Talk:Zeroth law of thermodynamics
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[edit] 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)
[edit] 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.
[edit] ==
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 eqilibrium 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)
[edit] 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)
[edit] 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)
[edit] 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)

