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)

The current version of the article (April 26, 2023) does not resemble our notion of transitivity. It essentially states that if A = B and additionally A = C and B = C, then A = B = C. The author(s) seem(s) to have preferred to avoid the stronger form: (A = B) & (B = C) => (A = C), perhaps with good reasons, but those reasons are not discussed. — Preceding unsigned comment added by 130.20.197.45 (talk) 05:57, 26 April 2023 (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)

@Hernlund

Talk to Boldsey 2409:40C2:103:62A6:8000:0:0:0 (talk) 08:59, 30 August 2024 (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 — Preceding unsigned comment added by 82.32.48.177 (talk) 08:54, 14 April 2012 (UTC)

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)

If you put two previously separate isolated systems in equilibrium with themselves in contact then I would expect that they become one isolated system and through the action of the second law come to a new single equilibrium different from both of the previously different isolated systems. Seems trivial to me. Convince otherwise....

Avram Primack (talk) 23:30, 1 February 2013 (UTC)

a well-known editor is currently having an unchecked field day at the article on Thermal equilibrium

I think hardly anyone watches the article on Thermal equilibrium. Because of this, I think, a well-known editor is currently having an unchecked field day there.Chjoaygame (talk) 18:52, 9 October 2012 (UTC)

What's a "generalization principle"?

Currently this article begins:

The zeroth law of thermodynamics is a generalization principle [...]

What's a "generalization principle"? Maybe I can guess, but it's not something people say very often, so it sounds strange, and I *don't* think it's a good way to start this article. Could someone try to improve it? John Baez (talk) 19:39, 12 October 2012 (UTC)

new statement

The newly proposed statement is not sourced. Sourcing is relevant here, because we are looking at a long previously established idea, the term 'zeroth law' for it being an arbitrary label proposed in a single textbook (Fowler and Guggenheim 1939), who in the very same sentence label it also as the "postulate of the ″Existence of temperature″[p. 56.]. The statement is not uniform amongst competent writers, and the re-wording of the statement proposed here is therefore an arbitrary and unsourced proposal by a Wikipedia editor. Perhaps one historically original source statement, not labeled with the term 'zeroth law', was by Rankine in 1853. The statement by Maxwell in 1871 was also not labeled as the 'zeroth law'; Maxwell did, however, offer the term 'Law of Equal Temperatures'.

The newly proposed statement is moreover verging on being self-contradictory. It reads: "A system is said to be in thermal equilibrium when it experiences no net change in thermal energy in time. The most precise statement of the zeroth law is that thermal equilibrium constitutes an equivalence relation on pairs of thermodynamic systems." This statement uses the term 'thermal equilibrium' in two ways: once as referring to a single system (not specified as being open or closed to exchange of matter), and in the next sentence, without notice, a second time as referring to a relation between two systems (again not specified as being open or closed to exchange of matter). This is hardly compatible with an insistence on rigorous precision of logic.Chjoaygame (talk) 00:12, 19 January 2013 (UTC)

restored section

The usual rule is that the editor should find the reliable source before posting the material. An unsupported claim that "this is good material" does not override that rule.Chjoaygame (talk) 17:22, 19 January 2013 (UTC)

If that were strictly true, there would be no use for the "citation needed" tag. In other words, we have options, and I think we should use those options as constructively as possible, not as destructively as possible. I think anybody who puts a "citation needed" tag on unsourced material has a responsibility to at least try to find a source, and I accept that responsibility. You have a mastery of sources that exceeds my own, and I would appreciate any help you could give me in this endeavor. PAR (talk) 17:55, 19 January 2013 (UTC)

Hmm.Chjoaygame (talk) 19:05, 19 January 2013 (UTC)

The proposed section starts: "Many systems are said to be in equilibrium if the small, random exchanges (due to Brownian motion or photon emissions, for example) between them do not lead to a net change in the total energy summed over all systems. A simple example illustrates why the zeroth law is necessary to complete the equilibrium description."

This smacks already of original research. At best it is slipshod and vague. Not an auspicious start.Chjoaygame (talk) 22:11, 19 January 2013 (UTC)

A main problem with this proposed section is that it pretends to present a rational argument, but fails to do basic things for that, such as clearly and explicitly expounding its selection of premises, and perhaps reasons for that particular selection. It seems to produce a wonderful conclusion out of scarcely any ingredients, but it achieves that simply by hiding the identities of the ingredients. This is a very serious failure in a Wikipedia article, especially in one such as this, in which there are many recognized and reasonable ways of selecting the premises.Chjoaygame (talk) 02:26, 20 January 2013 (UTC)

Well, it's a very clear argument, and I was about to tell you it was true, but I decided to check it in detail. The result is that it is probably OR, and erroneous OR at that. The author made an error, namely that Jacobi's theorem implies that "for N even we find that all of the entries must vanish", which is a false statement, only true when N=2. In fact, for any N and any choice of T's, the determinant is identically zero, except for N=2. So the whole argument is crap. Please revert my edit. I wonder if there IS a simple direct example that demonstrates the need for the zeroth law? PAR (talk) 04:04, 20 January 2013 (UTC)

With respect, I think it is unclear about what it means by writing about 'equilibrium'. Does it intend thermal equilibrium? How does it intend that? How did it define temperature and entropy, with or without reference to thermal equilibrium? I had the feeling that it was a case of trying to divide by zero, but I have to say that was only a very vague feeling. Surely the task of deletion now falls to you, since you found a straightforward mathematical error?Chjoaygame (talk) 06:52, 20 January 2013 (UTC)

Done. I think the argument was clear - It was posed as a conundrum of classical thermodynamics (including all laws) which could not be resolved without invoking the zeroth law. Unfortunately it can be resolved without invoking the zeroth law. PAR (talk) 15:00, 20 January 2013 (UTC)

Original research and synthesis in history section?

Much of the content in the history section appears to be original research and synthesis. We should be very careful in constructing our own history from primary sources to avoid inferences or conjectures and be vigilant in avoiding all original analysis of historical texts. We need secondary historical works to support whatever we say there. I propose we remove content that is not supported by such secondary sources. Jojalozzo 01:55, 24 January 2013 (UTC)

Yes, and let's take the same attitude to the rest of the article.Chjoaygame (talk) 02:35, 24 January 2013 (UTC)

As someone who has a much better understanding of this topic than I, please have at it. Jojalozzo 03:12, 24 January 2013 (UTC)

Have at what?Chjoaygame (talk) 03:27, 24 January 2013 (UTC)

Please feel free to remove interpretive content not supported by secondary sources (i.e. if it's not a simple summary, paraphrase or direct quote of primary sources). Jojalozzo 15:42, 24 January 2013 (UTC)

Why isn't this an incomplete triviality

This seems to be a restatement of the logical statement that if A is equal to B and B is equal to C then A is also equal to C. To me this is too trivial to be a law of thermodynamics. If it is this important then there should be corollaries for mass, energy, and any combination of mass and energy that taken together are equivalent to other combinations of mass and energy. Why should I care? Make me care by putting an explanation at the head of the article.

Avram Primack (talk) 23:27, 1 February 2013 (UTC)

Equivalence relationships seem trivial when the equivalence is intuitive. When trying to prove something, however, you have to state even the obvious. Euclid's laws of geometry seem trivial as well. "Two parallel lines never meet" - duh! But when you explicitly lay down your assumptions, you can start to talk about their consequences, and the consequences of suspending or violating them.

The zeroth law deals with unmoving, closed systems. There is no need to state conservation of momentum for such systems, and to say they are closed is to imply mass conservation. Energy conservation is the first law of thermodynamics. When you get into fluid dynamics, an extension of equilibrium thermodynamics, you will in fact have conservation of mass and momentum as anchors to the whole theory.

I fully agree that a clear example of the use of the zeroth law is missing and should be given. PAR (talk) 19:53, 2 February 2013 (UTC)

Restore direct statement

Why would anyone want to replace a direct statement of the zeroth law, in which there is no concept of temperature, with

"Another interpretation of the law is that all valid temperature scales must agree with a common temperature scale as to whether or not two bodies have the same temperature."

The statement "A mathematically precise statement..." then goes on to give a mathematically imprecise statement.

Please, if the statement is to be edited, improve it rather that clouding the issues.

If you have problems with the idea of a Euclidean relationship, try googling "zeroth law Euclidean" to see about 11,200 hits. PAR (talk) 19:53, 2 February 2013 (UTC)

With respect, a Google search does not automatically constitute a citation of a reliable source.

There is in the present article no actual citation of a reliable source for the statement in the article that is specifically defended here in the restoration, "The most precise statement of the zeroth law is that thermal equilibrium constitutes an equivalence relation on pairs of thermodynamic systems." This statement may be more or less true, and has certainly long been recognized here as the view of a respected editor. That editor has had ample time to find a reliable source for it, and must surely be well aware of that.

That editor proposes in the above comment that the re-write that I put up, hoping to quell a continual trickle of complaints, has, "clouded the issues". I am not convinced that my effort did cloud the issues as proposed by that editor.

From some reading of the literature I do not recall ever noting an occurrence in this context of thermodynamic literature the use of the term 'Euclidean relation'. I am aware that it has been in the Wikipedia for some time. My reading of the literature is of course far from complete, and as recently shown here, my faculty of recall is fallible, but I think I am justified in asking for an explicit citation of a reliable source for this usage in this context. Those who like to use the term 'Euclidean relation' in this context have had plenty of time to find a reliable source for it, and they must surely be aware of that, in view of the number of complaints about it on this page.

There are not too many careful and thorough and mathematically rigorous developments of classical thermodynamics in the literature. One of those few, by Landsberg, states the zeroth law directly as a statement of transitivity using that term. Others that I recall do not use the term 'Euclidean relation'. This may or may not be an indication of their defective knowledge, but the Wikipedia is not the arbiter of correctness; its mission is to report reliable sources in context.

My edit intended to look at the zeroth law from a general theoretical physical viewpoint as well as from the viewpoint of a mathematical physicist, but the restoration has deleted a fair number of reliably sourced statements of mathematical content with a greater emphasis on the physical than the pure statement that "The most precise statement of the zeroth law is that thermal equilibrium constitutes an equivalence relation on pairs of thermodynamic systems."

If someone wants to know about the use of the term 'Euclidean relation' in this context, he has the option of doing a Google search for it. So far as I understand it, the Wikipedia is not a substitute for Google. Especially I would think is so for a rather abstract question in theoretical physics. Wikipedia has a policy of reliable sourcing, which distinguishes it from Google.

I would have thought that a fair response to my re-write, from those who want to restore the statement "The most precise statement of the zeroth law is that thermal equilibrium constitutes an equivalence relation on pairs of thermodynamic systems" would have been to produce a reliable source for it. Likewise for the term 'Euclidean relation'.Chjoaygame (talk) 22:17, 2 February 2013 (UTC)

Can I ask you, what is your understanding of the zeroth law? From your own understanding, how would you explain it to someone? PAR (talk) 03:01, 3 February 2013 (UTC)

Are you asking me to say more than what I have found from reliable sources? As for what I have found from reliable sources, my re-write was my attempt to put or summarize that in ordinary language suitable for the Wikipedia.Chjoaygame (talk) 04:20, 3 February 2013 (UTC)

No, I mean what is your understanding of the zeroth law, after reading those various reliable sources? PAR (talk) 15:42, 3 February 2013 (UTC)

As for the law itself, after reading the sources, my understanding of it is in my re-write. Things can be taken further from there, to other subjects that arise as developments, from the law combined with the other laws, but I don't think you are asking me about that?Chjoaygame (talk) 18:02, 3 February 2013 (UTC)

Ok, good

My understanding is that the zeroth law logically precedes the first and second law. Therefore, the zeroth law must make no mention of any concept defined in the first and second law when it is expressed, or else you have circular logic.

I think it is perfectly fine to reconsider the zeroth law in light of the definitions introduced by the first and second laws, but not before the law is stated. To do otherwise is to imply that the zeroth law requires the concept of temperature or temperature scales for its statement. A strong distinction should be made between the statement of the zeroth law and the description of these later consequences.

The zeroth law should first be stated, without reference to temperature or temperature scales. It is an equivalence relationship established on pairs of equilibrated thermodynamic systems.

The consequence of this equivalence relationship should then be explained - all thermodynamic systems may be separated into groups. Every system is a member of only one group and is in thermal equilibrium with every other system in that group, and is not in thermal equilibrium with those of any other group.

The various statements of the zeroth law should then be explained, explaining why they are, with varying degrees of rigor, aiming towards the same goal - the equivalence relationship.

FINALLY, we can discuss the consequences of the zeroth law in light of the concepts introduced by the first and second law, including temperature, temperature scales, the concept of "hot" and "cold", etc.

I think you can see why I strongly object to your edit, not because you misunderstand them, but because they have the development all mixed up. The first sentence begins "Another interpretation...." is very bad. This is the section where the only interpretation is about to be presented! It begins immediately talking about temperature and temperature scales, using concepts which have nothing to do with the statement of the zeroth law.

Please don't ask me to back these statements up with references at this time, that would totally miss the point of what I am saying. Its a question of an understanding of the zeroth law, not of references. If you could please explain to me if and where and why you disagree with the above, without discussion of references, I would appreciate it. PAR (talk) 04:01, 4 February 2013 (UTC)

I do not wish to enter into disagreement with you, nor to push for my edit.

Nevertheless it may be of interest to discuss the questions you raise.

I think your focus is on the logical sequence of steps of reasoning.

In particular, you want to state the zeroth law without using the concepts defined in the context of the first, second, and third laws. You think that there is a unique and well-defined proper way to develop the ideas of classical thermodynamics.

I would reply to that that I do not see a law as defining anything. I see it as making a physical assertion in terms that have full meaning in their own right prior to the physical assertion made in the law. There are not many really rigorous and full presentations of classical thermodynamics. One careful presentation is by Münster 1970, though that is not nearly as rigorous and mathematical as for example are Landsberg 1961 or Lieb and Yngvason 1999. Münster uses a concept that he calls 'theorem of experience'. There are few of them, and they roughly correspond to my idea of the basic laws of thermodynamics. I am not asking that you read or think about Münster's presentation. I mention it only to try to make clear how I distinguish between a definition, a mathematical theorem, and a law of nature. I just mean to clarify why I don't think of a law of thermodynamics as making a definition. Thus it seems that I think differently from you, at least in some respects. I do not mean to say that I think your way of thinking is unacceptable. I just mean to say that it seems that it doesn't coincide with mine, and that I don't think mine is unacceptable.

As I see it, the zeroth law is a theorem of experience. It has a physical meaning. It tells what you find when you do a particular experiment, under certain physical conditions.

I find that your definition of thermodynamic temperature is not that used by Carathéodory, who in some ways is regarded as a leader in this field. He was the pure mathematician who put on the map, at the request of Max Born, the definition of heat as a residual of internal energy change after measurement of the work done by a body on its surroundings when transfer of matter is excluded, the definition that Count Iblis refers to, and that is often regarded as authoritative. One of the prime triumphs of Carathéodory was that he had banished the use of cyclic processes. So I was a little surprised to read your definition of thermodynamic temperature. I am not remotely suggesting that I find any fault in your definition. I am just saying it came as a little surprise to me. So I am guessing that your uniquely correct logical sequence is not that of Carathéodory, which is used as a more or less authoritative guide by some writers, such as Fowler and Guggenheim 1939. Carathéodory's development of the theory is considered radically defective by other respected authors, but I will not go into that here. My observation is that Fowler and Guggenheim are not a uniquely correct and authoritative source on these matters. That Fowler invented the label 'zeroth law' is not by itself sufficient to establish that he is a uniquely correct and authoritative source about the axiomatics of classical thermodynamics.

My view of an axiomatic system for a physical theory is that one starts with a collection of primitive concepts which are mutually coherent and consistent. This view I got from Alfred North Whitehead, the co-author, with Bertrand Russell, of Principia Mathematica. In terms of the primitive concepts, one selects and states some axioms. Then one may develop the logical consequences of the axioms in any way one pleases; there is no rule that one development is uniquely correct. I think this may not meet with your approval. But I don't think it can be dismissed very easily.

My concern is that readers new to the game must find the zeroth law without context hard to deal with. They are entitled to ask 'What is this all about? Why do I need a lesson in algebra at this point?' The sentence at the beginning of the section that you find "very bad" is intended as an introductory motivation. Textbooks often use just such an introductory motivation.

The zeroth law was stated by eminent physicists long before Carathéodory 1909 used it, and long before it was given the label 'zeroth' law, apparently by Fowler. It was always in those old days stated in rather elaborate context of physical ideas. According to Arnold Sommerfeld, the label was invented by Fowler when he was praising the 1935 A Treatise on Heat of Saha and Srivastava. That text states the law in the context of a prior primitive notion of temperature. It may be that Saha and Srivastava were wrong to ignore Carathéodory there. But it may also be noted that Carathéodory himself assumed prior primitive experimental establishment of his thermodynamic systems, including the existence of walls permeable only to heat. His fully defined closed systems had just one "non-deformation" variable. That is to say, Carathéodory has in effect assumed, as a theorem of experience, that each system has one variable that could be used as a thermometric variable against which to compare other systems, by connection through a wall permeable only to heat. The "non-deformation" variable was undoubtedly measured on a real number scale. This was regarded by Carathéodory as a theorem of experience, if you like. The name 'zeroth law' was not in 1909 attached to the statement used by Carathéodory that is nowadays most often called the zeroth law. It was not marked out as one of his axioms, but it was part of the basic set-up of his development. I think it would be fair to say that he did not state his development as rigorously as did Landsberg 1961 or Lieb and Yngvason 1999, and did not state all his axioms explicitly labeled as axioms. So the fact that Carathéodory did not label something as a law does not establish that it does not have the effective status of a theorem of experience for him.

Thus I think physicists don't often think of the zeroth law without context. If so, I guess perhaps that you would say they are in some respects wrong there.

As I see it, the physics underlying all this is that classical thermodynamics makes the entropy a positive real variable, has only one thermodynamic temperature, and has only one kind of wall permeable only to heat. There are not several kinds of heat distinguished by their respective several kinds of walls selectively permeable only to their respective kinds of heat, nor several kinds of entropy, nor several kinds of temperature, one for each respective kind of wall selectively permeable only to its respective kind of heat. This is a substantial physical finding. It is not just chatter. The theorem of experience stated in the usual form of statement of the zeroth law leads to an equivalence between systems, and this equivalence has underlying it the physical fact that the hotness manifold is one-dimensional, and contributes to the argumentative establishment of that manifold. The mathematical construction of a one-dimenstional manifold is not necessarily obvious or simple. Whether or not one regards hotness as primitive depends on how one chooses to develop one's ideas. As I read you, you do not regard it as primitive. Some others do.

The Wikipedia is not, I think, just a treatise presenting the one and only uniquely correct rigorous axiomatic development of classical thermodynamics.

Nevertheless, because I can see that your ideas are dear to your heart, I do not wish to try to stand in your way. In particular I am not at present intending to try to restore what you have deleted of my edit. I reserve my right to change my mind about that.Chjoaygame (talk) 08:13, 4 February 2013 (UTC)

Thinking about it, I am not clear why the zeroth law is logically prior to the first. As I understand it, the first law can be stated without reference to heat or to temperature. One takes the body to the state of least possible energy, as a reference state. Then one adds energy by doing adiabatic work on it, and identifies the states so produced. The assumption here is that every state of the body can be reached by doing adiabatic work in this way. The operation of 'adding' two previously separated bodies and letting them come to a new internal equilibrium as new body seems permitted here.

The zeroth law is about a basis for temperature, and should not be needed for the first law? Should one not re-number the previously so-called 'first law' as the zeroth law, and call the thermal comparison statement the first law?

In the ultra-rigorous development of the theory by Lieb and Yngvason 1999, the presently labeled 'zeroth' law is not introduced until after they have developed the entropy. Should one re-number the previously so-called 'second law' as the first? Lieb and Yngvason say that they are not sure if the zeroth law is really needed at all, because of a 1989 paper by Buchdahl, which claims that it is not needed but can be deduced from other things (a paper which I have not read).Chjoaygame (talk) 16:01, 4 February 2013 (UTC)

I think much of your above discussion, while interesting to me, and much of which I agree with, is not focused on the section we are discussion - what is the zeroth law and what does it mean?

I know that there is not one axiomatic development of thermodynamics, and we should not pretend that there is. The zeroth law may or may not be necessary, depending on which axiomatic system you want to develop. I have read, but do not fully grasp Buchdahl's statement that the zeroth is not necessary at all. This is all irrelevant to the section we are discussing. This section is about the zeroth law, its statement and its consequences. Discussion of how it fits into the larger theory of thermodynamics should wait for a later section.

The zeroth is prior to the first because the first defines heat and internal energy. The second then defines temperature and entropy. All of these concepts are not needed in the statement of the zeroth. I don't believe the zeroth is necessary until the second law, where temperature is finally defined. I think you might be right, then, that the first and zeroth could be renumbered, but do not need to be, so we go with the historical numbering. Again, this is all irrelevant to the section we are discussing. This kind of pondering should wait for a later section.

The section we are discussing should state clearly the zeroth law and explain the various other statements, and the direct consequences of that statement, and that's all. Once the statement is grasped, we can intelligently go on to explain how it fits into the larger picture. PAR (talk) 23:14, 4 February 2013 (UTC)

"What is the zeroth law and what does it mean?" For a Wikipedia editor the zeroth law is what reliable sources say it is, and it means what they say it means. I don't think this can be separated from "how it fits into the larger theory of thermodynamics", because it is mostly not so separated in the sources. The sources are not uniform about how they state "the zeroth law", nor indeed about "how it fits into the larger picture".

"... the first defines heat and internal energy." I don't think that a law defines things. It states substantial generalities. Carathéodory's 1909 presentation does not define quantity of energy transferred as heat at all.

"The second then defines temperature and entropy." Again, I don't think laws make definitions. They state substantial generalities. Perhaps some textbooks seem to make the laws define things; if so, depending on the case, I would expect to consider them poor in logic and perhaps not reliable sources on such matters.

Hidden in all of this is that Carathéodory's principle is not enough to deliver all of the contents of the second law, but people conveniently forget that.

As an argument that some physicists do not use the term 'Euclidean relation', I instance Buchdahl 1968 who says that the zeroth law asserts transitivity, but then states the law in the usual ABC way, which the Wikipedia editors think should be correctly called the 'Euclidean relation' way. Another example is Landsberg 1961. I think it is not the job of the Wikipedia to correct authorities such as these. If the authorities don't find it notable, Wikipedia has no duty to say they ought to.

You have a definite view about what "the zeroth law" is really saying. I do not wish or intend to try to stand in your way on this.Chjoaygame (talk) 02:44, 5 February 2013 (UTC)

Thinking a little more. I am wondering if, to clarify this matter, it is a good idea to radically distinguish empirical temperature from thermodynamic temperature. The zeroth law may mean one thing to a student of thermodynamic temperature and a radically different thing to a student of empirical temperature.

If so, we may look at the zeroth law from the viewpoint of a student of empirical temperature, without prejudice as to how a student of thermodynamic temperature would look at it. The student of empirical temperature has a bewildering array of thermometers, which in general disagree with one another. Yet he still thinks each measures temperature. Our friend of the 'sucks bigtime' philosophy has a point here. If one doesn't exactly know what one is measuring, one is exploring a concept rather than a simple physical quantity. For example, Saha and Srivastava on page 2 write: "It follows that temperature is not a measurable quantity in the sense that a length or mass is." This is a rather subtle statement, and is not emphasized in other texts quite in such explicit and direct terms, so far as I have noticed (perhaps I will notice now that I am on the lookout for it). (One can argue about what geometry underlies one's concept of length, for example.) The present concept may be expressed by saying that temperature measures hotness, dare I say it, on a numerical scale. One is looking at a concept of hotness. The solution here is to believe in the existence of the hotness manifold. The question is how to get from the many unreconciled scales to the manifold which reconciles them. All valid empirical thermometers must agree that a certain curve is an isotherm. They must agree on more: that one body is the hotter of two; this is not stated in the usual aphoristic expression of the zeroth law, but it is in the context of most statements of it, and I think it hard to exclude it from being part of the zeroth law. The hotness manifold puts the isotherms into an order that can be parametrized by the real numbers. The constituent points of an isotherm are members of an equivalence class. The zeroth law says that this construction will work; considering the contexts in which this is often presented, it is not accurate reporting of the sources to present the zeroth law as a lesson in algebra; these people are not interested in axiomatics so much as they interested in constructing the hotness manifold. You may say that it is illegitimate to think of the hotness manifold as telling about temperature because temperature is the sole preserve of the Kelvin definition. Perhaps you may be right. But many presentations of the zeroth law are definitely in this context. Saha and Srivastava 1935 is definitely an example.

They may be very wicked, but their text was the one that triggered Fowler to invent the term 'zeroth law'. Their chosen aphoristic statement, in a separate italicized paragraph, was in effect that any non-deformation variable is an empirical thermometer that reads a numerical scale.

They said nothing about equivalence relations.

Maybe they should have done, but they didn't. They definitely presupposed that temperature scales were expressed as real numbers. The lead sentence of the paragraph in which this occurs talks about heat flow. They wrote: "Experience tells us that when two bodies at different temperatures are placed in contact, exchanges of heat take place and finally as state of "temperature (or thermal) equilibrium is attained, after which no further change takes place. From this follows the law:—If a body A is in temperature equilibrium with two bodies B and C, then B and C will themselves be in temperature equilibrium with each other." They were talking about empirical temperature. The explicitly identify body A as "the thermometer". There is no reason to say that they really meant to talk about a binary relation of equivalence as such. Experimentally, the procedure for testing for thermal equilibrium is the measurement of the respective non-deformation variables of the two bodies. The non-deformation variables conform with the definition of empirical temperatures. It would do violence to the source to say that it intended to focus on the concept of an equivalence relation.

Again, we may ask what a student of the thermodynamic temperature wants from the zeroth law. Your definition of thermodynamic temperature, as I read it, does not directly and explicitly rest on the zeroth law. It rests simply on the first law, to identify quantities of energy transferred as heat. The ratio of two thermodynamic temperatures is the ratio of two quantities of energy transferred as heat. There is no guarantee here that the thermodynamic temperature is positive or that it has other desirable properties. I see no call on the zeroth nor on the second law as being needed for your definition. The question then arises, 'is the thermodynamic temperature also an empirical temperature that has a map into the hotness manifold?' and many other questions arise about it. These questions can be answered by the use of various axioms and lines of reasoning. Some developments seem to need the zeroth law to be able to identify an equivalence relation, perhaps others don't. I will not go into this right now. The point here is that the axiomatic structure of classical thermodynamics has been tackled in many ways, and perhaps the best way hasn't yet been found. Considering the axiomatic structure of classical thermodynamics, Lieb and Yngvason 1999 are not sure about the place of the zeroth law stated simply as a thing that generates an equivalence relation. As I mentioned above, Carathéodory's principle is routinely asked to do more than it can. Perhaps the zeroth law is a kind of prop for this effort. I don't know. Perhaps some ideas will come. My conclusion now is that I am far from confident understanding of the place of the zeroth law stated as a thing that generates an equivalence relation, to be used by the student of thermodynamic temperature, without prejudice as to what might interest a student of empirical temperature.

Arnold Sommerfeld writes on page 1 of his text:

       The science of thermodynamics, as already stated in the preface, is an

axiomatic science. In accordance with its spirit we introduce the concept

of temperature by stating the following axiom:

       There exists a property — temperature. Equality of temperature is a

condition for thermal equilibrium betweeen two systems or between two parts of

a single system.

       The preceding statement was purposely formulated in the same way as

those which will be used later to state the First and Second Laws of thermo-

dynamics and, following a suggestion by R. H. Fowler,¹ we shall refer to it

as the "Zeroth Law" of thermodynamics.

Just above that he writes: "Temperature is a property or parameter of state." He is talking about a numerical variable. The footnote refers to Saha and Srivastava 1935. Sommerfeld is reliable in the sense that it is said that he had more Nobel Prize winning students than any other physicist. Perhaps he is wrong here, but some good evidence would be needed to establish that he is not a reliable source here.Chjoaygame (talk) 06:22, 5 February 2013 (UTC)Chjoaygame (talk) 12:30, 5 February 2013 (UTC)Chjoaygame (talk) 14:52, 5 February 2013 (UTC)

The empirical temperature approach is taken by Bailyn 1994 (A Survey of Thermodynamics, American Physical Society, ISBN 0-88318-797-3, pp. 19–23). He says that "An important consequence of the law of equilibrium, one that is usually treated as an independent and basic postulate in itself is (31 his footnote says the earliest statement of it that he knows is in Helmholtz 1884): THE ZEROTH LAW OF THERMODYNAMICS: Two systems in thermal equilibrium with a third are in thermal equilibrium with each other." He goes on to define empirical temperatures on this basis, not relying on the first or second laws, which he treats in subsequent chapters. He talks later about Carathéodory's use, in his axiomatic development, of this proposition, but does not mention (that I recall) Sommerfeld or Fowler or Maxwell in this context. He does not use or mention (according to his index) the zeroth law in his further development of classical thermodynamics. He does mention it in a footnote, well after the thermodynamics, in his introduction to the microscopic explanation. The footnote is about how Carathéodory seems to have derived some of his approach from Helmholtz. Bailyn's own personal formulation of the zeroth law is "All diathermal walls are equivalent."Chjoaygame (talk) 19:18, 5 February 2013 (UTC)

---

I have tried to extract from your statement only those statements that are relevant to the statement of the zeroth law. All statements about Caratheodory and Lieb/Yngvason are irrelevant. If they do not discuss the statement or meaning of the zeroth law, then they have nothing to add to this section, which is a statement of the zeroth law. The fact that they ignore it or question its usefulness is irrelevant. It seems I cannot state this enough: This section is not about the usefulness of the zeroth law in an axiomatic system, it is about the statement of the zeroth law, useful or useless as it may be. It is about the statement of the zeroth law, not about its consequences, not about useful illustrations of its use.

There are a number of properties of thermodynamic temperature:

• Equivalence for systems in thermal equilibrium - the possibility is postulated by the zeroth law.
• Ordering - the idea that if two systems are not thermally equilibrated, one is hotter, one is colder (NOT postulated by the zeroth law)
• Continuity or nearness - The idea that a system can be much hotter or a little hotter than another. (NOT postulated by the zeroth law).

These are informal statements, but they address simply some of the concepts flying around.

You write: "What is the zeroth law and what does it mean?" For a Wikipedia editor the zeroth law is what reliable sources say it is, and it means what they say it means. I don't think this can be separated from "how it fits into the larger theory of thermodynamics", because it is mostly not so separated in the sources. The sources are not uniform about how they state "the zeroth law", nor indeed about "how it fits into the larger picture".

No, our job as editors is not to quote sources and marvel at the differences. Our job is to understand what they are saying, understand it well enough to determine when they are saying essentially the same thing and when they are not. Our job is to transmit this understanding to the reader, to bring coherence to the sources, and to refer the reader to the sources for further understanding. For other editors, also with an understanding of the subject, the sources can be checked to see if the editor using them has properly interpreted them, and correct them if necessary.

You write: As an argument that some physicists do not use the term 'Euclidean relation', I instance Buchdahl 1968 who says that the zeroth law asserts transitivity, but then states the law in the usual ABC way, which the Wikipedia editors think should be correctly called the 'Euclidean relation' way. Another example is Landsberg 1961. I think it is not the job of the Wikipedia to correct authorities such as these. If the authorities don't find it notable, Wikipedia has no duty to say they ought to.

Again, it is not a matter of correcting them, it is a matter of understanding them. There is no dispute over what constitutes a transitive relationship or a Euclidean relationship. Buchdahl is correct - the zeroth law asserts transitivity (because an equivalence relationship implies transitivity). If he states it as a Euclidean relationship, and then offers as a consequence the equivalence relationship, then we must assume he is implicitly assuming reflexivity. Either that or he is stupid, and he is not stupid.

Regarding a "non deformation variable" - the "non deformation variable" cannot be directly measured. An empirical thermometer measures the deformation of the working substance, mercury, alcohol, whatever. To postulate the existence of a non-deformation variable such that it is equal for systems in equilibrium is yet another statement of the zeroth law. Note the word "equal" again, with no further properties of ordering or continuity. There's that equivalence relationship again.

As for Sommerfeld's statement:

There exists a property — temperature. Equality of temperature is a condition for thermal equilibrium betweeen two systems or between two parts of a single system.

I have no problem with this. This is where understanding comes in. What he is saying is that there is a method of separating thermodynamic systems into disjoint subsets such that every member of a given set has a unique "tag". He says that there exists a certain tagging system called "temperature". That's it. This is another statement of the equivalence relationship. Do you see the word "Equality"? That's the equivalence relationship, right there. He makes no mention of temperature being a real number, having any "hot" or "cold" properties, no ordering, no continuity, just equality. Just as does the other statements of the zeroth law. No mention of empirical temperature, thermodynamic temperature, relationship to entropy, energy, none of that. Just equality, which is the equivalence relationship.

Further: Just above that he writes: "Temperature is a property or parameter of state."

This cannot be shown to be true without the second law, where, temperature is defined. I can define a tagging system for thermodynamic systems such that when the tags are the same, the systems will be in equilibrium, when they are not, they are not. I can define such a tagging system which is not a state variable. If you think that Sommerfeld is saying that the zeroth law implies the existence of a state variable, you have very simply misunderstood him.

It appears to me that you have amassed many statements on the zeroth law, but you do not attempt to find the common thread. You see the many varied statements, illustrations, comments, but you don't differentiate between statements, half-statements, illustrations and comments. You don't turn the puzzling mess of different verbiage into a coherent understanding of the zeroth law. Please, rather than search for the differences, search for the common thread - they are all aiming at the same thing, the equivalence relationship. PAR (talk) 05:43, 6 February 2013 (UTC)

I have tried to indicate that an important more or less common aspect, stated abstractly, is that the reliable sources seem to say that the zeroth law expresses the idea that empirical temperature refers to a one-dimensional hotness manifold, into which the diverse non-deformation variables have suitable maps; not all of those maps are one-to-one, but that can be dealt with. As I understand you, I am mistaken there, due to my lack of understanding. The one unique truth, to which you have direct personal access, is that "they are all aiming at the same thing, the equivalence relationship." I am not trying to stand in your way. I am not trying to restore my edit which you undid.Chjoaygame (talk) 12:51, 6 February 2013 (UTC)

I understand that, but "hotness manifold" implies order and continuity. Can you explain how the statements of the zeroth law bring order and continuity to the concept of temperature? How can I use the zeroth law to determine which system is hot and which system is cold? PAR (talk) 14:57, 6 February 2013 (UTC)

You write as if you believe that you know the one and only uniquely correct statement of the zeroth law, and that it is just the contextless statement "if two systems are each in thermal equilibrium with a third system, they are also in thermal equilibrium with each other." I don't think that is supported by the reliable sources. You write as if you believe that you know the one and only uniquely correct aim of those who state the zeroth law, and that it is the equivalence relation. I don't think that is supported by the reliable sources. You seem to insist on framing this discussion on the prior assumption that your beliefs that I have just stated are finally and bindingly correct. You write as if any expressions of deviation from complete and exact compliance with your beliefs that I have just stated are irrelevant.

Carathéodory derives his definition of empirical temperature from a proposition about equilibria between systems separated by a wall permeable only to heat: "Whenever each of the systems S₁ and S₂ is made to reach equilibrium with a third system S₃ under identical conditions, the systems S₁ and S₂ are in mutual equilibrium." This proposition in Carathéodory is far from being contextless. Carathéodory does not derive or use the fact that thermal equilibrium is a an equivalence relation. He chooses one, S₃, of the three systems as his empirical thermometer. He does not in his definition of temperature offer to say which system is hot and which is cold. Order and continuity arise for him from the fact that the non-deformation variable is a real variable. From empirical temperature he goes on to prove that some scale of temperature must exist that is "absolute", the same for all systems, which is a monotonic function of his empirical temperature based on system S₃. He uses the steam point and the ice point of water at prescribed pressures to fix the numbers for his absolute temperature. Carathéodory is thus an example of a source that uses the proposition that you think is the one and only uniquely correct statement of the zeroth law, who does not seem to aim at the proposition that the binary relation of thermal equilibrium is an equivalence relation.Chjoaygame (talk) 02:43, 7 February 2013 (UTC)

I don't mean to give the impression that I am unshakingly certain in my thinking. I am never unshakingly certain about anything technical. I am willing to listen to any argument to the contrary. If I wasn't, I wouldn't be carrying on this conversation with you. Please preface every one of my absolutely-certain-sounding declarations with "I think", so we can dispense with this problem.

Caratheodory's statement:

Whenever each of the systems S₁ and S₂ is made to reach equilibrium with a third system S₃ under identical conditions, the systems S₁ and S₂ are in mutual equilibrium.

This is the Euclidean statement of the zeroth law, with symmetry implied. It lacks only reflexivity to make it an equivalence relationship. You cannot reasonably argue against that. You state correctly, that order and continuity follow from the fact that the non-deformation variable is a real variable, but this cannot be derived from the above statement. He proves that some scale of temperature must exist that is absolute. This cannot be derived from the above statement. He uses the steam point and ice point of water to fix the numbers for the absolute temperature. This cannot be derived from the above statement.

To be technical, I think that any invocation of the zeroth law in thermodynamics will make use of only the symmetric and Euclidean properties of the zeroth law. If you deny the equivalence relationship, but demand symmetry and the Euclidean relationship, you are left unable to define the temperature of an equilibrated body which is not in equilibrium with any other body, and if you want to argue against introducing reflexivity and thereby turning Caratheodory's symmetric Euclidean statement into an equivalence relationship, then that is how you should argue it. But to say that Caratheodory uses the symmetric Euclidean statement as only part of the zeroth law is, wrong, and to say that he somehow uses the zeroth law to prove order and continuity is also wrong. If you think I am wrong, then please show me your line of reasoning. PAR (talk) 03:44, 7 February 2013 (UTC)

According to Buchdahl (1986, J. Phys. A 19: L561–L564) "This conventional statement of the zeroth law (e.g. Woods 1975) needs to be supplemented with a general assumption. To state it succinctly, let it be agreed that, with the index J going over the range A, B, C, the system K_J shall have n_J coordinates, collectively denoted by X_J, exactly one of which is a non-deformation coordinate. Then

K_J and K_B are in mutual diathermic equilibrium if and only if their states satisfy one condition f_AB (X_A, X_B) = 0.             (A)"

Buchdahl 1986 writes in the last paragraph of his paper: "... one may well take the position that (A) should be taken as one of the basic 'laws'—the 'zeroth law'—rather than as an 'ancillary assumption'."

Carathéodory uses this "general assumption". It is part of the meaning of the statement, what I have referred to as part of the context of the statement. Carathéodory's statement copied above is clause 4. of a list of four clauses that he uses to define a rigid wall permeable to heat. It is not a contextless statement. The other three clauses are essential context. It is hardly practical for me to copy here all the contexts of the source statements that I refer to. This goes also for what Sommerfeld has to say.

I do not wish to pursue this further.Chjoaygame (talk) 07:07, 7 February 2013 (UTC)

Regarding the "rules", it is not "reliable sources" that decide, it is consensus. Regarding the zeroth law discussion, by no longer contesting my edits, we have effectively established consensus, since no other editors were involved. I see from your comments above that this is sort of a "false consensus", since you still do not agree with my edits but rather are tired of discussing it with me. Perhaps we should submit an RFC at Wikiproject:Physics and try to come up with a better consensus involving more editors, so that we could both be more certain. PAR (talk) 06:03, 10 March 2013 (UTC)

I do not wish to pursue this further.Chjoaygame (talk) 11:04, 10 March 2013 (UTC)

Physical meaning

The "Physical meaning" section says "These ideas may be regarded as helping to clarify the physical meaning of the usual statement of the zeroth law of thermodynamics." This does not seem to be true; the section doesn't talk at all about what heat is. Instead this section seems to be covering the question of whether or not the axioms of thermodynamics require the assumption that heat and temperature exist. I'm thinking we should retitle this section and trim it to focus on that question? -- Beland (talk) 14:42, 23 June 2021 (UTC)

A fair concern. I agree that the section is a bit awkward.

Not quite too easy to fix this. The section is largely about how Carathéodory rethought some aspects of thermodynamics, stimulated by the suggestion of Max Born. In physics, the word 'heat', since the latter days of the nineteenth century, has a rather specialised meaning. It refers to energy in transfer from one body to another, not to energy belonging to just one body. The Carathéodory concept was that this could be defined without actually saying positively how the transfer occurs, but rather by exclusion, saying that it occurs by paths other than transfer of matter, and other than as thermodynamic work. Carathéodory was a mathematician, particularly interested in topology. He was concerned to get conceptual parsimony more than physical lucidity. He wasn't the first to think like this. For example, Bryant had also thought this way. Thermodynamic work is also a bit subtle to define. It is primarily defined as work done by the body on its surroundings when that can occur spontaneously as a result of a thermodynamic operation that freshly exposes the body to conditions that allow it to spontaneously do work. For example, the operation might be a change in the externally imposed electric field that allows the body to do electrostatic work. If the externally imposed change is such as to make the surroundings do work on the body, this does not count as allowing the body to spontaneously do work on the surroundings. The difference is that when the surroundings do work on the body, inevitably, according to the second law, there is an element of friction that transfers energy to the body as heat, in addition to that transferred as pure work. Some part of the work done by the surroundings, as measured in the surroundings, is received by the body not as thermodynamic work, but instead as heat. The thermodynamic work is measured by the change in polarisation of the body. In the case of P–V work, this gives rise to the term 'isochoric work', referring to work done by the surroundings on the body. This is all a bit tangential to the physical meaning of the zeroth law. Maxwell said that all heat is of one and the same kind. This is true in one sense, but it doesn't reveal the diversity of heating mechanisms. Besides transfer by conduction and radiation, as Maxwell was perhaps thinking, heat can arise in a process that is dominated by friction, as in Joule heating and in the Joule measurement of the mechanical equivalent of heat with a paddle wheel, or as in Rumford's cannon boring.

I will think about making such an improvement as you suggest.Chjoaygame (talk) 20:55, 23 June 2021 (UTC)

I'm not sure what that was all about, but I've rearranged some things and refocused the section. -- Beland (talk) 04:42, 15 July 2021 (UTC)

Comment on new edit

This edit has the cover note "this does not relate to the physical meaning - heat is short-distance motion of atoms".

In the nineteenth century people often enough talked of heat as it were the erratic motion of the microscopic constituents of bodies of matter and radiation, but in the early twentieth century, that usage became viewed as poor physics, with good reason. Carathéodory was not the first to clarify this, but, with the support of Max Born, he was influential in clarifying that heat in physical terminology is not a property of a single body. Rather, it is energy transported under certain conditions between the thermodynamic system and its surroundings, or between two thermodynamic systems. Carathéodory was perhaps the first to popularize the notion of a compound thermodynamic system, comprised of two or more simple thermodynamic systems, separated by walls. The notion of a selectively permeable wall is one of the fundamentals of thermodynamics. For such thinking, what matters is the existence of a certain kind of wall, specially intended by Carathéodory to forestall talk of 'heat' as a property of a body.Chjoaygame (talk) 12:06, 15 July 2021 (UTC)