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Cheatsheet last updated by: Headbomb { ταλκ – WP Physics: PotW} 04:43, 23 June 2008 (UTC)
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. Brian j d 14:21, 2005 Jan 29 (UTC)
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.
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 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 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)
An equivalence relationship consists of
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)
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)
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)
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)
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.
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 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)
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)
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. Joja lozzo 16:25, 30 August 2011 (UTC)
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.
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.
temperature is just such a labeling process which uses the real number system for tagging.
practicality leads us to employ a labeling process based on temperature and the real number system
Such temperature scales bring additional continuity and ordering (i.e., "hot" and "cold") properties to the concept of temperature.
and thereby establishes a theoretical basis for continuity, ordering (i.e., "hot" and "cold") and measurement of thermodynamic systems.
"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."
"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."
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.
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.
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 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)
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 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)
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)
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)
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)
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)
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)
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)
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. Joja lozzo 01:55, 24 January 2013 (UTC)
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)
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)
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 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:
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".
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.
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.
Further: Just above that he writes: "Temperature is a property or parameter of state."
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 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)
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.
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)
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)
Y 2402:3A80:13A4:35C6:0:0:D71D:D1F8 ( talk) 06:07, 22 February 2023 (UTC)
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![]() | This article may be too technical for most readers to understand.(September 2010) |
![]() | It is requested that a physics diagram or diagrams be
included in this article to
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Tasks
Do not remove the elements, but rather strike the text as they becomes useless or irrelevant (i.e write
text to be struck) to indicate that this element was verified and found to be alright.
Cheatsheet last updated by: Headbomb { ταλκ – WP Physics: PotW} 04:43, 23 June 2008 (UTC)
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. Brian j d 14:21, 2005 Jan 29 (UTC)
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.
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 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 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)
An equivalence relationship consists of
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)
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)
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)
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)
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.
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 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)
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)
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. Joja lozzo 16:25, 30 August 2011 (UTC)
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.
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.
temperature is just such a labeling process which uses the real number system for tagging.
practicality leads us to employ a labeling process based on temperature and the real number system
Such temperature scales bring additional continuity and ordering (i.e., "hot" and "cold") properties to the concept of temperature.
and thereby establishes a theoretical basis for continuity, ordering (i.e., "hot" and "cold") and measurement of thermodynamic systems.
"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."
"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."
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.
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.
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 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)
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 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)
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)
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)
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)
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)
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)
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)
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. Joja lozzo 01:55, 24 January 2013 (UTC)
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)
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)
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 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:
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".
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.
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.
Further: Just above that he writes: "Temperature is a property or parameter of state."
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 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)
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.
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)
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)
Y 2402:3A80:13A4:35C6:0:0:D71D:D1F8 ( talk) 06:07, 22 February 2023 (UTC)