Talk:Third law of thermodynamics

message: There is an error in the calculation of entropy. k log Omega is not k log N.
----  — Preceding unsigned comment added by Dakkacord (talk • contribs) 05:53, 11 March 2014 (UTC)
thread_title:  Error 

message: An anon user put in the following:
:The third law of thermodynamics (hereinafter "Third Law") states that "as a system approaches the zero absolute temperature (hereinafter "ZAT"), all processes cease and the entropy of the system approaches a minimum value. That minimum value is zero in the case of a perfect crystalline substance. Succinct statements of the Third Law include: 
*All the temperature of a system approaches ZAT, all processes cease; 
*As temperature goes to ZAT, the entropy of a system approaches a constant.
I have reverted this contribution based on the opinion that: (1) the style-format is very poor and (2) no thermodynamics texts use this format.--Sadi Carnot 20:47, 24 April 2006 (UTC)
thread_title:  Reverting ZAT notation 

message: I have been redirected to this page when searching for "Nernst Heat theorem". I am trying to understand this theorem in the form quoted by Planck on page 133 of his book "The theory of heat radiation". There the theorem is written in form of a characteristic function of an ideal gas and in terms of Nernst's chemical constant. I would also like to know what does this constant represent.--R vardavas 09:09, 11 November 2006 (UTC)
thread_title: Query

message: In the fourth paragraph of Overview, the text says
"they may order in an antiferromagnetic sense, with all moments antiparallel to each other."
2 things may be antiparallel, but 3 or more cannot be all antiparallel.
Could the text be rewritten as follows:
"they may order in an antiferromagnetic sense, with pairs of moments antiparallel to each other."
Maybe someone can think of a better way to be precise. Kinzele (talk) 19:59, 26 November 2008 (UTC)
replies: text: "...with neighboring pairs of moments antiparallel to each other". --Steve (talk) 01:17, 27 November 2008 (UTC)
thread_title:  "all antiparallel" 

message: There needs to be at least a brief mention of what the variables in the Law stand for.  —Preceding unsigned comment added by 68.230.127.25 (talk) 11:55, 23 July 2009 (UTC)
replies: text: I deleted that "formula", it was just a restatement of the text but more ambiguous and less accessible. --Steve (talk) 16:09, 23 July 2009 (UTC)
thread_title:  Variable descriptions 

message: i cleaned up some of the stuff on residual entropy, and defined a perfect crystal. it would help if someone put the formula s=kbomega. there were a few places where it seemed to be saying the third law was being violated. i also included a reference on the subject of residual entropy.  it turns out there are ways to add catalysts to remove the imperfects and release the residual entropy. Sperfect = 0 = Sdefect - S residual. The links to those publications are found in the reference i posted.Alchemist314 (talk) 10:48, 13 November 2010 (UTC)
replies: text: That seems OK. If "perfect crystal" means translational invarience, then of course it's a unique microstate. I tried to rephrase the proton-disorder-in-ice statement. --Steve (talk) 20:55, 13 November 2010 (UTC)
thread_title:  residual entropy 

message: The definition described as "the most common" was incorrect. I fixed it. In general, the article confused notions of equilibrium structure at 0K (not necessarily crystalline!) with the Third Law (which defines the zero of entropy). There was also some confusion about magnets and ground states. The role of spins is the same as that of any other degree of freedom in a solid. I fixed all this in the introduction and overview, and haven't touched the rest. 66.127.52.193 (talk) 20:59, 3 January 2011 (UTC)
thread_title:  Incorrect definition 

message: As I look at the article now it is stated that
'This version states not only ΔS will reach zero at 298 kelvins, but S itself will also reach zero as long as the crystal has a ground state with only one configuration.'
Am I confused or is the figure of '298 kelvins' incorrect?
I would also like to point out that the correct way to record absolute zero is '0 K' rather than '0K'.  — Preceding unsigned comment added by Anstopd (talk • contribs) 06:09, 5 October 2011 (UTC)
thread_title:  298 kelvins 

message: The third law is not statistical - 8digits seems to have confused it for the second law. Waleswatcher (talk) 16:34, 5 February 2012 (UTC)
replies: text: The impossibility of reaching absolute zero is discussed above on this page. This idea does not come from nowhere--it's discussed in sources--but I remain unconvinced that the general statement is defensibly a consequence or part of the third law. Still waiting for better sources on this. I agree with reverting it until we have convincing sources that discuss and explain this. As for "statistical law", I agree that's misleading and should be reverted, although one can argue that it is "a law that has something to do with statistics". --Steve (talk) 19:27, 5 February 2012 (UTC)

text: UPDATE: Here seems to address the origin and explanation of "impossibility of reaching absolute zero". As much as I am not fond of 8digits and his editing, he is correct that "impossibility of reaching absolute zero" is relevant to third law and not currently addressed by the article. The best solution is for the article to address this issue well. I'm too busy for the time being...maybe later... --Steve (talk) 03:52, 7 February 2012 (UTC)
thread_title:  8digit's edits 

message: I'm trying to understand Adwaele's expansion to the article, and immediately ran into a couple problems...
:"as one is free to chose the zero of the entropy it is convenient to take S(0) = 0."
One is not free to choose the zero of entropy! Entropy is the logarithm of the number of microstates. If there is more than 1 microstate, you're not free to say that the entropy is 0. See residual entropy for a discussion of how entropy may not be 0 at 0K.
:"the value of S(0,X) is independent of X. In mathematical form, S(0,X) = S(0)."
Again, this seems inconsistent with residual entropy systems such as glass. For glass, the entropy at 0K depends on the conditions under which you approached 0K, such as pressure, speed of cooling, etc. Hmm, I guess you're trying to say "Once the system is very close to absolute zero, anything you do to it--like change the magnetic field, pressure, etc.--will not change its entropy." Heating it up and cooling it down is not allowed. Is that right?
Also, where possible, it would help to put the microscopic explanation of the different aspects of the law. For example, the heat capacity of a system goes to zero near absolute zero, I presume, because there are no accessible degrees of freedom into which the system can put extra energy. Is that right? I'm not sure, but anyway, when it is possible to explain why something is true, it helps the reader visualize it and remember it. It is much harder to remember and understand something where "it's an axiom, because I said so, you just have to trust me".
Please clarify, thanks! --Steve (talk) 13:33, 17 April 2012 (UTC)
thread_title:  Adwaele's edits 

message: Continuing the objections from just above, there are the following difficulties in the section Mathematical formulation starting at
the phrase There are three steps. It states:
:1: in the limit T0→0 the integral in Eq.(4) is finite.
Why? Is this the content of the third law, or part of it, or a consequence of it (as formulated in some previous section)? Which formulation, then? It's not true purely from math.
:2. the value of S(0,X) is independent of X.
Is this the content of the third law? If so, it should be announced as such !! A bit later:
:Equation (6) can also be formulated as
:
\lim_{T \rightarrow 0}\left( \frac { \partial S(T,X)}{ \partial X}\right)_T = 0.	(8)
:In words: at absolute zero all isothermal processes are isentropic. Eq.(8) is the mathematical formulation of the third law.
Okay, so this is the third law. But then the assertions in steps 1. and 2. above are left hanging. They aren't the third law, and they don't follow by math from earlier results. I understand that the three steps are being done gradually for pedagogical reasons. But the logic needs reworking. 
And to repeat the objection of Steve: S(0,X) = S(0) seems inconsistent with residual entropy systems such as glass. So a caveat should be worked in above. A small one, just a tiny reminder that the third law isn't actually universal.
178.38.125.245 (talk) 23:05, 22 April 2015 (UTC)
thread_title:  Logical difficulties in section called "Mathematical formulation" 

message: I slightly rephrased some of these formulations of the third laws. I assume they are not exact original words, but crafted for pedagogical purposes.
:The Nernst–Simon statement of the third law of thermodynamics concerns thermodynamic processes at a fixed, low temperature:
::The entropy change associated with any condensed system undergoing a reversible isothermal process approaches zero as the temperature at which it is performed approaches 0 K.
Here I felt that it was important to emphasize that the reversible isothermal process actually occurs at a fixed temperature, which then takes on a sequence of values going to zero.
Otherwise the non-thermodynamic reader imagines a process in which the temperature is gradually lowered, and wonders how this could be isothermal...maybe you just do it really slowly, so the temperature remains constant???
I moved the definition of condensed matter out of the statement of the law, which should be pithy.
I also wrote:
:A classical formulation of the Nernst–Simon statement (not obviously equivalent to the above) is:
followed by the statement about a finite number of steps. This formulation is called "classical" because it is close to the Nernst quote that occurs later in the article. I don't think of it as "simpler" because it's not the same thing; it's merely qualitative and you can't actually derive the whole third law from it, as far as I can tell. So, strictly speaking, it shouldn't even be called a formulation of the third law, but rather a consequence of it. I think of it as a lagniappe. Or is there something I've missed?
178.38.125.245 (talk) 00:04, 23 April 2015 (UTC)
replies: text: I noticed all the comments above about the "finite number of steps" statement. The upshot is that it's just a consequence. So I changed the article to reflect this. 178.38.125.245 (talk) 00:26, 23 April 2015 (UTC)
thread_title:  Rephrased quotes in introduction 

message: I was wondering who refers to it as the Nernst-Simon statement? Simon doesn't get mentioned anywhere else in the article and neither the German nor the French wikis mention anything even resembling Simon.
And which Simon would that be? This guy https://en.wikipedia.org/wiki/Francis_Simon ? 195.75.72.179 (talk) 13:31, 6 July 2015 (UTC)
thread_title:  Nernst-Simon statement 

message: Generally it's bad form to say a physical law has been "proven mathematically". More correctly it would be said that it has been restated, or shown as deriving from a more fundamental principle. However, there's nothing technically wrong with that statement, if one keeps in mind what being "proven" means in the context of physics. But it is misleading in context of popular science. Opinions? 93.103.25.142 (talk) 09:52, 30 March 2017 (UTC)
thread_title:  3rd law of TD was "proven"...? 

message: : If the system is composed of one-billion atoms, all alike, and lie within the matrix of a perfect crystal, the number of combinations of one-billion identical things taken one-billion at a time is Ω = 1.
Is this really a helpful way of explaining why the entropy of a crystal at T = 0 is zero?   What do combinations have to do it with?   Why are we considering a combination of a billion things taken a billion at a time here?
In physics more relevant is whether the crystal is in a pure state, i.e. a state that cannot be expressed as a nontrivial convex linear combination of other states.  Pure states have entropy zero.   John Baez (talk) 16:48, 31 July 2022 (UTC)
thread_title:  Combinations