# Talk:Third law of thermodynamics

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## Error

There is an error in the calculation of entropy. k log Omega is not k log N.

— Preceding unsigned comment added by Dakkacord (talkcontribs) 05:53, 11 March 2014 (UTC)

## Reverting ZAT notation

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)

## Query

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)

## Fixing classical-quantum confusion

I have made one major change and two minor changes. The major change as to eliminate a discussion contrasting classical and quantum systems in the T=0 limit. The discussion was not just wrong, it was almost exactly the opposite of the truth. Zero-point motion is a property of unique quantum states, and thus makes no contribution whatsoever to entropy. The minor fixes were: 1. to include the Kramers degeneracy. 2. To eliminate a nonsense sentence about how non-equilibrium defects represent the second law at work (opposite of the truth) and replace it with a somewhat clarified discussion of the role of non-equilibrium entropy. There's plenty of room left for further clarifications and for links to other relevant physics and chemistry. Also, in my opinion, the separate discussion of magnetic systems, etc., actually decreases the clarity of the presentation. However, as a new editor I wanted to do a minimal revision for now.--Mbweissman 15:11, 23 December 2006 (CST)

## Impossibility of attaining absolute zero

Can someone provide a citation that the third law of thermodynamics states that it is impossible to attain absolute zero temperature in a finite time? Of course I agree it's true, but I'm not sure it's part of the "third law". In particular, my favorite thermodynamics textbook, Thermal Physics by Kittel and Kroemer, doesn't mention that when it defines the third law. --Steve (talk) 16:08, 5 November 2008 (UTC)

I think it's generally accepted as a consequence of the Third Law, or at least as a consequence of the various theories which are summarized in the Third Law. To quote a common summary of the Laws of Thermodynamics:
"The First Law says that you can never win, you can only break even.
The Second Law says that you can only break even at Absolute Zero.
The Third Law says that you can never get to Absolute Zero…"
Physchim62 (talk) 14:11, 6 November 2008 (UTC)
OK, but is there a reliable source? --Steve (talk) 15:52, 6 November 2008 (UTC)
Is there a reliable source that France is a country in Western Europe? Physchim62 (talk) 21:12, 6 November 2008 (UTC)
Yes, for example any politics textbook, geography textbook, or atlas would confirm that France is a country in Western Europe. Likewise, if we look at thermodynamics textbooks, it should be very easy to confirm that this is a consequence of the third law of thermodynamics. As I said above, I have a well-known thermodynamics textbook, and it describes the third law, but it does not say that the impossibility of reaching absolute zero is a consequence of it. Perhaps other textbooks do. If so, let's see it.
A catchy, clever slogan is not a reliable source; see WP:RS. :-) --Steve (talk) 22:14, 6 November 2008 (UTC)
I wasn't suggesting that the little ditty was a reliable source! Merely that it is a widely accepted consequence. Absolute zero seems to have a source for the assertion, although I don't have access to it myself. Physchim62 (talk) 23:40, 6 November 2008 (UTC)
When I get a chance I'll look up that reference from Absolute zero. That article doesn't make it clear whether/how the impossibility of reaching absolute zero in a finite number of steps is related to the third law. It does explain why the third law might imply that you can't reach absolute zero in an adiabatic process for a substance that forms a nondegenerate perfect crystal, but that argument doesn't apply to things with residual entropy (e.g. glasses) and doesn't apply to the most general "processes" or "steps" that one might imagine. So I'm still confused (and a little bit skeptical) about the connection, and I'll go to the library when I get a chance. --Steve (talk) 06:18, 7 November 2008 (UTC)
Found this in the article Absolute zero: "The Nernst postulate identifies the isotherm T = 0 as coincident with the adiabat S = 0, although other isotherms and adiabats are distinct. As no two adiabats intersect, no other adiabat can intersect the T = 0 isotherm. Consequently no adiabatic process initiated at nonzero temperature can lead to zero temperature. (≈ Callen, pp. 189–190) An even stronger assertion is that It is impossible by any procedure to reduce the temperature of a system to zero in a finite number of operations. (≈ Guggenheim, p. 157)" I think it should be clarified, as I don't understand the last sentence completely. Would be nice if someone could provide a clear, understandable proof. Anyway, I remember to have learned also that the unreachability of absolute zero is a direct consequence of the third law. So I would vote to include it. -- O.mangold (talk) 18:10, 17 August 2010 (UTC)

## "all antiparallel"

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)

"...with neighboring pairs of moments antiparallel to each other". --Steve (talk) 01:17, 27 November 2008 (UTC)

## Variable descriptions

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)

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)

## Mathematical Expression

Mathematical expression could make the Nernst postulate more clear.Nobleness of Mind (talk)

In an isothermal process

${\displaystyle \Delta G=\Delta H-T\Delta S\,}$.

${\displaystyle {\Delta H-\Delta G \over T}=\Delta S\,}$.

${\displaystyle {\frac {d\Delta H}{dT}}\left.{\!\!{\frac {}{}}}\right|_{T=0}-{\frac {d\Delta G}{dT}}\left.{\!\!{\frac {}{}}}\right|_{T=0}=\lim _{T\to 0}\Delta S}$

${\displaystyle \lim _{T\to 0}\Delta S=0\,}$

Since ${\displaystyle \Delta H\,}$ and ${\displaystyle \Delta G\,}$ have the same slope at ${\displaystyle T=0\,}$.Nobleness of Mind (talk) —Preceding undated comment added 08:45, 9 August 2010 (UTC).

The section on mathematical evaluation doesn't cite any sources. It's also not very illuminating. How do we know that ${\displaystyle \Delta H\,}$ and ${\displaystyle \Delta G\,}$ have the same slope at ${\displaystyle T=0}$? I think this whole section should be removed. --jwmerrill
I deleted it -- It looks like original research, and certainly is contradicted by mainstream thermodynamics references. Nobleness of Mind, I appreciate that you put so much effort into the article, sorry that we have to delete it, and I encourage you to post your derivations on your own website, discuss them on physicsforums.com or elsewhere, publish them, etc. You can still find the exact words you wrote here. --Steve (talk) 20:09, 17 August 2010 (UTC)

## residual entropy

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)

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)

## Incorrect definition

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)

## 298 kelvins

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 (talkcontribs) 06:09, 5 October 2011 (UTC)

## 8digit's edits

The third law is not statistical - 8digits seems to have confused it for the second law. Waleswatcher (talk) 16:34, 5 February 2012 (UTC)

Regarding his/her latest edit, it's grammatically wrong and doesn't fit with the sentence immediately after ("The third law of thermodynamics is often stated that it is impossible to reduce any system to absolute zero in a finite series of operations. It is sometimes stated as follows:").

I have no problem at all including alternate versions of the 3rd law, but they should be formatted in a readable way and sourced. Waleswatcher (talk) 16:34, 5 February 2012 (UTC)

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)
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)

Yes, I agree that should be included. 8digits - As I said above, "I have no problem at all including alternate versions of the 3rd law, but they should be formatted in a readable way and sourced." If you want to include that form, you need to inser it into the body of the article and THEN mention it in the lead, it needs to be written in clear and correct English (we can help with that), it should be sourced, and it needs to be organized in a logical, pedagogically coherent way. The reason your edits keep getting reverted is that they meet none of those requirement. Thanks. Waleswatcher (talk) 04:07, 7 February 2012 (UTC)

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)

## Logical difficulties in section called "Mathematical formulation"

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
 ${\displaystyle \lim _{T\rightarrow 0}\left({\frac {\partial S(T,X)}{\partial X}}\right)_{T}=0.}$ (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)

## Rephrased quotes in introduction

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)

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)

## Nernst-Simon statement

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)