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Article #675

Re: THE MYSTERY OF THE CARNOT THEOREM

#675
From: Pentcho Valev
Date: Sun, 28 Mar 2010 06:46
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Einstein's relativity is not the first "theory" that just silently
died. Classical thermodynamics has had a similar heyday but now even
epitaph-like texts are difficult to find:

http://www.beilstein-institut.de/bozen2004/proceedings/CornishBowden/CornishBowden.htm
Athel Cornish-Bowden: "The concept of entropy was introduced to
thermodynamics by Clausius, who deliberately chose an obscure term for
it, wanting a word based on Greek roots that would sound similar to
"energy". In this way he hoped to have a word that would mean the same
to everyone regardless of their language, and, as Cooper [2] remarked,
he succeeded in this way in finding a word that meant the same to
everyone: NOTHING. From the beginning it proved a very difficult
concept for other thermodynamicists, even including such accomplished
mathematicians as Kelvin and Maxwell; Kelvin, indeed, despite his own
major contributions to the subject, never appreciated the idea of
entropy [3]. The difficulties that Clausius created have continued to
the present day, with the result that a fundamental idea that is
absolutely necessary for understanding the theory of chemical
equilibria continues to give trouble, not only to students but also to
scientists who need the concept for their work."

(Here Athel Cornish-Bowden denounces thermodynamics but elsewhere he
fiercely defends it:  http://bip.cnrs-mrs.fr/bip10/valevfaq.htm )

http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink: "The historian of science and mathematician Truesdell made
a detailed study of the historical development of thermodynamics in
the period 1822–1854. He characterises the theory, even in its present
state, as 'a dismal swamp of obscurity' and 'a prime example to show
that physicists are not exempt from the madness of crowds'. He is
outright cynical about the respect with which nonmathematicians treat
the Second Law: "Clausius' verbal statement of the second law makes no
sense [. . . ]. All that remains is a Mosaic prohibition; a century of
philosophers and journalists have acclaimed this commandment; a
century of mathematicians have shuddered and averted their eyes from
the unclean. Seven times in the past thirty years have I tried to
follow the argument Clausius offers [. . . ] and seven times has it
blanked and gravelled me. [. . . ] I cannot explain what I cannot
understand." [...] What is it that makes this physical law so
obstreperous that every attempt at a clear formulation seems to have
failed? Is it just the usual sloppiness of physicists? Or is there a
deeper problem? And what exactly is the connection with the arrow of
time and irreversibility? Could it be that this is also just based on
bluff? Perhaps readers will shrug their shoulders over these
questions. Thermodynamics is obsolete; for a better understanding of
the problem we should turn to more recent, statistical theories. But
even then the questions we are about to study have more than a purely
historical importance. The problem of reproducing the Second Law,
perhaps in an adapted version, remains one of the toughest, and
controversial problems in statistical physics. [...] This summary
leads to the question whether it is fruitful to see irreversibility or
time-asymmetry as the essence of the second law. Is it not more
straightforward, in view of the unargued statements of Kelvin, the
bold claims of Clausius and the strained attempts of Planck, to give
up this idea? I believe that Ehrenfest-Afanassjewa was right in her
verdict that the discussion about the arrow of time as expressed in
the second law of the thermodynamics is actually a RED HERRING."

ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/markovsky/reports/06-46.pdf
"From the pedagogical point of view, thermodynamics is a disaster. As
the authors rightly state in the introduction, many aspects are
"riddled with inconsistencies". They quote V.I. Arnold, who concedes
that "every mathematician knows it is impossible to understand an
elementary course in thermodynamics". Nobody has eulogized this
confusion more colorfully than the late Clifford Truesdell. On page 6
of his book "The Tragicomical History of Thermodynamics" 1822-1854
(Springer Verlag, 1980), he calls thermodynamics "a dismal swamp of
obscurity". Elsewhere, in despair of trying to make sense of the
writings of some local heros as De Groot, Mazur, Casimir, and
Prigogine, Truesdell suspects that there is "something rotten in the
(thermodynamic) state of the Low Countries" (see page 134 of Rational
Thermodynamics, McGraw-Hill, 1969)."

Only a few profiteers in science are still making career and money by
publishing anything (there is no one in the world who would care about
whether the concept of entropy was VALIDLY deduced from "heat will
flow into cold but not the opposite"):

http://newsblaze.com/story/20100327150646blue.nb/topstory.html
"In 1988, Stephen Hawking gave the world A Brief History of Time. Now
Sean Carroll goes From Eternity to Here. [...] There are many ways to
think about entropy. The concept was initially expressed in terms of
thermodynamics: heat will flow into cold but not the opposite. It has
also been thought of as a trend toward chaos, and many people may want
to say that their lives increase in entropy, but this is also an
inadequate expression since chaos can be low-entropy too. Neither is
entropy just a state of equilibrium. Perhaps a good way to describe it
without invoking a long, scientific explanation is the uselessness and
inability to do work. Once a bottle of perfume opens, it will settle
into the air, which is its most likely state of configuration, and
everything about our experience tells us that it will not flow back.
But entropy is merely a tendency, and if time were an inscrutable
thing, having no affect upon us so that we may observe its passage in
years that can only be expressed in large exponents, the perfume may,
in fact, go back into the bottle. Because the perfume is initially in
the bottle, and because the rest of the universe does not seem to
exist in a state of maximum entropy, it most likely evolved from a
state of low entropy, which accounts for every moment since the Big
Bang. It is the thing before the Big Bang that galvanizes physicists
to search for more complete theories of the universe. Carroll cannot
answer every question (I'd like to think that our universe is alone,
and in lieu of that I'm partial to the baby universe explanation), but
readers should also feel stimulated and enthralled when he asks them.
After reading the book, maybe eternity won't feel so long after all."

Pentcho Valev wrote:

What is the probability that Mr. X looks like Mr. Y? Clearly the prior
(Mr. X and Mr. Y are identified but there is no additional information
concerning them) probability is virtually zero. This means that for
the argument:

Premise: Mr. X and Mr. Y are identical twins.
Conclusion: Mr. X looks like Mr. Y.

the combination "false premise, true conclusion" is virtually
impossible.

Consider an oversimplified version of the Carnot theorem:

Premise: Heat is an indestructible substance (cannot be converted into
work in the heat engine).
Conclusion (prototype of the second law of thermodynamics): The heat
engine X working between the temperatures T1 and T2 is just as
efficient as the heat engine Y working between the same temperatures.

The premise turned out to be false in the end. Is the prior
probability of the conclusion virtually zero? Is the combination
"false premise, true conclusion" virtually impossible?

Pentcho Valev
pvalev@yahoo.com
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From: Pentcho Valev <pvalev@yahoo.com>
Newsgroups: sci.physics.relativity,sci.physics,fr.sci.physique,fr.sci.astrophysique
Subject: Re: THE MYSTERY OF THE CARNOT THEOREM
Date: Sat, 27 Mar 2010 23:46:29 -0700 (PDT)
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