Talk:Second law of thermodynamics

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 Definition Entropy S is a state variable of a thermodynamic system; when a system of temperature T absorbs heat DQ reversibly, then dS = DQ/T; during an irreversible (spontaneous) state change dS > DQ/T. [d] [e]
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What does "rest heat" mean?

Paul, in the "Discussion of the second law" section, you refer to Qc as the "rest heat". Did you mean "heat at rest" or did you mean "the rest of the heat" or the "remaining heat"? I made no changes, but I do think that if you meant "remaining heat", then the wording needs to be changed. Perhaps to "remainder heat"?

If, on the other hand, you really meant "heat at rest", then the wording also needs to be changed, because "rest heat" needs to be clarified as to what is meant. Milton Beychok 19:58, 6 November 2009 (UTC)

About the use of DQ

Paul, in the term DQ/T. What is D? is that meant to be Delta? If so, then I think it might be better to use the symbol δ or Δ. I am certainly not the mathematician you are by any stretch of imagination, but I simply have never seen that terminology used to denote a small amount of heat (or anything else). Milton Beychok 20:17, 6 November 2009 (UTC)

How about using this quote somewhere in this article?

The statement by Clausius that "Die entropie der welt strebt einem maximum zu" (The entropy of the universe tends (strives?) to a maximum) is one that that has stuck in my mind ever since I first heard it in a university thermodynamic class over 65 years ago. How about using that quote somewhere in this article? Milton Beychok 20:38, 6 November 2009 (UTC)

Revised Metadata template

Changed the cat "Chemical engineering" to sub "Chemical Engineering", because Chemical Engineering (with a captal E) is a subgroup. Also added the cat "Engineering". Milton Beychok 03:00, 7 November 2009 (UTC)

Populated the Related Articles subpage

I also populated the Related Articles subpage, Paul. If you disagree with any of the links, just revise or delete them. Milton Beychok 03:18, 7 November 2009 (UTC)


Milt, thank you for reading the article. I really appreciate it.

First a very minor thing: Fig. versus figure/Figure. Different journals use different standards. I leave it as you changed it. Further I used "equation (1)", in some journals this would be Eq. (1) and in others Equation (1).

By rest heat I indeed mean "remaining", "remainder", or "waste" heat, in any case the heat that a power station flushes into a river or a nearby sea (this reminds me of the Manatees that I saw swimming in the warm water near a nuclear reactor at Crystal River on the Florida Gulf coast). What term would you prefer?

About DQ: I don't like δQ because it is used for variation of Q (something different, defined for functions). I don't like ΔQ because it would mean Q(x2)−Q(x1) for some parameter x, and the point is that Q is not a function of any x, it is just a small quantity. I've learned it a long time ago as a barred "d" (in some TeX implementations this is \dj), but I couldn't find that character. I've seen several books (among them by T. L. Hill) that use the capital D and that is why I used it. Some texts refer to it as an "inexact" differential, but I avoided that term, in my view it is not a differential, although by the magic of the 2nd law it becomes one if you divide it by T. Would you prefer a barred "d" and do you know where to find it?

PS. I checked Guggenheim and he writes simply q and w for small amounts of heat and work.

I would love to use the Clausius quote, provided I can give the exact source. Would you know where to find it? Further I read in the meantime (in a book by T. S. Kuhn) that Kelvin was the first to realize that the entropy of the universe increases. But still, when you know where Clausius wrote it I'm more than happy to include it.

Cat/related articles is OK, thank you for taking care of that.

--Paul Wormer 09:08, 7 November 2009 (UTC)

Taking the above items, one at a time:
  • As for "rest heat", I would prefer "remaining heat"
  • As for DQ, how about just defining what D means by a brief footnote? Or describe it in the text just as you did in Internal energy?
  • Gibbs quotes that saying by Clausius of "Die entropie der welt strebt einem maximum zu" in his paper "On the Equilibrium of Heterogeneous Substances" and he references it as "Clausius, R. (1865), The Mechanical Theory of Heat—with its Application to the Steam Engine and to Properties of Bodies, London:John van Voorst, MDCCCLXVII. I found that here and here (see reference 7). I also found it here in Google books and then using the search function for "die entropie".
Milton Beychok 19:05, 7 November 2009 (UTC)
The quote is also contained in the 1864 volume "Abhandlungen über die mechanische Wärmetheorie", at p. 44. Please note the capitalization. --Daniel Mietchen 20:48, 7 November 2009 (UTC)
Daniel's reference is very interesting, because I wrote in entropy that Clausius introduced the term "Entropie" in a 1865 paper that appeared too late to be included in his 1864 book. I now see that entropy is included in the 1864 book. I got my (erroneous) information from a 1977 book by T. S. Kuhn (History of black body radiation) who is very explicit about the history of the term. If we can't trust Kuhn, who can we trust? I'll change entropy and will adapt the present article later today.--Paul Wormer 07:47, 8 November 2009 (UTC)
PS. I take back what I just wrote: Google books gives in fact two books, part I appeared in 1864 and does not contain entropy and part II is of 1867 and contains a 1865 paper (by Clausius) that introduces entropy. So we may trust Kuhn after all. In my earlier quick scan I overlooked the fact that Google books has the parts in one file.--Paul Wormer 10:26, 8 November 2009 (UTC)