develops between points of a single metal at the same temperature, one must use a circuit of two different metals (Figure 13.1 [diagram of a thermocouple ]) connected sothat one junction is at a temperature T1 and the other (bridged only by the voltmeter) at a temperature T0 ≠ T1. Such a measurement yields the difference in the thermoelectric voltages developed in the two metals.
 * 2) To measure the absolute thermoelectric voltage in a metal, one can exploit the fact that no thermoelectric voltage develops across a superconducting metal. Hence when one of the metals in the bimetallic circuit is superconducting, the measurement yields directly the thermoelectric voltage across the other.
 * 3) The points in the circuit joined by the voltmeter have different electrostatic potentials and different chemical potentials. If, as in most such devices, the voltmeter reading is actually IR, where I is the small current flowing through a large resistance R, then it is essential to realize that the current is driven not just by the electric field E, but by $$\scriptstyle{ \mathbf{\mathcal{E}} ~=~ \mathbf{E} ~+~ \left(1/e\right)\nabla \mu}$$. This is because the chemical potential gradient leads to a diffusion current, in addition to teh current driven mechanically by the electric field. As a result, the voltmeter reading will not be $$\scriptstyle{-\int \mathbf{E} ~\cdot~ d\mathbf{\ell}}$$ but $$\scriptstyle{-\int \mathbf{\mathcal{E}} ~\cdot~ d\mathbf{\ell}}$$.

Yes, page 257 is 100% clear: "a voltmeter measures not the electric potential but the electrochemical potential". BUT page 593 [and following pages] is equally clear that "the chemical potential [on the two sides of a p-n junction in thermal equilibrium] does NOT vary with position" but the electrochemical potential DOES. Look at Eq. (29.9) (phi is electric potential not measured voltage). Even more explicit is Fig. 29.2 on p594: The top shows the electrochemical potential being different on the two sides; the bottom shows the chemical potential being the same on the two sides.

Well, since writing that section a couple years ago, I've seen more and more---even in solid-state physics books---the expected definition that electrochemical potential is constant in equilibrium. I don't think I've seen the "backwards" definition anywhere except Ashcroft and Mermin page 593, and now I know that that even includes earlier text in the same book! Therefore I propose that Ashcroft and Mermin page 593 is simply a mistake and we should ignore it.

UPDATE: I edited the article accordingly. When Petergans posts the new version I'm happy to re-edit that section. --Steve (talk) 14:56, 5 May 2012 (UTC)

Major revision
I have done a major revision, principally to clarify the thermodynamics and to give chemical potential its chemical context. This was based mainly on Atkins, Physical Chemistry. The ordering of some material has been changed. For example, history was moved from the lead-in to the history section.

The questions regarding electrochemistry are still to be resolved (see above). Atkins, Sections 7.5-7.9 devotes 15 pages to electrode potentials, but there is no mention of the internal/external issue, nor is there any reference to chemical potentials on those pages; the whole treatment is in terms of the free energy and reaction quotient. Petergans (talk) 09:08, 5 May 2012 (UTC)

 * The first two sentences still seem problematic to me. The energy released in a chemical reaction is more properly the internal energy or enthalpy, right?  Also, why is chemical potential assigned as "potential" energy.  In reality, some of the Gibbs energy is "kinetic" (molecules moving) and some is "potential" (e.g. intermolecular forces).  Finally, the second sentence would seem to be confusing at minimum with a key property about the chemical potential, which is that the chemical potential of a substance in the a phase is equal to the chemical potential of the substance in another phase if the phases are in equilibrium.  What exactly is changing during a phase transition?Stieltjes (talk) 17:43, 29 August 2012 (UTC)
 * The energy released in a chemical reaction is free energy not enthalpy. In fact a reaction may be endothermic, ΔH=<0, and still occur spontaneously because of the entropy contribution. Some of the free energy released can indeed be turned into kinetic energy, for example in an explosive decomposition, which is why the term "potential" is apt.Petergans (talk) 07:49, 30 August 2012 (UTC)

Request: define variables in equations
All: I'm not qualified to edit this article, but have a small request for those who are working on it. It would be helpful for those not versed in the field if the terms in at least the important equations (e.g. the first one in the "Thermodynamic Definitions" section) were defined. The article on Helmholtz Free Energy for example, does a good job of this.

It also might be helpful to make the reference to "Gibbs energy" an inline link to that article.

Thanks to all for your effort! Ma-Ma-Max Headroom (talk) 18:05, 10 September 2012 (UTC)

Recent changes and reversions
Recent reversions by User:Nanite and User:Xxanthippe are a matter of concern.

User:Nanite claims that his changes are improvements. They are not. For instance, in Thermodynamic definitions it is incorrect to include $$\mu_i=\left(\frac{\partial U}{\partial N_i} \right)_{S,V, N_{j \ne i}}$$ because chemical potential is defined as the partial derivative of free energy. Whatevever the rights and wrongs, this reversion war has to stop. The onus is on User:Nanite to justify his edits, with citations, here, on the talk page before introducing them into the body of the article. My previous edits were based on "Physical Chemistry" by Peter Atkins. Petergans (talk) 10:14, 10 February 2014 (UTC)

 * Don't worry friend, it's a bit hasty to hail this as a reversion war. I undid an unexplained reversion of Xxan presuming that he/she mistook my edits for vandalism (Xxan seems to be a busy editor, it would be understandable for such editors to snag false positives every once in a while. No harm done.). As far as I can tell, that's all that happened.
 * A perfect citation for $$\mu_i=\left(\frac{\partial U}{\partial N_i} \right)_{S,V, N_{j \ne i}}$$ would be the first ever description of chemical potential, just as presently described in the article's History section. Allow me to quote: If to any homogeneous mass in a state of hydrostatic stress we suppose an infinitesimal quantity of any substance to be added, the mass remaining homogeneous and its entropy and volume remaining unchanged, the increase of the energy of the mass divided by the quantity of the substance added is the potential for that substance in the mass considered. Gibbs p.149, freely available here
 * In other words, the definition in terms of U is the "original definition", if that counts for anything. Regardless, it does not matter anyways since that definition is completely equivalent to the one in terms of G. The proof of this is elementary thermodynamics and I can elaborate if it's not obvious. (Actually I'm surprised your textbook doesn't mention this fact. I'm not familiar with the book, but perhaps it is oriented to a specific application such as chemistry, rather than general thermodynamic fundamentals.) Anyway, the point is that any of the equivalent definitions are equally valid, though for convenience one or the other might be preferred depending on the system in question.
 * You have seen in my edits that you reverted, that I had added the missing citation to Gibbs' book, and moreover (in relation to the previous point) I had expanded the quote to include Gibbs' remark on the equivalence of defining chemical potential in terms of U, A, or G. I really do think these and all of my edits were improvements and I'm sad to hear you disagree.
 * Anyway, I'm not interested in arguing and wasting time getting prior permission to edit articles as that is totally not the point of wikipedia, so I'll leave you to improve this page and I'll focus my efforts elsewhere. Let me know if you're interested in my input, as there are a few glaring problems with the article that I was planning to fix. Bye for now. Nanite (talk) 19:59, 10 February 2014 (UTC)
 * Hold on Nanite! I suggest you go ahead with your edits in your sandbox and let's see what they produce. When an editor starts to make changes to an important and well-established article it helps if he describes what he is up to on the talk page first. There are many equivalent expressions for chemical potential and yours looks a correct one. @ Petergans: I don't think that "Physical Chemistry" by Peter Atkins is a good source for a Wikipedia as it is a broad and often superficial undergrad text. Better sources in that genre are Kittel+Kromer, Reif and Mandl. Xxanthippe (talk) 21:56, 10 February 2014 (UTC).
 * From the point of view of a chemist, the definition in terms of free energy is the most important because chemical reactions involve free energy changes. Historically and in other contexts chemical potential can be defined in terms of internal energy. I am not aware of any applications of this concept. Is constant entropy physically realizable? I think we should be careful about using too broad definitions without reference to specifics. When I did the major revision of this article I had equilibrium chemistry very much in mind. Petergans (talk) 11:13, 11 February 2014 (UTC)
 * The notion of chemical potential applies to any equilibrium system with a variable number of particles and has a much broader application than equilibrium chemistry so the article should not be written from that point of view only. The basic expression for chemical potential given above by Nanite in this thread drops out naturally from the fundamental equation of thermodynamics dU = T*dS - P*dV + mu*dN. Chemical potential may be expressed as a derivative of any of the thermodynamic potentials. These other expressions are not alternative definitions but follow logically from the equation for dU and the definitions of the potentials H, F and G. The only reason why the Gibbs Free Energy G is of interest is because it is easier to maintain a chemical system at constant P and T than at S and V. I would like to see the article start out with the definition based on U and not that based on G. Xxanthippe (talk) 05:03, 12 February 2014 (UTC).
 * I'm not against the more general approach, but each definition should be related to real-world phenomena, not just as a mathematical construct. It's important to explain the context in which a definition is useful. Constancy of V and T can be important in atmospheric and oceanic contexts, where pressure is variable with depth. In what physical/chemical circumstances can S and V be held constant? Petergans (talk) 10:41, 12 February 2014 (UTC)

Definitions
The statement "The definitions given above are mathematically equivalent" appears to me to be meaningless. The three possible definitions
 * $$\mu_i=\left(\frac{\partial G}{\partial N_i}\right)_{T,P,N_{j\neq i}}$$
 * $$\mu_i = \left(\frac{\partial H}{\partial N_i} \right)_{S,P, N_{j \ne i}}$$.
 * $$ \mu_i = \left(\frac{\partial U}{\partial N_i} \right)_{S,V, N_{j \ne i}}$$

correspond to three different ways of defining partial molar free energy. There is no way in which the three definitions can be considered to be "equivalent" as there is no way in which Gibbs free energy (G), Helmholtz free energy (H) and internal energy (U) are equivalent.

The second and third definitions are of little practical value because they apply at constant entropy (S), a condition which is virtually impossible to achieve in practice; I have included them for the sake of completeness because they can be found in texts on thermodynamics. Petergans (talk) 09:33, 13 May 2015 (UTC)

 * The thermodynamic potentials are all related by Legendre transformations, a fact so well known that there is even a Wikipedia section on it . Xxanthippe (talk) 03:48, 20 May 2015 (UTC).
 * This is very misleading. Although there is a mathematical relationship, the definitions are not "equivalent" because they relate to different physical quantities.Petergans (talk) 08:28, 20 May 2015 (UTC)
 * They are equivalent in the sense that they are all equal to each other. Do you have a better term to use? PAR (talk) 21:10, 20 May 2015 (UTC)

A Legendre transformation is not the same as either equality or equivalence. It is clearer to state the nature of the relationship, ,as in my last edit, than to merely state that they are "equivalent" without explaining why this is so. Petergans (talk) 10:46, 21 May 2015 (UTC)

I have 39 years' experience as a lecturer in chemistry at the University of Leeds. I think that this qualifies me as an expert. Please remove the offensive "expert" tag. It appears to refer to one disputed sentence, so the tag is not relevant to the article as a whole. Petergans (talk) 07:27, 23 May 2015 (UTC)

Standard state
User:Chanwu claims that the following statement in chemical potential is wrong

 * $$\mu_i = \mu_i^{std} + RT \ln a_i,$$

The equation is correct. It is given by Atkins & De Paula, 8th. edition, Equation 5.53 on page 161 (Section 5.7(c), Activities in terms of molalities). In the text I used the term "concentration" rather than "molality". This is also correct as molality is a measure of concentration. In fact the equation is valid for all concentration units as the standard state will be defined in the same unit as the solute concentration. Petergans (talk) 15:55, 31 May 2015 (UTC)
 * This defines the relative activity then. ✅

Free energy not Potential energy
Chemical potential is the partial free energy in a species that gives the appearance of causing a system to move spontaneously toward lower free energies / chemical potentials, just like total free energy and spontaneous reactions (eg, Gibbs free energy).

In macroscopic physics like gravitational and electrical, there is such little entropy of the system that merely the potential energy itself is what primarily governs spontaneous motion / state transition. So it makes a kind of sense to call free energies in entropy-dominated systems "potentials", but let's be clear that they are most certainly not the difference between the total energy that never changes and kinetic/thermal energies, which are Potential energies.

This is extremely confusing since Chemical potential energy is a very real and important quantity: among other things, it is the latent energy reserve otherwise-inert matter has that exothermic chemical reactions draw from. Whereas Chemical Potential / Free Energy is how much of this energy is available to do useful work (electrically or mechanically) and which governs how the system will spontaneously move as it endeavors to increase total entropy.

Free energy is of the 2nd Law, and Potential energy is of the 1st Law.

(I've updated the article and am working on the article Chemical energy now. Please feel free to disagree!, but let's put any discussion about chemical potential vs. chemical potential energy on this article if you don't mind just for consistency (and since the naming of Chemical potential energy isn't cause for concern). )

--RProgrammer (talk) 10:45, 1 March 2016 (UTC)

 * I just found something related that's troubling to me: in the section "Electrochemical, internal, external, and total chemical potential"
 * It seems that Free energies are being added to Potential energies. At first this struck me as concerning, but then I realized a possible explanation.  I didn't finish polishing it and put it in the article because I feel it constitutes original research, and I lack the societal credentials to say it somewhere in public and cite myself XD
 * So I'll just post the rough draft here:

 * The reason why potential energies such as qV or mgh can be directly added to thermodynamic free energies such as the internal chemical potential $$\mu_{\mathrm{int}}$$ to produce a total free energy is that these potential energies have such little entropy all of their energy is available to do useful work. (This can be thought of as the entropy term in some FE = E - TS equation becoming zero as entropy does, yielding FE = E, and thus the lack of a distinction between Free Energy and Potential Energy in non-thermodynamic (low-entropy) physics)

 * (not part of the draft, but another way to word it is that you are using the electrical or gravitational free energy when summing with thermodynamic free energies, and the potential energy with thermodynamic potential energies—it's simply that electrical/gravitational/etc. free energy exactly = electrical/gravitational/etc. potential energy due to the negligible entropy / all of it being available to do useful work, and thus no distinction is made)
 * RProgrammer (talk) 11:10, 1 March 2016 (UTC)
 * You are corect. This is OR. Xxanthippe (talk) 21:17, 1 March 2016 (UTC).

 * To me the clearest situation which shows the distinction (internal/total chemical potential, and internal/total energy) is to imagine an enormously tall vertical test tube containing water, in a gravitational field, and in equilibrium (at room temperature). Quantities such as pressure and internal chemical potential will vary with height: in the middle of the test tube you'll find liquid water, at the bottom you will find water that has solidified from ultra high pressure, and at the top you will find a low pressure atmosphere of water vapor. Yet, the temperature and total chemical potential will be uniform throughout. When you examine total-energy quantities (Hamiltonian energy, free energy, etc.) you will find the usual thermodynamic relations hold just fine (in terms of total chemical potential), although the system is not extensive and so you can't invoke, e.g., Gibbs-Duhem equations, and you cannot define a uniform pressure variable (it becomes important where the volume is varied).
 * On this basis, I am not sure how total/internal µ distinction relates to availability of work as has suggested. And indeed it seems like OR to interpret too much into it. --Nanite (talk) 09:40, 2 March 2016 (UTC)

Thermodynamic definition
I have rewritten this section, based on the monograph of Mandl, to make it more logical. The previous version started by defining the two quantities G and $$\mu$$ in one equation! The proper logical progression is that $$\mu$$ appears first in the fundamental equation for U, as in the definition of Gibbs given in the History section. The other equivalent expressions for it are obtained mathematically by Legendre transformations. There is further discussion above on this talk page. Xxanthippe (talk) 03:59, 27 April 2016 (UTC).
 * I find this re-write lacks the clarity of the previous version. In writing the the old one I followed Atkins (8th. edition, p138) in defining chemical potential as the partial derivative of the Gibbs free energy. Atkins adds, on the next page, a section on "the wider significance of the chemical potential". This is a much clearer exposition than that of the current article. The constant pressure definition is by far the most important in practice for chemical reactions. What do people think? I will revert to the previous text unless there is a consensus that the current version is better. Petergans (talk) 07:41, 27 April 2016 (UTC)
 * As the editor has a WP:COI in the matter, being the author of the previous version, it might be better, after debate has taken place according to WP:BRD, to leave it to another editor to revert to the previous version, if consensus finds that is superior. Xxanthippe (talk) 03:26, 28 April 2016 (UTC).
 * There is no conflict of interest. We simply disagree on how best to present the material. Petergans (talk) 10:01, 28 April 2016 (UTC)
 * An actual COI is a pretty different concept from a potential COI (that anyone with an employment has when editing anything). From COI, Conflict of interest (COI) editing involves contributing to Wikipedia about yourself, family, friends, clients, employers, or your financial or other relationships. Any external relationship can trigger a conflict of interest. (Extra emphasis mine.) YohanN7 (talk) 11:07, 28 April 2016 (UTC)
 * You are correct. A better policy to refer to would have been WP:Own. Xxanthippe (talk) 01:33, 3 May 2016 (UTC).
 * I prefer the current version. Starting with the fundamental equation for U makes a lot of sense presentation wise, since it emphasizes the similarity with more familiar concepts such as temperature and pressure. The current version also makes much clearer why definition in terms of Gibbs free energy is so much more practical. TR 15:20, 28 April 2016 (UTC)
 * I also prefer Special:Permalink/717436442, which I believe is also called the "current version" for the same reason as stated above (U is more fundamental then G). When I took Thermo as an undergraduate (circa 1973), we did not mention Gibbs free energy until near the end of the course. (FYI - we used Kittel, which is probably not the best "authority" one could cite)---Guy vandegrift (talk) 15:40, 28 April 2016 (UTC)
 * Just to clarify. The new version, corrected for links and typos, is . The previous version is . Incidentally, I think Kittel is an excellent book for this subject, as are Mandl and Reif, not to forget Gibb's classic work Xxanthippe (talk) 10:56, 29 April 2016 (UTC).

This is all very well, but the article is about chemical potential, not fundamental thermodynamics. The definitions
 * $$\mu_i = \left(\frac{\partial G}{\partial N_i} \right)_{T,P, N_{j \ne i}} $$, $$\mu_i = \left(\frac{\partial H}{\partial N_i} \right)_{S,P, N_{j \ne i}} \text{ and  } \ \mu_i = \left(\frac{\partial F}{\partial N_i} \right)_{S,V, N_{j \ne i}}$$

do not refer to U, so why bring it in? It's an unneccesary distraction in this article. Incidentally, please can we use either the symbol G or F consistently for Gibbs energy. Petergans (talk) 10:09, 29 April 2016 (UTC)

 * The new version is better, but the fact that the expression for dU defines the chemical potentials should be explained better. For us this is a trivial step, but not necessarily for the readers. So, you just explain that you can consider U as a function of S, V, and the $N_j$ and that this function will have some partial derivative w.r.t. the $N_j$, one then defines the chemical potentials as these partial derivatives.

 * At the end, what is missing is that the Gibbs energy for an extensive system will be given by $$G = \sum_j \mu_i N_i$$. This is easy to explain to the readers after the relation $$dG = \sum_i \mu_i dN_i$$ at constant T and P is given. You just note that with the intensive variables kept fixed, G is a linear function of the particle numbers. The Gibbs-Duhem relation mentioned the next section follows directly from this. Count Iblis (talk) 23:22, 7 May 2016 (UTC)
 * Thanks for your comment. In such a short section one cannot develop thermodynamics from its foundations so I started from the fundamental equation of thermodynamics, which a new reader will have to refer back to. This equation already incorporates the notions of entropy and thermodynamic temperature, which are the greatest conceptual achievements of the subject and probably the most difficult to understand. So a great deal of the work has already been done. Xxanthippe (talk) 03:41, 8 May 2016 (UTC).

 * I lack the expertise to know Count Iblis is right, but I certainly think he might be right. I once looked carefully at entropy and realized that defining entropy through the differential, $$dU = T dS - P dV$$, is incomplete because it fails to establish that entropy can be integrated (i.e., that it is a state function and not a process function or equivalently, not an Inexact differential.  If this is what Count Iblis is talking about, then I agree: we need to provide, or better yet, point to an explanation.--Guy vandegrift (talk) 01:22, 8 May 2016 (UTC)

Disputed Introduction
See http://www.icsm.fr/Local/icsm/files/286/JFD_Chemical-potential.pdf --129.69.120.91 (talk) 12:47, 22 December 2017 (UTC)
 * At chemical equilibrium added stoichiometric coefficients. The rest is still not right. --Biggerj1 (talk) 12:53, 22 December 2017 (UTC)
 * Atkins & de Paula, Physical Chemistry O.U.P. 8th. edn. p 138, quote: "For a substance in a mixture, the chemical potential is defined (Atkins italics) as the partial molar Gibbs energy
 * $$\mu_i=\left( \frac{\partial G}{\partial n_i}\right) _{p,T,n'}$$".
 * Edits reverted. Petergans (talk) 15:15, 23 December 2017 (UTC)
 * Your Point is unrelated and not touched! What I e.g. improved is that at chemical equilibrium $$\Sigma _i \nu _i \mu_i =0 $$ and not as stated before $$\Sigma_i \mu_i=0$$ which is just wrong! Biggerj1 (talk) 16:57, 23 December 2017 (UTC)
 * adressed the points ✅

About the function in the section of "Chemical Potential in Ideal vs. Non-Ideal Solutions"
I am now translating this page into Chinese. I notice something not understandable to me. In the section of "Chemical Potential in Ideal vs. Non-Ideal Solutions", there is a function:

𝜇𝑖=𝜇𝑖0(𝑇,𝑃)+𝑅𝑇𝑙𝑛(𝑥𝑖)

Here it seems that 𝑥𝑖 is the amount of certain species. However, if the amount is zero, then this logarithm diverges. Is this well?

Besides, is there any special name for the term 𝜇𝑖0(𝑇,𝑃)? It looks like the chemical potential when 𝑙𝑛(𝑥𝑖)=0. — Preceding unsigned comment added by Swenly (talk • contribs) 18:58, 30 April 2018 (UTC)
 * Hi Swenly, Consider the asbolute ideal chemical potential $$ \mu_i^\text{ideal} = kT \ln(\lambda_i^3 c_i) $$ (this you get also via the difference quotient $$\mu=(F(N)-F(N-1))/1$$. For the concentration $$c_i=0$$ the ideal chemical potential approaches $$-\infty kT$$. However consider that the free energy of such a system goes like $$F(N,V,T)=TS-pV+\sum_i \mu_i N_i $$ This means that the free energy contriubtuion of the chemical potentials is given by $$ \sum_i \underbrace{c_i V}_{N_i} \underbrace{kT ln(c \lambda_i^3)}_{\mu_i}$$ which goes to zero and does not diverge in the limit (all) $$c_i$$ to zero.--Biggerj1 (talk) 11:41, 3 May 2018 (UTC)

Chemical potential
Recommend changing the confusing wording of this statement in the article: "Therefore, at thermodynamic equilibrium, the chemical potential of photons is always and everywhere zero. The reason is, if the chemical potential somewhere was higher than zero, photons would spontaneously disappear from that area until the chemical potential went back to zero; likewise, if the chemical potential somewhere was less than zero, photons would spontaneously appear until the chemical potential went back to zero."

- to -

"Therefore, at thermodynamic equilibrium, the chemical potential of photons is always and everywhere zero. If the chemical potential of a region is higher than the chemical potential of the photons in or entering that region (chemical potential greater than zero), photons would spontaneously disappear from that region until the chemical potential went back to zero; likewise, if the chemical potential of a region was less than zero, photons would spontaneously appear until the chemical potential went back to zero."

Or similar such language to explicate that it's a comparison between the chemical potential of the region, and the chemical potential of the photons. 71.135.39.238 (talk) 07:29, 9 June 2021 (UTC)

Recent changes
Editors who want to change the article substantially should follow WP:BRD and gain consensus for their changes here. I have reverted some unneeded edits from a user who puts citations to his own papers into the article. Other editors may care to comment. Xxanthippe (talk) 03:49, 7 February 2022 (UTC).

 * Thank you for letting at least some of my corrections stand. Nevertheless, the reversion of other edits has reintroduced several scientific errors:

 * 1) For an open system that can exchange particles with the surroundings, the Gibbs free energy is not at a minimum in chemical equilibrium. This applies only if the system cannot exchange particles - the derivation relies on the laws of thermodynamics for closed systems. For instance, if the system is open, heat cannot be uniquely defined. Consider a volume of water as an open system. Now you place it in contact with a crystal of copper sulfate, which partially dissolves in the water, increasing the Gibbs free energy of the open system.

 * 2) The fundamental equation of thermodynamics does not apply to irreversible processes in general. It contains T and P, which are obviously not defined if the irreversible process is an explosion, for instance. So the equation cannot apply to uncontrolled processes like that. Quoting textbooks here probably won't do, since they routinely get the equations for irreversible processes wrong (for instance, adding a subscript ext on the pressure in infinitesimal work, leaving out the subscript surr on the temperature in the inequality of Clausius, etc.). You had asked me explicitly to add sources. When I did that, you turned around and criticized me for one out of multiple sources that I added. That's not fair. But of course I don't object if you replace this source with your own important reference that points out that the fundamental equation of thermodynamics does not apply to irreversible processes in general.

 * 3) To discuss ice cubes in liquid water above 0 °C is a bad idea. Students learn already in middle school, correctly, that ice water is at 0 °C. Almost as soon as an ice cube is dropped into warmer water, it is surrounded by water at 0 °C.

 * 4) In many chemistry texts, the chemical potential is never written exactly as on this page. The derivative is taken with respect to the amount of substance (unit: mol), not with respect to the particle number. I had added a brief sentence pointing this out, but it was deleted. It is not acceptable for an editor to suppress input from a field where the topic is important, and chemical potential is obviously important in chemistry.

 * Please correct these four errors.

 * Klaus Schmidt-Rohr (talk) 13:34, 7 February 2022 (UTC)
 * I have checked the 4 assertions and confirm that they are correct. Petergans (talk) 15:37, 7 February 2022 (UTC)
 * Indeed. I made a few minor edits to address 4 before I saw this discussion and I hope they will serve. Chemical potential has common usage both ways (per mole or per particle) depending on the context. In statistical mechanics derivations, per particle is often simplest; in applications to thermodynamics, per mole is often best, at least for me. KeeYou Flib (talk) 22:50, 11 February 2022 (UTC)
 * The use of the talk page of an article is to improve the article by reference to reliable sources. It is not to discuss the topic itself, which should be done on the numerous forums that exist for this purpose. Nonetheless, I comment briefly on the four points raised that are relevant to the second section of the article: 1 and 3 are unsourced statements of opinion. For 2, it should be understood that the mathematical symbol "d" that appears in the first equation of the article is an infinitesimal; in other words, the changes described are infinitesimally small, so, for example, dU is an infinitesimally small change in U. An explosion is not an infinitesimally small change. Point 4. has been well addressed by User:Qflib. Xxanthippe (talk) 04:23, 12 February 2022 (UTC).

The claim above that "(textbooks)..routinely get the equations for irreversible processes wrong" is questionable and unsupported. It would be better to cite a book that gets them right. Note that Atkins & De Paula (8th edn. p.76) does not use the term "irreversible". Instead they state that "No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work". Obviously, such a process is not reversible in the thermodynamic sense. Petergans (talk) 11:01, 12 February 2022 (UTC)

 * Comment. There is a Thread that refers to this article at Conflict of interest/Noticeboard. Xxanthippe (talk) 02:50, 22 February 2022 (UTC).

Links
@Petergans. I see that you have restored a link that I recently deleted. The reason that I deleted the link is that the source looked a bit idiosyncratic and flaky. However, if you think that the data is good, then your change is OK with me. Xxanthippe (talk) 02:46, 13 February 2022 (UTC).
 * There is a link to the list of sources of the data on the main page of the site.
 * "Ag-Au	|	B-Br	|	C	|	Ca-Cd	|	Cl-Cu	|	D-He	|	Hg-Kr	|	La-Mo	|	N-Nb	|	Ne-P	|	Pb-S	|	Sb-Sr	|	Te-U	|	V-Zr	|	Sources"
 * Looks good to me.Petergans (talk) 07:55, 13 February 2022 (UTC)

The chemical potential of Van der Waals gases

Hello, I submitted a section about the chemical potential of Van der Waals gases by showing how the chemical potential of Van der Waals gas depends on the Van der Waals constants $$a$$ and $$b$$ as well as on the entropy, and how these dependencies can be explained. The submitted section was deleted by user Xxanthippe. The plots, in my opinion help to understand the basic dependencies of the chemical potential from the constants of a pure gas. — Preceding unsigned comment added by E-gabrielyan (talk • contribs) 04:07, 4 July 2022 (UTC)
 * The opinions of individual editors are not enough for inclusion in Wikipedia. Original research WP:OR is not acceptable. Reliable sources WP:RS are needed to obtain consensus of other editors. Xxanthippe (talk) 04:28, 4 July 2022 (UTC).
 * I was committed to provide a high quality and useful contribution. The section which I added was removed while I was inserting the references into the text. The entire section was removed within only minutes from the submission, completely, without specific requests, and without discussion. Not having seen any interest and transparency, all desire to invest time into the improvement of articles vanished. E-gabrielyan (talk) 06:52, 4 July 2022 (UTC)
 * See my comment on your talk page. Xxanthippe (talk) 08:06, 4 July 2022 (UTC).

This is a very specialized development for one gas model on a page discussing the general concept and I don’t think it’s a great match. I think that you should consider developing this on the page for the van der Waals gas instead. Qflib, aka KeeYou Flib (talk) 16:00, 4 July 2022 (UTC)

Equations
Hi Xxanthippe, the punctuations are not part of the equation and I think the formulas look much cleaner without such punctuation or at least not in the same font style as the equation. Without punctuation is how textbooks normally show these too. What do you think? I was looking for MOS on this, but tried visual first.  Ramos1990 (talk) 00:55, 5 February 2024 (UTC)

title: Talk:Chemical potential


text:
Talk:1959/60 United States network television schedule

Untitled
These titles should all replace American with United States. In this context, it is more accurate to 'Americans' and the rest of the world alike. 119 08:56, 21 Feb 2005 (UTC)

 * There are over 40 articles created. If you're willing to move them all, go right ahead. Mike H 08:56, Feb 21, 2005 (UTC)

from Vfd
On 21 Feb 2005, this article was nominated for deletion. The result was keep. See Votes for deletion/1959-60 American network television schedule for a record of the discussion.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Boxcar (band)

Boxcar were an Australian electronic dance pop group formed in Brisbane in 1986. Their founding mainstay was David Smith on vocals, guitar and keyboards. Three of their singles appeared on the Billboard dance chart top 20, "Freemason (You Broke the Promise)" (1988, No. 8), "Insect" (1990, No. 20) and "Gas Stop (Who Do You Think You Are?)" (1990, No. 8). They released two albums on Volition Records/Sony Music Australia, Vertigo (1990) and Algorhythm (1994), before disbanding in 1997. They briefly reformed in 2010 and in 2014.

History
Boxcar were an Australian electronic dance pop band. They formed in 1986 in Brisbane by Carol Rohde on vocals and keyboards (ex-Ironing Music) and David Smith on vocals, guitar and keyboards. They were soon joined by keyboardist, Brett Mitchell, and somewhat later by drummer-percussionist Crispin Trist.

Boxcar independently issued cassette-only material including an album, P.C.M.. Their early work sounded similar to contemporaries, Cabaret Voltaire and Severed Heads. Australian musicologist, Ian McFarlane, explained "the intention was to combine noise with a beat, technology with a decent song." AllMusic's Michael Sutton felt they "sounded more like New Order [the similarity] is mainly in the weary vocals of [Smith], which easily recalls Bernard Sumner's melancholic tone."

Boxcar played live shows in the Brisbane area and then other capitals; at gigs they wore gas masks. Performing electronic music live was a difficult feat given the preference in Australian live venues for guitar-driven pub rock and they would sometimes be jeered by members of the crowd. McFarlane observed "[they] made little headway, mostly due to a general lack of interest in electronic dance-pop within the rock milieu, rather than any lack of talent on the musicians' part."

They signed with Volition Records/Sony Music Australia to release a single, "Freemason (You Broke the Promise)", in November 1988. When issued in the United States via Arista Records/Nettwerk Records in the following year, it hit No. 8 on the Billboard dance chart. Initially criticised in the local press for being derivative of New Order they nevertheless built a local following, despite a lack of commercial radio airplay for electronic music. They followed with two more singles, which also appeared on the Billboard dance chart: "Insect" (remixed by noted producer Arthur Baker) at No. 20 and "Gas Stop (Who Do You Think You Are?)" (remixed by Francois Kevorkian) at No. 8. In Australia, "Gas Stop" peaked at No. 82 on the ARIA singles chart.

The group's first album on Volition, Vertigo, was released in November 1990. Boxcar's line-up was Mitchell on additional programming; Rohde on keyboards and programming; Smith on vocals, guitars and keyboards; and Trist on drums and programming. It was produced by Robert Racic (Severed Heads, Single Gun Theory) and recorded at Sun Studios, CBS Studios, and Albert Studios, Sydney.

Vertigo received mixed reviews from critics: AllMusic's William Cooper rated it at two-and-a-half stars out-of five and explained "[a]lthough the New Order inspired arrangements are derivative, Vertigo is redeemed by Boxcar's upbeat, catchy melodies"; McFarlane opined that it "was a very accessible collision of sound, song and dance beats." It had a fairly pop feel, however the band also included more experimental instrumentals, such as "Comet" (also on the B-side of the "Freemason" single) and "Lelore" (featuring an eerie wailing as the centrepiece "vocal", which was released as a single in its own right). The group toured Australia as supports for New Order, Depeche Mode, Erasure and then Pet Shop Boys.

In 1992 Rohde and Trist left the group, which relocated to Sydney, where they added a keyboardist, Stewart Lawler. In September of that year they issued a remix album, Revision, with re-workings of Vertigo' tracks by various producers. One of the remixers is Tom Ellard from Severed Heads.

Boxcar's second studio album, Algorhythm, was released in November 1994. The Canberra Times' Nicole Leedham reported "[it] is pure techno and is best heard on a dance floor, but if your house doesn't come equipped with one of those the best alternative is to light some candles and lose yourself in the hypnotic sound." McFarlane noticed "[i]t was another modern-sounding album without being too clean or sterile."

Algorhythm was a notably more trance and house-influenced effort than the synth-pop of Vertigo and provided the singles "Universal Hymn", "What Are You So Happy About?" (featured on the soundtrack to the 1996 film Love and Other Catastrophes) and "People Get High". The album took almost another two full years until it was released in the United Kingdom and Europe in 1996 on Pulse-8. Although not officially defunct, it was around about 1997 that Boxcar started to play fewer live dates.

In October 2007, an announcement was made of their return gig participating in the Upgrade night at QUT. There is also a new track on their website, named for the infamous Atari ST game, Llamatron. It is also indicated that Brett Mitchell is no longer a member of the band.

Boxcar are featured in "BNE - The Definitive Archive: Brisbane Independent Electronic Music Production 1979-2014", which is a hardcover book and USB music archive published by Trans:Com in September 2014. Boxcar contributed 3 previously unreleased tracks to BNE, and reformed to headline the launch event on 6 September 2014 at the Brisbane Powerhouse, with a lineup that included David Smith, Alison Cole, James Wingrove, and original member David Corazza.

ARIA Music Awards
The ARIA Music Awards is an annual awards ceremony that recognises excellence, innovation, and achievement across all genres of Australian music.

 * 1995 || "What Are You So Happy About" || Best Dance Release || Nominated
 * 1995 || "What Are You So Happy About" || Best Dance Release || Nominated

title: Boxcar (band)


text:
Recycling symbol

The universal recycling symbol ( or in Unicode) is a symbol consisting of three chasing arrows folded in a Möbius strip. It is an internationally recognized symbol for recycling. The symbol originated on the first Earth Day in 1970, created by Gary Anderson, then a 23-year-old student for the Container Corporation of America. The symbol is not trademarked and is in the public domain. Many variations on the logo have been created since its creation.

The unicode U+2672 glyph is: ♲

History
Worldwide attention to environmental issues led to the first Earth Day in 1970. Container Corporation of America, a large producer of recycled paperboard, sponsored a contest for art and design students at high schools and colleges across the country to raise awareness of environmental issues. The contest, which drew more than 500 submissions, was won by Gary Anderson, whose entry was the image now known as the universal recycling symbol. Anderson, then a 23-year-old college student at the University of Southern California, was awarded a $2,500 scholarship. The public-domain status of the symbol has been challenged, but this challenge was unsuccessful owing to the wide use of the symbol. However, the universal recycling symbol may have been inspired by similar existing symbols at the time, such as one featuring two arrows chasing each other in a circle that Volkswagen stamped in the early 1960s into some automobile parts it remanufactured.

Variants
The recycling symbol is in the public domain and is not a trademark. The Container Corporation of America originally applied for a trademark on the design, but the application was challenged, and the corporation decided to abandon the claim. As such, anyone may use or modify the recycling symbol, royalty-free.

Though use of the symbol is regulated by law in some countries, countless variants of it exist worldwide. Anderson's original proposal had the arrows form a triangle standing on its tip—upside down compared with the versions most commonly seen today—but the CCA, in adopting Anderson's design, rotated it 60° to stand on its base instead.

Both Anderson's proposal and CCA's designs form a Möbius strip with one half-twist by having two of the arrows fold over each other and one fold under, thereby canceling out one of the other folds. However, most variants of the symbol used today have all the arrows folding over themselves, producing a Möbius strip with three half-twists. Existing single half-twist variants of the logo do not generally agree on which of the arrows is the one to fold underneath. The logo is usually displayed with the arrows circulating clockwise, but the underlying Möbius strip exists in two topologically distinct mirror-image forms of opposite handedness.

The American Paper Institute originally promoted four different variants of the recycling symbol for different purposes. The plain Möbius loop, either white with an outline or solid black, was to be used to indicate that a product was recyclable. The other two variants had the Möbius loop inside a circle—either white on black or black on white—and were meant for products made of recycled materials, with the white-on-black version to be used for 100% recycled fiber, and the black-on-white version for products containing both recycled and unrecycled fiber. For example, a paper envelope might have both the first and last of these four symbols to indicate that it was recyclable and made from both recycled and unrecycled fibers.

In addition to the resin identification codes 1–7 in the triangular recycling symbol, Unicode lists the following recycling symbols:
 * (indicates product contains recycled paper)
 * (indicates product contains partially recycled paper)
 * (e.g. for acid-free paper)
 * (indicates product contains recycled paper)
 * (indicates product contains partially recycled paper)
 * (e.g. for acid-free paper)

An ISO/IEC working group has researched and documented some of the variations of the recycling logo in use during 2001 and has made recommendations for adding some more of them to the Unicode standard.

With the rapid expansion of materials converted to printer filament for 3D printing using recyclebot technology, a large expansion of resin identification codes has been proposed.

Resin identification code
In 1988, the American Society of the Plastics Industry (SPI) developed the resin identification code that is used to indicate the predominant plastic material used in the manufacture of the product or packaging. Their purpose is to assist recyclers with sorting the collected materials, but they do not necessarily mean that the product/packaging can be recycled either through domestic curbside collection or industrial collections. The SPI symbols are loosely based on the Möbius loop symbol, but feature simpler bent (rather than folded over) arrows that can be embossed on plastic surfaces without loss of detail. The arrows are formed into a flat, two-dimensional triangle rather than the pseudo-three-dimensional triangle used in the original recycling logo.

The resin identification codes can be represented by Unicode icons

Recycling codes extend these numbers above 7 to include various non-plastic materials, including metals, glass, paper and cardboard, and batteries of various types.

Other variants
♾, an infinity sign (∞) inside a circle, represents the permanent paper symbol, used in packaging and publishing to signify the use of durable acid-free paper. In some ways, this logo expresses the opposite intention from the recycle logo, in that the acid-free paper is intended to last indefinitely, rather than being recycled. Nevertheless, acid-free paper does not usually contain toxic materials (although certain inks do), so it is easily recycled or composted.

A satirical version of the classic recycling logo also exists, in which the three arrows are twisted from a circular pattern to pointing radially outward, thus symbolizing wasteful one-time usage rather than environmentally friendly recycling. This message is reinforced by the circular inscription, "THIS PROJECT WAS ENVIRONMENTALLY UNFRIENDLY", surrounding the modified logo. The satirical logo appears in the 1998 catalog of an installation art work in Bayonne, New Jersey, in which the artist Steven Pippin modified a row of glass-doored washing machines in a laundromat to operate as giant cameras. The cameras were used to take sequential photographs in the manner of pioneering stop motion photographer Eadweard Muybridge. The front-loading washing machines were then used to develop and process the 24 inch (61 cm) diameter circular film negatives.

title: Recycling symbol


text: User talk:68.57.52.200

title: User talk:68.57.52.200


text:
W. K. Kellogg Foundation

The W. K. Kellogg Foundation was founded in June 1930 as the W. K. Kellogg Child Welfare Foundation by breakfast cereal pioneer Will Keith Kellogg. In 1934, Kellogg donated more than $66 million in Kellogg Company stock and other investments to the W. K. Kellogg Trust (equivalent to $ in ). As with other endowments, the yearly income from this trust funds the foundation.

In the early twenty-first century, the foundation is the seventh largest philanthropic foundation in the U.S. In 2005, the foundation reported that the total assets of the foundation and its trust were US$7.3 billion; about US$5.5 billion of this was in Kellogg Company stock. The foundation funded US$243 million in grants and programs in its 2005 fiscal year. 82% of this was spent in the United States; 9% in southern Africa; and 9% in Latin America and the Caribbean.

In 1996, it supplied a multi-year grant worth $750,000 ($ million in dollars) to start mass salt fluoridation programs which were then carried out by the Pan American Health Organization (PAHO), covering 350 million people in Bolivia, Dominican Republic, Honduras, Nicaragua, Panama, and Venezuela. The project was part of a multi-year plan launched by PAHO in 1994 to "fluoridate the entire region of the Americas." More recently, they have provided funding for HealthCorps to prevent childhood obesity by encouraging students to take personal responsibility for their health and wellness.

Grants
The foundation provides a number of grants to organizations across the United States and other countries on a number of topics.

In 2016, the Kellogg Foundation was funding more than forty projects in Native American country, with a total value of more than $30 million in open grants. According to the non-profit's website, the foundation has funded 380 Native American projects since 2008. Many grants are for health, education and language programs for children and youths. In 2009 it granted the third-highest amount of money to Native American projects, after the Robert Wood Johnson Foundation and the Ford Foundation.

Early childhood
One grantee is the Birth to Five Policy Alliance, whose mission is to increase public and private support so young children, particularly those facing the most challenges, get the high-quality services they need to be successful.

Education
The foundation has made grants to prominent educational institutions, including:
 * Cal Poly Pomona in Pomona, California
 * Michigan State University in East Lansing, Michigan
 * Kellogg College, Oxford, a constituent college of the University of Oxford, United Kingdom

Programs
The foundation supports multiple programs for optimal child development.

It supports oral hygiene. In 2010, the W. K. Kellogg Foundation started a dental therapy program in five states to educate children and their families about the importance of healthy teeth. Mobile dental vans travel to rural areas to give families access to dental care. Additionally, the foundation gives grants to help minorities attend school for dentistry.

The foundation also supports New Options Initiative (For Youth), an initiative that seeks to establish new pathways connecting out-of-school young adults ages 16–24 with meaningful career opportunities.

Perception
The philanthropy expert Waldemar A. Nielsen said that the Kellogg Foundation "is substantially better than it is generally seen to be."

title: W. K. Kellogg Foundation


text:
Janet Rowley

Janet Davison Rowley (April 5, 1925 – December 17, 2013) was an American human geneticist and the first scientist to identify a chromosomal translocation as the cause of leukemia and other cancers, thus proving that cancer is a genetic disease. Rowley spent the majority of her life working in Chicago and received many awards and honors throughout her life, recognizing her achievements and contributions in the area of genetics.

Early life and education
Janet Davison was born in New York City in 1925, the only child of Hurford and Ethel Ballantyne Davison. Her father held a master of business administration degree from Harvard Business School, and her mother a master's degree in education from Columbia University. Her parents were educators at the college and high school levels, respectively, and her mother later gave up teaching to become a school librarian.

Davison attended an academically challenging junior high school in New Jersey and became especially interested in science. In 1940, aged 15, she was granted a scholarship to study in an advanced placement program at the University of Chicago Laboratory Schools where she finished high school and the first two years of college, followed by completion of her degree at the University of Chicago, where she earned a Bachelor of Philosophy degree in 1944, a Bachelor of Science degree in 1946, and Doctor of Medicine degree in 1948, aged 23. Davison, only 19 years of age, had to wait 9 months in order to attend the university because their quota had already been filled for that semester. During that time only 3 out of 65 students were to be women in each class accepted. She married Donald Adams Rowley, also a physician, the day after graduating from medical school. He then went on to become a distinguished pathologist later in life. In 1951, both Janet and Donald Rowley completed internships at the United States Public Health Service's Marine Hospital in Chicago. Rowley continued her work throughout Chicago and worked in a clinic for children with Down Syndrome. Rowley worked part-time until the youngest of her four sons was 12 years old.

Career
After earning her medical license in 1951, Dr. Rowley worked as attending physician at the Infant and Prenatal Clinics in the Department of Public Health, Montgomery County, Maryland. In 1955 she took up a research post at Chicago's Dr. Julian Levinson Foundation, a clinic for children with developmental disabilities, where she remained until 1961. She also taught neurology at the University of Illinois College of Medicine.

In 1962, Rowley's interest in cancer and chromosomes was sparked as an NIH trainee, studying the pattern DNA replication in normal and abnormal human chromosomes. Dr. Rowley then returned to the University of Chicago, as a research associate in the Department of Hematology. She became an associate professor in 1969 and a full professor in 1977. In the 1970s, she further developed the use of existing methods of quinacrine fluorescence and Giemsa staining to identify chromosomes, and demonstrated that the abnormal Philadelphia chromosome implicated in certain types of leukemia was involved in a translocation with chromosome 9 in some cases. Translocation is the process by which a piece of one chromosome breaks off and joins another chromosome, or when two chromosomes exchange material when both break. She also identified translocation between chromosomes 8 and 21 in acute myelogenous leukemia, and between 15 and 17 in promyelocytic leukemia. Rowley also aided in the discovery, through her research, of the formation of retinoid acid, a drug that is able to help return normal function to certain protein receptors.

The first chromosomal translocation was discovered by Rowley in 1972 in acute myelogenous leukemia. When Dr. Rowley published her findings in the 1970s, she argued that specific translocations caused specific diseases, going against the established view of the cause of cancer which gave little significance to chromosomal abnormalities. Although there was some resistance to her ideas at first, her work has proven immensely influential, and by 1990 over seventy translocations had been identified across different cancers.

Awards and honors
In 1984, Dr. Rowley was made the Blum-Riese Distinguished Service Professor of medicine, cell biology, molecular and human genetics at the University of Chicago. She also served as the interim deputy dean for science. In 1989, she was not only presented with the Charles S. Mott Prize by General Motors Cancer Research Foundation, but the Clowes Memorial Award as well. In 1991, she was elected as a member into the American Philosophical Society. In 1998, she was one of three scientists awarded the prestigious Lasker Award for their work on translocation, and received the National Medal of Science in 1998. In 1999, Dr. Rowley received the Golden Plate Award of the American Academy of Achievement. In 2002, Discover magazine recognized her as one of the 50 most important women in science. In 2003, she received the Benjamin Franklin Medal for Distinguished Achievement in the Sciences of the American Philosophical Society. In 2007, she was awarded the Award for Excellence in Molecular Diagnostics by the Association for Molecular Pathology. In 2009, Dr. Rowley was awarded the Presidential Medal of Freedom, the United States' highest civilian honor, by then-President Barack Obama, and the Gruber Prize in Genetics. Then in 2010, she was awarded the Jesse Stevenson Kovalenko Medal by the National Academy of Sciences. In 2012, Dr. Rowley was selected for the Hope Funds for Cancer Research Award of excellence in the area of Basic Research and was elected to the Hope Funds Scientific Advisory Board. Also in 2012, she won the Japan Prize for Healthcare and Medical Technology with two other scientists for her role in the creation of Gleevec. For Rowley's scientific contributions she has received honorary doctor of science degrees from multiple institutions some of which include Yale University and Harvard University. She is also a member of multiple scientific and honorary societies. These distinguished groups include the American Academy of Arts & Sciences and the National Academy of Sciences. She published more than five hundred articles and continued her research at the University of Chicago until shortly before her death. In 2017, she was posthumously inducted into the National Women's Hall of Fame.

Death
On December 17, 2013, Rowley died at home at the age of 88 from complications of ovarian cancer.

title: Janet Rowley


text:
Wikipedia:Articles for deletion/Cabbage Hit

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was speedy delete for patent nonsense and recreation. -- AllyUnion (talk) 10:50, 24 Feb 2005 (UTC)

Cabbage Hit
BJAODN- --Box of Rice 09:04, 21 Feb 2005 (UTC)
 * BJAODN You beat me :) Preisler 09:06, 21 Feb 2005 (UTC)
 * No, just delete. User:Box of Rice, if you think that this is BJAODN, why did you write it in the first place? And why did you remove my ? -- Hoary 09:48, 2005 Feb 21 (UTC)

 * What the hell are you talking about? I never wrote it- just look in the history!, and what delete notice? You never put one up. stop ruining this for everyone. This is a vote, not a complaint centre. --Box of Rice 09:54, 21 Feb 2005 (UTC)
 * Comment I think something very odd has happened here. Some kind of edit conflict perhaps. But Box of Rice, the history says you created the page. Preisler 10:02, 21 Feb 2005 (UTC)
 * Comment The edit pattern shown by Special:Contributions/Box_of_Rice seems a little bizarre to me. What has happened here? -- Brhaspati (talk, contribs) 10:07, 2005 Feb 21 (UTC)
 * User:Box of Rice is under the illusion that he's a very witty fellow, and is subjecting us all to his wit. Some might call it vandalism. -- Hoary 10:17, 2005 Feb 21 (UTC)
 * I actually find it pretty amusing but nominating yourself to BJAODN is a little much so changing my vote to delete. Hoary don't let the vandals get to you. Preisler 10:25, 21 Feb 2005 (UTC)
 * Patent nonsense, belongs to BJAODN. Delete. - Mike Rosoft 12:54, 21 Feb 2005 (UTC)
 * BJAODN well, I got a laugh out of it. Andrew Lenahan - St ar bli nd 12:55, Feb 21, 2005 (UTC)
 * Article nominated for deletion by its own author and sole (apart from deletion taggers) editor. Speedy delete under criterion G7. Uncle G 14:04, 2005 Feb 21 (UTC)
 * Speed deleted as silly vandalism. Wile E. Heresiarch 17:15, 21 Feb 2005 (UTC)

The page has been resurrected. I have listed it for VfD again. 193.167.132.66 09:58, 24 Feb 2005 (UTC)

This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.


text:
Talk:Jonathan Routh

Stubbiness
Bishonen removed the stub macro. I've reinserted it, because the article says virtually nothing about most of Routh's work. Yes, there's a moderate amount about one set of books -- but that's all.

I suspect that Routh is now better known for his "Nuns" series: I've never seen these, they're not in any library to which I have access, and I certainly don't want to buy them merely in order to write them up. If somebody else would like to write them up, perhaps the stub macro could then be removed. -- Hoary 09:07, 2005 Feb 21 (UTC)

The bio-stub was removed again, and (after some discussion and thought) I've replaced it with the UK-bio-stub. -- Hoary 02:19, 2005 Mar 16 (UTC)

And that was removed too, so I've reinserted it. -- Hoary 06:46, 2005 Apr 3 (UTC)

John Reginald Surdeval Routh
Who is John Reginald Surdeval Routh and why are we being told about him within an article on Jonathan Routh? -- Hoary (talk) 14:48, 9 March 2008 (UTC)

 * ditto to the above. Where's Superman?200.116.41.172 (talk) 22:03, 19 June 2013 (UTC)

limited editions of original paintings
The article says:

 * In March 2008, Routh issued limited editions of his original paintings through Chisholm Gallery.

Does this mean that he painted something and then copied it a limited number of times? -- Hoary (talk) 09:09, 3 January 2015 (UTC)

External links modified
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 * Added archive https://web.archive.org/web/20041015184723/http://www.unionwithchrist.com/icon.html to http://www.unionwithchrist.com/icon.html

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title: Talk:Jonathan Routh


text:
The Dalles Bridge

The Dalles Bridge is a bridge on U.S. Route 197 (US 197) that spans the Columbia River in the United States between The Dalles, Oregon and Dallesport, Washington.

Description
The steel cantilever truss bridge is located just downstream from The Dalles Dam. Although the bridge reaches into the state of Washington, it is maintained by the Oregon Department of Transportation. The average daily traffic on the bridge (US 197) is nearly 8,400. US 197 connects Washington State Route 14, a few miles to the north of the bridge, with Interstate 84 and US 30, both just south of the bridge, and with U.S. Route 97, about 67 mi to the south.

History

Ferry service operations began at the site in 1854, but just over a decade later, in 1865, plans for a bridge began. However, it took about another 85 years and the construction of The Dalles Dam before the bridge was finally built. Although the bridge was built in connection with the dam, the bridge opened December 18, 1953, but the dam was not completed until 1957. Due to issues with the dam, the bridge had to be redesigned as a longer one and the location moved slightly farther downstream than originally planned. Notwithstanding, the already fabricated steel components (for the original bridge design) were successfully modified and used in the newly designed bridge. The cost of construction was $2.4 million (equivalent to $ million in ).

The bridge had a toll from its opening until November 1, 1974, when the bridge's construction bond (which had been issued by Wasco County in Oregon) was paid off.

title: The Dalles Bridge


text:
Tate's Cairn Highway

Tate's Cairn Highway, opened on 26 June 1991, is a dual 3-lane expressway in Hong Kong. It links Tate's Cairn Tunnel and Ma Liu Shui Interchange, forming a part of Route 2 (formerly known as Route 6).

From the Ma Liu Shui Interchange, where it connects with Route 9, the expressway crosses the estuary of the Shing Mun River. It then turns southwards, interchanging at Shek Mun with a distributor road (Tai Chung Kiu Road), and reaches Siu Lek Yuen, where the highway splits. One branch leads to Tate's Cairn Tunnel (which continues as Route 2), and the other leads to Sha Lek Highway, which eventually joins Route 1 at Sha Tin Road.

The highway is named after Tate's Cairn.

Interchanges
Tate's Cairn Highway in its entirety falls within the boundaries of Sha Tin District.

{| class="plainrowheaders wikitable" !scope=col|Location !scope=col|km !scope=col|Interchange name !scope=col|Exit !scope=col|Destinations !scope=col|Notes
 * + Hong Kong road sign (Expressway Begins).svg Tate's Cairn Highway
 * rowspan=2|Ma Liu Shui
 * style="text-align:right"|18.6
 * rowspan=2|Ma Liu Shui Interchange
 * style="text-align:center; background:#dff9f9;"|–
 * style="background:#dff9f9" | (Tolo Highway) – Tai Po & Fanling
 * style="background:#dff9f9" |Northern terminus; end of
 * style="text-align:right"|18.4
 * style="text-align:center;"|7A
 * Chak Cheung Street – Ma Liu Shui, University, Science Park, Pak Shek Kok, Race Course
 * Northbound exit and southbound entrance
 * A Kung Kok
 * style="text-align:right"|17.4
 * style="text-align:center"|7
 * Ma On Shan Road – Ma On Shan & Sai Kung
 * Shek Mun
 * style="text-align:right"|16.0
 * Shek Mun Interchange
 * style="text-align:center;"|6
 * Tai Chung Kiu Road and A Kung Kok Street – Shek Mun, Tai Shui Hang, Sha Tin Central, Tsuen Wan
 * rowspan=5|Siu Lek Yuen
 * style="text-align:right"|15.1
 * rowspan=4|
 * style="text-align:center;"|4
 * Siu Lek Yuen Road and Sha Tin Wai Road – Siu Lek Yuen, Prince of Wales Hospital
 * Southbound exit and northbound entrance
 * style="text-align:right"|15.1
 * rowspan=2 style="text-align:center;"|5
 * Hong Kong road sign (Expressway Begins).svg Sha Lek Highway – Kowloon (Central, West)
 * Southbound exit and northbound entrance
 * style="text-align:right"|14.4
 * Hong Kong road sign (Expressway Begins).svg Sha Lek Highway – Sha Tin Central
 * Northbound exit and southbound entrance
 * style="text-align:right"|14.3
 * style="text-align:center;"|4
 * Sha Tin Wai Road – Siu Lek Yuen, Prince of Wales Hospital
 * Southbound exit and northbound entrance
 * style="text-align:right"|
 * style="text-align:center; background:#dcdcfe" |–
 * style="background:#dcdcfe" |HK_Tunnel.svg Tate's Cairn Tunnel
 * style="background:#dcdcfe" |Southern terminus; continues
 * Hong Kong road sign (Expressway Begins).svg Sha Lek Highway – Sha Tin Central
 * Northbound exit and southbound entrance
 * style="text-align:right"|14.3
 * style="text-align:center;"|4
 * Sha Tin Wai Road – Siu Lek Yuen, Prince of Wales Hospital
 * Southbound exit and northbound entrance
 * style="text-align:right"|
 * style="text-align:center; background:#dcdcfe" |–
 * style="background:#dcdcfe" |HK_Tunnel.svg Tate's Cairn Tunnel
 * style="background:#dcdcfe" |Southern terminus; continues
 * style="text-align:center; background:#dcdcfe" |–
 * style="background:#dcdcfe" |HK_Tunnel.svg Tate's Cairn Tunnel
 * style="background:#dcdcfe" |Southern terminus; continues

title: Tate's Cairn Highway


text:
Swami Siddheshwarananda

Swami Siddheswarananda (1897-1957) was a monk of the Ramakrishna Mission.

Gopal Marar of the Kottilil house or Tharavaad (maternal joint family) of Thrissur, was a prince of the House of Cochin, Kerala in his pre-monastic days. He was initiated by Swami Brahmananda and popularly called Gopal Maharaj. A charming person, he served as the President of the Mysore branch of Ramakrishna Math. During this time, he was instrumental in shaping the career of Puttappa, legendary Kannada poet Kuvempu. He had great regard for Sri Ramana Maharshi. He founded the Ramakrishna Ashrama at Gretz (Centre Vedantique Ramakrichna), outside Paris, France, in 1947 and spread the message of Vedanta in the French language, becoming well known in France as an author and lecturer.

Some of his writings are:
 * Hindu Thought and Carmelite Mysticism ISBN 81-208-1510-6
 * Le Yoga et Saint Jean de la Croix : pensée indienne et mystique carmélitaine ISBN 22-260-8621-8
 * Some Aspects of Vedanta Philosophy (Lectures given at the University of Toulouse in 1942)(1979 Pbk) ISBN 0-87481-471-5
 * Meditation According to Yoga- Vedanta
 * Metaphysical Intuition : Seeing God with Open Eyes - Commentaries on the Bhagavad Gita, translation Andre van den Brink
 * Rambles in Religion
 * God-Realization through Reason

title: Swami Siddheshwarananda


text:
User:Carlosm1

A Special Thanks to Those who have Added to The Pope Clement X Information. This Pope is according to Family myth an ancestor of mine, so any additions and corrections are appreciated. (One must keep history Factual).

title: User:Carlosm1