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> > In 1824 Sadi Carnot deduced the prototype of the second law of
> > thermodynamics:
>
> > All reversible heat engines working between two fixed temperatures
> > have the same efficiency.
>
> > from two premises:
>
> > 1. Perpetuum mobile of the first kind is impossible.
>
> > 2. Heat is conserved (cannot be converted into work by the heat
> > engine).
>
> > Then the second premise was officially declared false but the
> > conclusion, the prototype of the second law of thermodynamics,
> > remained gloriously true. More precisely, the glory was introduced by
> > Clausius who, in 1850, managed to convince the world that the false
> > premise should be forgotten and replaced by a true one:
>
> > 2'. Heat flows spontaneously from hot to cold.
>
> > Theoreticians and philosophers of science have never seen any problem
> > in the fact that, originally, a false premise was ESSENTIAL in the
> > deduction of a true conclusion. At least they should have considered
> > the following hypothesis:
>
> > The conclusion, the prototype of the second law of thermodynamics, is
> > false as well; Clausius' 1850 ad hoc deduction was invalid.
>
> Why Clausius' 1850 ad hoc deduction is invalid: Clausius' claims given
> below in capitals: "THE ONLY CHANGE" and "WITHOUT ANY EXPENDITURE OF
> FORCE OR ANY OTHER CHANGE" - are false:
>
> http://web.lemoyne.edu/~giunta/Clausius.html
> "Ueber die bewegende Kraft der Warme" 1850 Rudolf Clausius: "Carnot
> assumed, as has already been mentioned, that the equivalent of the
> work done by heat is found in the mere transfer of heat from a hotter
> to a colder body, while the quantity of heat remains undiminished. The
> latter part of this assumption--namely, that the quantity of heat
> remains undiminished--contradicts our former principle, and must
> therefore be rejected... (...) It is this maximum of work which must
> be compared with the heat transferred. When this is done it appears
> that there is in fact ground for asserting, with Carnot, that it
> depends only on the quantity of the heat transferred and on the
> temperatures t and tau of the two bodies A and B, but not on the
> nature of the substance by means of which the work is done. (...) If
> we now suppose that there are two substances of which the one can
> produce more work than the other by the transfer of a given amount of
> heat, or, what comes to the same thing, needs to transfer less heat
> from A to B to produce a given quantity of work, we may use these two
> substances alternately by producing work with one of them in the above
> process. At the end of the operations both bodies are in their
> original condition; further, the work produced will have exactly
> counterbalanced the work done, and therefore, by our former principle,
> the quantity of heat can have neither increased nor diminished. THE
> ONLY CHANGE will occur in the distribution of the heat, since more
> heat will be transferred from B to A than from A to B, and so on the
> whole heat will be transferred from B to A. By repeating these two
> processes alternately it would be possible, WITHOUT ANY EXPENDITURE OF
> FORCE OR ANY OTHER CHANGE, to transfer as much heat as we please from
> a cold to a hot body, and this is not in accord with the other
> relations of heat, since it always shows a tendency to equalize
> temperature differences and therefore to pass from hotter to colder
> bodies."
>
> In fact, the process considered by Clausius and essential for his
> deduction presupposes the constant action of an OPERATOR; this
> operator constantly and unavoidably undergoes CHANGES, changes that
> are absent when heat spontaneously "shows a tendency to equalize
> temperature differences and therefore to pass from hotter to colder
> bodies".

Encouraged by his 1850 successful introduction of a new logic of
science (when a precious conclusion follows from a false premise, you
are allowed to abandon the premise and rededuce the precious
conclusion from another premise, true this time), later Clausius
gloriously introduced the concept of entropy. Yet consider:

http://www.me.umn.edu/education/courses/me3331/modules/3331-Mod-28.pdf

more precisely "The Clausius Theorem" and the assumption entitled
"Equivalent reversible and irreversible processes" according to which
any "Irreversible Process" can be closed by a reversible process (in
this case consisting of a "Reversible Adiabat", "Reversible Isotherm"
and "Reversible Adiabat") to become a cycle. Is the assumption
correct? If it is not, what remains of the concept of entropy?

This is one of the most dangerous questions in thermodynamics. For 140
years it has been asked only once, by Jos Uffink:

http://philsci-archive.pitt.edu/archive/00000313/
p.39: "A more important objection, it seems to me, is that Clausius
bases his conclusion that the entropy increases in a nicht umkehrbar
[irreversible] process on the assumption that such a process can be
closed by an umkehrbar [reversible] process to become a cycle. This is
essential for the definition of the entropy difference between the
initial and final states. But the assumption is far from obvious for a
system more complex than an ideal gas, or for states far from
equilibrium, or for processes other than the simple exchange of heat
and work. Thus, the generalisation to all transformations occurring in
Nature is somewhat rash."

That is, again, a possibly false premise has given a precious
conclusion. The answer to the dangerous question is implicit in
Uffink's statement:

http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink: "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."

At the end of his career Clausius, just like Einstein, became somewhat
honest but it was too late:

http://philsci-archive.pitt.edu/archive/00000313/
"On many occasions Clausius was criticised by his contemporaries. I do
not know If, in his own time, he was criticised in particular for his
famous formulation of the second law as the increase of the entropy of
the universe. However, Kuhn (1978, pp. 13-15, p. 260) has pointed out
the remarkable fact that in the book (Clausius 1876) he eventually
composed from his collected articles, every reference to the entropy
of the universe and even to the idea that entropy never decreases in
irreversible processes in adiabatically isolated systems is deleted!
The most general formulation given to the second law in this book,
which may be regarded as the mature presentation of Clausius’ ideas,
is again the relation (10), where the system is supposed to undergo a
cycle, and entropy increase is out of the question."

Pentcho Valev
pvalev@yahoo.com