Tragicomical Thermodynamics

The Clausius statement of the second law of thermodynamics:

"Heat can never pass from a colder to a warmer body without some other change connected therewith, occurring at the same time."

This version of the second law of thermodynamics is very popular because, like "Entropy always increases", it makes no sense (scientists love nonsensical statements and never abandon them):

http://link.springer.com/book/10.100...-1-4613-9444-0
Clifford Truesdell, The Tragicomical History of Thermodynamics, 1822–1854, p. 333: "Clausius' verbal statement of the "Second Law" makes no sense, for "some other change connected therewith" introduces two new and unexplained concepts: "other change" and "connection" of changes. Neither of these finds any place in Clausius' formal structure. 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."

Here is an oversimplified presentation of Clausius' 1850 argument:

Premise: Heat can never pass from a colder to a warmer body SPONTANEOUSLY.

Conclusion: Heat can never pass from a colder to a warmer body REVERSIBLY.

The premise is (trivially) true but the conclusion does not follow from it (the argument is invalid). This would have been easily noticed if Clausius had not made another mistake that fatally confused the issue: his 1850 formulation of the conclusion actually coincided with the premise. That is, Clausius deduced, even though invalidly, the conclusion

"Heat can never pass from a colder to a warmer body REVERSIBLY",

but the terms he used in the formulation of the conclusion were misleading so nowadays the conclusion is known as

"Heat can never pass from a colder to a warmer body without some other change connected therewith, occurring at the same time",

a statement which coincides with the premise.

Here is Clausius' 1950 text:

http://www.mdpi.org/lin/clausius/clausius.htm
"Ueber die bewegende Kraft der Wärme", 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."

It is easy to see that the two-substances process considered by Clausius presupposes the 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". So the trivial fact that, in a spontaneous process, in the absence of an operator, heat always flows from hot to cold by no means implies that heat will flow from hot to cold in a non-spontaneous operator-driven process as the one considered by Clausius.

Clausius' argument is not just invalid; Clausius additionally confused it so it became "not even wrong". Such idiocies are impossible to eradicate. Like Clausius' 1865 argument concluding that "Entropy always increases", and like Einstein's 1905 argument leading to the idiotic "travel into the future", Clausius' 1850 argument is a malignancy that belongs to the spirit of the civilization. Malignancies affecting human mind and their metastases will destroy the civilization quicker than material catastrophes.

Pentcho Valev