FALSE PREMISES AND INVALID ARGUMENTS

In 1850 Clausius deduced (the prototype of) the second law of
thermodynamics 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."

I have always been claiming that Clausius' premises are true but the
argument is INVALID. Here are the premises:

1. (TRUE) In the absence of irreversible changes in the surroundings
influencing the process, heat always flows from hot to cold.

2. (TRUE) Perpetuum mobile of the first kind is impossible.

In fact, there is a third FALSE premise used by Clausius which, if
explicitly added to the set of premises, makes the argument VALID:

3. (FALSE) The process Clausius considers occurs in the absence of
irreversible changes in the surroundings influencing it.

In physical sciences, invalidity of arguments can be interpreted in
terms of falsehood of premises.

Pentcho Valev