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THE CARNOT THEOREM:

http://philsci-archive.pitt.edu/archive/00000313/
pp. 17-19: "Sadi Carnot's Reflexions sur la Puissance motrice du Feu
Appeared in 1824. It was this work which eventually led to the birth
of thermodynamics. Still, Carnot's memoir itself does not belong to
what we presently understand as thermodynamics. It was written from
the point of view that heat is an indestructible substance, the so-
called calorique. This assumption proved to be in conflict with
empirical evidence. However, Carnot’s main theorem did agree with
experience. Classical thermodynamics was born from the attempts around
1850 to save Carnot's theorem by placing it on a different footing.
(...) CARNOT'S THEOREM: Let the furnace and refrigerator temperatures
T1 and T2 be given (with T1 > T2). Then: (i) all heat engines
operating in a reversible cycle have the same efficiency. Their
efficiency is therefore a universal expression depending only on the
temperatures T1 and T2. (ii) all other heat engines have an efficiency
which is less than or equal to that obtained by reversible cycles."

Clausius "saved" Carnot's theorem in this way:

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."

Questions: Did Carnot's false assumption really lead to a true
conclusion ("However, Carnot’s main theorem did agree with
experience")? If it did, the salvation argument offered by Clausius is
valid. If it did not, the salvation argument offered by Clausius is
invalid. Is it extremely difficult to verify the validity of
Clausius's salvation argument?

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