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Entropy increase



There is another interesting thermodynamic problem that we could resolve
(if there is interest of course). The most popular version of the second
law says that entropy always increases (in an isolated or adiabatically
isolated system). This statement originates from two premises raised by
Clausius:

Premise 1 (explicit): Closed integral of dQ/T =< 0

Premise 2 (implicit): Any irreversible process can be closed into a cycle
by a reversible process.

If the premises are true, the law of entropy increase can be shown to be
true as well. If the premises are false, we shall have to decide what to
do. But first let us see if the premises are true. In

http://philsci-archive.pitt.edu/archive/00000313/00/engtot.pdf

you can see Clausius' original "proof" of the validity of Premise 1. Do you
like it? Please think of a counterexample. Then please think of a
counterexample to Premise 2. There ARE counterexamples to both premises.

I am not sure I could convince anybody to think on this but still a teacher
should expect a student to go to him/her and ask: "How do you know that the
entropy always increases?"

Pentcho