Talk:Zeroth law of thermodynamics

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Cheatsheet last updated by: Headbomb {ταλκ – WP Physics: PotW} 04:43, 23 June 2008 (UTC)

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Status of the zeroth law of thermodynamics

That redirects here. But where is the subject in question on this article? This article certainly agrees that the status is disputed but doesn't seem to say much more. Brianjd 14:21, 2005 Jan 29 (UTC)

Old talk - no headings

The zeroth law does provide enough for a definition of temperature. The relation "is in equlibrium with" is symmetric by any reasonable definition.

Also, it is trivial to EXTEND that relation "is in equlibrium with" so that A~A.

The temperature so defined may indeed not look like the centrigrad temperature scale, or even be continous, but it is a temperature function.

Concerns about relevance and factual accuracy

Hi, I'm not quite sure what your point is. It is very true that the relation "is in equilibrium with" is meant to be both symmetric and transitive, but it seems to me that it can hardly be disputed that this is not part of the zeroth law. (At least not in its usual formulations, which you could object to.)

More importantly, the zeroth law does not imply an ordering of any kind. This is the main reason I'd claim that it does NOT "provide enough for a definition of temperature". - Victor Gijsbers

There is no requirement that temperature provide an "ordering" of equilibrium states.

HOWEVER... a particular system MAY have continuous states, in which case states of constant temperature will form surfaces, and the normal provide a natural order of nearby surfaces. It is then simple to construct a global temperature function that provides an ordering of states (which seems to be your definition of temperature)

Oz 00:14, 12 Sep 2003 (UTC)

Transitivity

Transitivity is usually stated as "A=B AND B=C THEN A=C". The article has the less commonly stated version "A=B AND A=C THEN B=C". Obviously they both mean the same thing, but since the zeroth law is usually stated the first way (look for instance at the first page of Google results for "Zeroth law of thermodynamics"), I'm changing the formula to the first version (which is also the way it is in Thermodynamics). — Asbestos | Talk 10:57, 15 Apr 2005 (UTC)

The external link at the bottom of the page suggests otherwise. 192.75.48.150 16:39, 20 June 2006 (UTC)

Restore equivalence relationship

An equivalence relationship consists of

• Transitivity A=B, B=C means A=C
• Reflexivity A=A
• Symmetry A=B means B=A

Simply stating the transitivity part does not establish an equivalence relationship. (I believe) the zeroth law states that thermal equilibrium between systems is an equivalence relationship, not that it is transitive. The other two properties should be included in the statement of the third law. To a physicist they seem trivial, but mathematically and logically they are very important. PAR 22:10, 20 June 2006 (UTC)

First, from a mathematical point of view, the article states "A=C, B=C -> A=B" not "A=B, B=C -> A=C". Symmetry is not required, only reflexivity (the proof is not hard). I have removed symmetry from your restored section.

I orginally left reflexivity in, but then I tossed it too because it follows from the definition of thermal equiblibrium (whereas transitivity, or symmetric-transitivty, does not). Nobody includes reflexivity in the statement of the zeroth law, as far as I can tell. Ultimately, this is not an article about equivalence relations, so I moved your restored section further down in the article, and shrunk it to just say technically a reflexivity requirement is needed -- and I am still inclined to remove it altogether. 70.30.114.134 03:01, 21 June 2006 (UTC)

Added a section on the even-odd paradox

I put in a simple example of why the first and second laws by themselves lead to a paradox that equality of temperatures (or equality of any other intensive variables) is only sctrictly required for an even number of systems, and then explained how the 0th law resolves it. I think this goes to the heart of some of the previous discussion on this topic above, but gives a clearer exposition of it. I hope you find this example useful. Hernlund 15:15, 5 March 2007 (UTC)

Transitivity definition

The Zeroth Law is important in science, and yet this article is particularly light. Also, the various thermodynamic articles such as heat, internal energy, thermal energy, etc. are often confusing and contradictory. In Halliday and Resnick Physics, one finds the statement:
"This discussion expresses the idea that the temperature of a system is a property which eventually attains the same value as that of other systems when all these systems are put in contact. This concept agrees with the everyday idea of temperature as a measure of the hotness or coldness of a system, because as far as our temperature sense can be trusted, the hotness of all objects becomes the same after they have been in contact long enough. The idea contained in the zeroth law, although simple, is not obvious. For example, Jones and Smith may each know Green, but they may or may not know each other. Two pieces of iron attract a magnet but they may or may not attract each other.
"A more formal, but perhaps more fundamental phrasing of the zeroth law is:

There exists a scalar quantity called temperature, which is a property of all thermodynamic systems (in equilibrium states), such that temperature equality is a necessary and sufficient condition for thermal equilibrium.

"This statement [J.S. Thomsen, "A Restatement of the Zeroth Law of Thermodynamics," American Journal of Physics, 30, 294, 1962] justifies our use of temperature as a thermodynamic variable; the formulation given above [ie. the transitive statement] is a corollary of this new statement. Speaking loosely, the essence of the zeroth law is: there exists a useful quantity called "temperature."
- Parsa (talk) 17:36, 5 December 2008 (UTC)

The Refrigerator and the Universe

Sadly, the otherwise excellent nontechnical intro to thermodynamics, Goldstein and Goldstein (1993), is silent about the Zeroth Law. Its history is especially murky. I see that the mathematical nature of the relation of thermal equilibrium has been the main bone of contention on this Talk page. It is indeed an equivalence relation, and I have revised the entry accordingly.123.255.28.179 (talk) 07:15, 26 December 2008 (UTC)

Circular definition of temperature and thermal equilibrium

This article claims that the zeroth law of thermodynamics makes the definition of temperature possible.

However, as stated in this article, the zeroth law of thermodynamics is about systems which are in thermal equilibrium.

The definition of thermal equilibrium in this article uses the notion of temperature. Thus we have a circular definition.

Perhaps this is just a misreading, in any case it is confusing and should be cleaned up.

Also the part of the zeroth law which talks about euclidean relations is just a show of silly formalism: "euclidean relation" is not a commonly used term. It would be better to first state the obvious facts that thermal equilibrium is reflexive and symmetric and then say the zeroth law implies it is transitive.

Is this article bullshit?

I am not a physicist. Can we get one to weigh in on this supposed law? This article is not only hard to understand, it is hard to believe. Is this some kind of inside joke from the physicists? Mea (talk) —Preceding undated comment added 04:53, 5 January 2010 (UTC).

I'm not a physicist but I can at least tell you that it's not a joke. BTW I doubt a non-physicist or non-engineer would ever have any use for this law (I sure as hell don't) so the fact that it's hard to understand really doesn't matter. 156.110.35.114 (talk) 07:41, 18 February 2010 (UTC)

I am a physicist. Could people AT LEAST check physics books before claiming that something is false because they don't understand it? How stupid is that? Geez... —Preceding unsigned comment added by 190.222.169.5 (talk) 17:45, 1 October 2010 (UTC)

No doubt. This is covered in introductory physics for sure. I think we even covered it in general chemistry. P. D. Cook ^{Talk to me!} 14:58, 9 December 2010 (UTC)

I don't think it's a joke, it's just very badly written, clearly by someone who has difficulty expressing him- or her-self in English. In this sentence, for example, the author has become so entangled in words what he has lost track of what he or she is trying to say "Systems are said to be in thermal equilibrium if they have no net exchange of heat, and, if they are not already connected by a conductor of heat or pathway for exchange of thermal radiation, would not do so if they were so connected". What does '..would not do so' refer to ? Would not 'do' what ? I think this refers to "...they have no net exchange of heat", so the author has forgotten that he starts of talking about systems 'having' something, and drifts, without realising it, into writing about systems 'doing' something. The article needs to be revised by someone who not only understands thermodynamics, but whose intellectual attention span is commensurable with the length of his sentences. Andrew Smith

Thermometer

User:Kbrose seems to have a problem with this. Although for the life of me, I can't figure out what it is besides xe doesn't like it. It's sourced reliably, so it should stay in the article regardless if xes personal feelings about the content. -Atmoz (talk) 14:56, 9 December 2010 (UTC)

Foundation of temperature

The Foundation of temperature section is awkwardly phrased. My attempt to improve a part of it was reverted with a comment that temperature had not be introduced yet and the flow was not logical. This may be true but the reversion introduced temperature even earlier than I had it and replaced the old flow which I find difficult to parse and awkward. We need to improve this section and simply reverting attempts to improve it doesn't help. Jojalozzo 16:25, 30 August 2011 (UTC)

Personally, I think that Jojalozzo has good reason to make some comment here.Chjoaygame (talk) 22:12, 30 August 2011 (UTC)

In the original:

The zeroth law establishes thermal equilibrium as an equivalence relationship. An equivalence relationship on a set (such as the set of thermally equilibrated systems) divides that set into a collection of distinct subsets ("disjoint subsets") where any member of the set is a member of one and only one such subset. In the case of the zeroth law, these subsets consist of systems which are in mutual equilibrium.

In the version I reverted:

The zeroth law establishes thermal equilibrium as an equivalence relationship. An equivalence relationship on a set (such as the set of thermally equilibrated systems) divides that set into a collection of distinct subsets ("disjoint subsets") where any member of the set is a member of one and only one such subset. The zeroth law divides a set of systems into subsets that are mutually equilibrated.

In the reverted version, the fact that the subsets referred to in the second sentence are in fact the disjoint subsets referred to in the first sentence is lost, or at least less clear. I see a lessening of clarity, rather than a gain, with no new information added.

In the original:

temperature is just such a labeling process which uses the real number system for tagging.

In the version I reverted:

practicality leads us to employ a labeling process based on temperature and the real number system

What does it mean "based on temperature and the real number system"?. Temperature (as measured by temperature scales) is a real number, the two concepts are not two disconnected concepts. The original makes the connection, the reverted version loses it. Again, a loss of clarity, with no new information added. I see now that my objection to the introduction of temperature at this point holds for the original as well. This part should be clarified.

In the original:

Such temperature scales bring additional continuity and ordering (i.e., "hot" and "cold") properties to the concept of temperature.

In the version I reverted:

and thereby establishes a theoretical basis for continuity, ordering (i.e., "hot" and "cold") and measurement of thermodynamic systems.

To say that temperature scales "establish a theoretical basis for continuity" is muddy and has no clear meaning. Continuity and ordering is imposed by the temperature scales, and is absent in the zeroth law. The fact that the temperature scales impose or "bring" continuity and ordering is lost or at least made less clear. Again, a loss of clarity, with no new information added.

I will be happy to discuss making this section clearer or better, but these additions, in each case, removed clarity and logical connections without adding anything.PAR (talk) 05:16, 31 August 2011 (UTC)

You make some good points, PAR. From my perspective the language of this section, as reverted, is inaccessible except to those who understand it already and it never says why temperature is important. As your exposition here shows, there are important ideas that are not stated but only implied by the flow and the structure. I would like to see those essential ideas expressed explicitly.

I think there are no changes in the first paragraph until the third sentence. My edit of it was "The zeroth law divides a set of systems into subsets that are mutually equilibrated.". I find that version more straight forward since it brings the zeroth law into active play. I find the phrase in the reverted version, "In the case of the zeroth law", vague. How about: "The zeroth law divides a set of systems into disjoint subsets that are mutually equilibrated."?

>Yes, but we should make clear that these disjoint subsets are those that are referred to in the equivalence relationship. I don't know how to say it better - please read this carefully, I am not just rambling - The zeroth law says that we may divide all systems that are in thermal equilibrium into a number of disjoint subsets. "Disjoint" means that each individual system is a member of only one subset. "Mutually equilibrated" means that each member of the subset is in thermal equilibrium with any other member of that subset. Since the subsets are disjoint, this means that any system is NOT in equilibrium with any other system that is not in the same subset. This is ALL that the zeroth law says. No mention or implication of continuity or ordering ("hotter" or "colder"). The zeroth law thus implies that we may "tag" each disjoint subset with a unique identifier. The concept of temperature, which is developed LATER, using special thermodynamic systems ("thermometers") provides one of an infinite number of tagging methods. We could also tag each system by taking the decimal expression of what we know as the temperature and reversing every two digits to the left and right of the decimal point. For example, if we have a system that has what we know is at a temperature of 76.0325 K, we could 'tag" all systems with this temperature by the real number 67.3052. The zeroth law would not be violated. But if we do "tag" systems in this way, the concepts of continuity and ordering are lost. This shows that the zeroth law does not imply nor provide for continuity and ordering. Continuity and ordering are imposed by considerations outside of the zeroth law. It is only when we establish empirical temperature scales using real thermodynamic systems ("thermometers") that we impose continuity and ordering to our tagging procedure. These empirical thermometers give a rough idea of what we call temperature. The volume of mercury, for example is very nearly (but not exactly!) linear in temperature. If a mercury thermometer is calibrated as if the expansion were perfectly linear, it will give us a mercury temperature scale, but this scale will not exactly agree with a similar one based on alcohol. They will both, however, provide us with continuity and ordering in their method of "tagging" equilibrated thermodynamic systems. In other words, the concept of temperature is not fully developed by the zeroth law. The second law provides for a very special thermometer, one that is independent of the particular substance employed, and this tagging method is what we commonly refer to as "temperature". Specifically it is called the "thermodynamic temperature". Thus, it is the zeroth law and the second law which finally provide us with the concept of temperature. And since we cannot formulate the second law without the first law, it is seen that we need the zeroth, the first, and the second laws to finally come to the thermodynamic definition of temperature. Any reference to thermodynamic temperature in expressing the zeroth and first laws is, strictly speaking, circular reasoning.PAR (talk) 02:08, 1 September 2011 (UTC)

That's very helpful. I think we need to add this in the article. Otherwise the reader is either left holding the bag or jumping to conclusions as I did. Jojalozzo 03:25, 1 September 2011 (UTC)

In the fourth sentence, I think that providing a reason for using temperature adds significant information. I propose: "practicality leads us to employ a labeling process based on called temperature and based on the real number system."

> Again, we can refer to temperature as a useful way of gaining insight into what we are doing, but we always keep in mind that at this point temperature, with all of its properties, is not yet defined.PAR (talk) 02:08, 1 September 2011 (UTC)

Here is the complete last sentence as I edited it:

"In this way the zeroth law provides the foundation for using thermodynamic systems such as thermometers to provide labelings with empirical temperature scales, justifies the use of the second law of thermodynamics to provide an absolute or thermodynamic temperature scale, and thereby establishes a theoretical basis for continuity, ordering (i.e., "hot" and "cold") and measurement of thermodynamic systems."

I don't read this to "say that temperature scales 'establish a theoretical basis for continuity'". I believe the subject of the sentence is the zeroth law, not temperature scales. From my perspective this summarizes the section quite well, helps clarify what it all was leading up to and verifies for the reader that they have understood its implications rather than leaving them guessing. If the zeroth law doesn't establish a theoretical basis for continuity and ordering (and thus measurement) then the section needs even more work than I thought.

> No, as explained above, the zeroth law does not provide the concepts of continuity of ordering. Empirical temperature scales do, but they will generally all disagree with each other. Only when you get to the second law do you have a temperature scale that is independent of the substance employed, and thus any temperature scale defined by the second law using one substance will agree with a second law temperature scale based on some other substance.PAR (talk) 02:08, 1 September 2011 (UTC)

For the most part, sufficient information is presented in the reverted version such that a knowledgeable reader could figure it all out and you may not consider it adding new information to spell out ideas that are only implied or assumed but I promise you new readers will appreciate it. Jojalozzo 14:50, 31 August 2011 (UTC)

Ah. Now I am seeing what confused you in my version of last sentence. Here is a revision:

"In this way the zeroth law provides the foundation for labelings with empirical temperature scales using thermodynamic systems such as thermometers using thermodynamic systems such as thermometers to provide labelings with empirical temperature scales, justifies the use of the second law of thermodynamics to provide an absolute or thermodynamic temperature scale, and thereby establishes a theoretical basis for continuity, ordering (i.e., "hot" and "cold") and measurement of thermodynamic systems."

Jojalozzo 15:13, 31 August 2011 (UTC)

The laws of thermodynamics have never been set in stone; they have been variously stated from their beginnings. The laws of thermodynamics are not exercises in logical parsimony; they are summaries of empirical facts. I do not recall ever having read any physics or mathematics textbook that uses the notion of a Euclidean relation; the Wikipedia article on the zeroth law of thermodynamics cites none and that on Euclidean relations cites only one, a book on epistemology; the notion of a Euclidean relation is not in mainstream thermodynamical usage. According to the Wikipedia article on Euclidean relations, if a relation is symmetric then it is Euclidean if and only if it is transitive; as noted above, if system A is in thermal equilibrium with system B, then system B is in thermal equilibrium with system A; thermal equilibrium between two bodies is a symmetric relation.

> All of theoretical science is an exercise in logical parsimony. It is an attempt to summarize empirical facts in as logically parsimonious a way as possible.PAR (talk) 02:08, 1 September 2011 (UTC)

The laws of thermodynamics have a good claim to be seen from the "thermodynamic" point of view, as opposed to the "mechanical" point of view most influentially posed by Constantin Carathéodory, who was a mathematician. Carathéodory's aims included the expunging of the notions of temperature and heat from thermodynamic axiomatics until they could be derived from his version of the second law. Carathéodory did not really expunge the notions of heat and temperature from the axiomatics; for he relied on the concept of an adiabatic process, which rests on the ideas of heat and temperature for its empirical content. The notion of entropy is far more general than, and is not needed to express, the notion that heat flows down temperature gradients. Max Planck and James Clerk Maxwell put the notions of heat and empirical temperature as presuppositions of thermodynamics.

>An adiabatic process does not need the concept of heat or temperature for its expression. It depends only upon the axiomatic ability to thermally isolate two systems. Without the primitive, axiomatic ability to thermally isolate two systems, there is no thermodynamics, we cannot even begin. PAR (talk) 02:08, 1 September 2011 (UTC)

I think that the best statement of the zeroth law is not that of Fowler and Guggenheim, but is James Clerk Maxwell's statement that "If when two bodies are placed in thermal communication, one of the two bodies loses heat, and the other gains heat, that body which gives out heat is said to have a higher temperature than that which receives heat from it."Chjoaygame (talk) 19:15, 31 August 2011 (UTC)

>I disagree. This definition relies on the concept of heat and temperature, neither of which have any meaning without the first and second laws, and thus is guilty of circular reasoning. Thermal equilibrium can, however, be defined without reference to heat or temperature. Using the axiomatic ability to thermally connect or disconnect two systems, we connect them and wait a long time. Yes, we have to bootstrap by having some sense of when is a "long time" long enough, but we cannot use the precise definitions of heat and temperature, because they are not yet defined at the point of the zeroth law. PAR (talk) 02:08, 1 September 2011 (UTC)

Reply to PAR

I can see that PAR thinks I am on the wrong track.

For example, he thinks that the concepts of heat and temperature do not have any meaning without the first and second laws. Perhaps he could try telling that one to Laplace and to Fourier, who knew neither law. Apparently PAR thinks that thermal isolation has physical meaning without reliance on the concepts of heat and temperature. I suppose that much of the thinking of PAR is derived eventually from the work of Carathėodory.

I do not wish to battle this out with PAR.Chjoaygame (talk) 19:59, 1 September 2011 (UTC)

We have had agreements and disagreements in the past, and we have never sunk to the level of mindless edit wars, so I am not worried. There is an aspect of axiomatic thermodynamics which I think is ignored in many cases - that is what I called "bootstrapping" or maybe a better term is "successive refinements". If you don't have an accurate thermometer, you cannot tell precisely when two systems are isolated. But you keep going, developing the theory, developing better thermometers, changing your theory, etc., you arrive at a very precise theory, but whose axioms are unattainable. You cannot begin to develop a theory of thermodynamics without the idea of an isolated system, yet you cannot precisely decide whether a system is isolated without precise instruments based on the laws and axioms. I think Laplace and Fourier must have had a rough notion of the laws, even though they were not precisely stated at the time. I think they were one step along the process of successive refinements in the development of axiomatic thermodynamics.

An analogy which stays in my mind is that of Euclidean geometry - a very precise, axiomatic approach to geometry. But when you try to bring it to the real world, you have some trouble. How do you create a straight line (i.e. a ruler) without having a straight ruler already to compare it to? How do you create a ruler that is straighter than the straightest ruler you presently have? When mirror grinders wish to make a plane surface, they take three roughly plane surfaces (A, B, and C) and grind two together, A and B lets say. This gives two curved smooth surfaces which match to within the size of the grinding sand. Then they grind B and C together, then they grind A and C together, and keep doing this until ultimately they have three surfaces which are flat to within the size of the grinding sand. In other words, they have not only used axiomatic Euclidean geometry, but also a set of techniques to provide them with tools to actually do geometry in the real world. I think axiomatic thermodynamics is fine, but to bring it to the real world, a set of techniques for tool creation based on these axioms and a series of successive approximations is an indispensable part of thermodynamics, and this whole process is not very formalized, but needs to be. Its also not very clear in my mind how this would work, but the bottom line is that axiomatic thermodynamics should read like axiomatic Euclidean geometry: certain concepts are taken as axiomatic and other concepts are derived, but no circular reasoning is allowed - no concept which is undefined can be used to define a new concept which is then used to define the undefined concept. You cannot use the concepts of heat and temperature to express the zeroth law, which is then used, along with the first and second laws, to define temperature and heat. You can, however, use rough tools, like the rough mirror blanks, to come up with more precise tools in accordance with the axiomatic theory by a series of succesive refinements. PAR (talk) 01:23, 2 September 2011 (UTC)

I appreciate a formal, axiomatic approach but I do not think it belongs in an expository project like this one. We need to provide all the navigational aids we can, including motivation, previews, and iterative refinement of the concepts. There needs to be a layperson's version that's accurate without being overly rigorous as well as more formal development of the ideas. If we accept the perspective PAR presents in which the first and second laws are critical to the concept of temperature, then we must explain that and accept the necessary assumptions it requires whether it breaks the chain of logic or not.

Should we be concerned about original research here? Are there sources that support this presentation or is this new work? Jojalozzo 04:00, 2 September 2011 (UTC)

I agree - the article should first give a general idea of the zeroth law accessible to a layperson, perhaps without being rigorously accurate, then go on to the precise axiomatic presentation. Both should be included. To ignore the rigorous statement of the zeroth law as being "too abstruse" is unacceptable, especially since it is really a rather simple concept. The rigorous statement of the zeroth law is the equivalence relationship among equilibrated thermodynamic systems, with "equilibrium" being defined without reference to heat or temperature, both of which are developed in later laws. The axiomatic development of the zeroth, first, and second laws is not original research and, I believe, is already referenced. Its just that some textbooks also sacrifice rigor for understanding, and sometimes these unrigorous attempts to convey meaning are mistakenly entered into Wikipedia as rigorous statements, without realizing that circular reasoning is being used. I think we can agree that as editors, we cannot ultimately be content with circular reasoning when presenting any scientific subject such as thermodynamics. How can we be content with describing the zeroth law in terms of temperature and heat, then go to the first law which defines heat, and then to the second law which defines temperature? The examples I gave to illustrate the meaning of the zeroth law are my own, but they follow from the axiomatic presentation of the zeroth law, and as such are not "research" of any kind. The ideas about the development of successively refined tools in concert with the three laws are my own, and would constitute original research, so they cannot be entered into the article without finding a peer-reviewed reference to support them. PAR (talk) 09:41, 2 September 2011 (UTC)

Sounds like we're in agreement on these points. Do you have time to work on this? Jojalozzo 12:32, 2 September 2011 (UTC)

I have time to do some edits, but not time to do research. PAR (talk) 13:57, 2 September 2011 (UTC)

Reply to Jojalozzo

Jojalozzo seems to accept the Fowler and Guggenheim statement of the zeroth law as definitive, as if it were chiseled in stone. It is true, so far as I know, that Fowler invented the label "zeroth law", though I have not actually found the original use of the term, so far as I know. Sommerfeld attributes it to Fowler alone, but gives no reference that I can trace; perhaps someone can help with that. The ideas expressed in the law are by no means original with Fowler and Guggenheim; they were repeatedly stated by many long before them. The invention of the label does not mean the invention of the law. Sommerfeld himself states the law, with its label, differently from Fowler and Guggenheim.Chjoaygame (talk) 19:59, 1 September 2011 (UTC)

I am agnostic (and ignorant - still trying to learn this). I was just trying to improve what's written in the section on temperature so it's more understandable and has more motivation. I took what was there at face value and and tried to add what I thought was being assumed or communicated implicitly. That did mean I accepted the presentation as it was - I didn't want to change the meaning - just to make it clearer and more explicit - but it doesn't mean I wouldn't be as willing to similarly edit a different presentation that develops some other perspective. I appreciate this discussion a great deal. Jojalozzo 03:34, 2 September 2011 (UTC)

Remove incorrect opinion

I replaced the statement "This ordinary language statement by-passes the complications of statements such as by Tait and by Planck mentioned just above, that talk in terms of As, Bs, and Cs." with a more correct statement.

The statements in terms of A,B, and C are precise, they are not "complications". Guggenheims statement is easily read and understood, but it is imprecise. For example, you cannot use Guggenheim's statement to show that if A is in equilibrium with B, then B is in equilibrium with A, (i.e. "in equilibrium with each other") unless A and B are in equilibrium with C. Specifying the zeroth law as an equivalence relationship does allow you to say this. I have no problem with imprecise, easily understood statements as an introduction to the zeroth law, but to confuse precision with "complications" is simply wrong. Once you understand, fully understand, an equivalence relationship, you will realize that it fully conveys the zeroth law and that ALL implications of the zeroth law can be derived from it.PAR (talk) 03:00, 4 September 2011 (UTC)

This definition of the Zeroth Law is incorrect ?

I was taught that the 0th Law was: In an isolated system any two bodies in contact will attain thermal equilibrium. (There exists a property/relationship called temperature such that...). Without this Thermodynamics becomes a meaningless exercise in logic with no real world use. -*- The definition in the article is: if T(A,B) and T(B,C) then T(A,C) for the property T(x,y) (thermal equilibrium between x & y). I find this to be silly, but perhaps I've missed the point? Why not claim that T(A,B)≡ T(B,A) ? Isn't that just as important? Or how about for the property temp, if temp(A) > temp(B) and temp(B) > temp(C) then Temp(A) > temp(C) This also is not stated, but is required for Thermodynamics to be coherent. I read what Fowler had to say, I'm not convinced he just hadn't fully articulated what he meant. As most of you probably know (and believe me I am way out of my depth here) the temperature of a system is not unambiguous. In excited states with population inversion, temperature does NOT have a unique meaning (electronic vs thermal). This area of thermo may postdate Fowler's 1935 work? Anyway, it seems to me that requiring temperature to be a property measured with real numbers (another Law ?? LOL) that actually exists is more important than to explicate the (arguably mathematical rather than physical) properties of real numbers and operations on them. Unfortunately, I have limited time and resources to do the leg work necessary to research this. I did want to post my objection to this and state that there is another (at least) school of thought on what the Zeroth Law is.71.31.149.105 (talk) 18:12, 21 March 2012 (UTC)

The definition you gave is not the one in the article. The zeroth law states that if T(A,B) and T(C,B) then T(A,C), with an added statement that T(B,B) is also true. It follows from this that if T(A,B) then T(B,A).

The zeroth law as stated above, allows you to divide all thermodynamic systems into "disjoint subsets" - any system is a member of one and only one subset, and all members of a subset are in equilibrium with each other, and out of equilibrium with any member not in the subset. This allows you to "tag" each subset with a unique ID number or letter, or whatever. Then you can say if the tags match, they are in equilibrium, if not, they are not.

And that's all.

The zeroth law makes no statement about the tags. It does not say they are real numbers, or letters of the alphabet, or species of birds, or anything. The zeroth law does not establish any order relationship on the tags or the subsystems, it does not have anything to say about the idea of "hotter" or "colder". The concept of thermodynamic temperature and the idea that these "tags" are in fact real numbers is not developed until the second law.

Why is this silly? PAR (talk) 07:37, 22 March 2012 (UTC)