More ENTROPY-GATE:

For a closed system doing reversible work of expansion the first law
of thermodynamics takes the form

dU = dQ - PdV /1/

where dU is the internal energy change, dQ is the heat absorbed, P is
pressure and V is volume. Since the system is CLOSED and undergoes
reversible changes the entropy change is, by definition, dS=dQ/T and /
1/ becomes:

dU = TdS - PdV /2/

J. Gibbs managed to convince the world that, if the system is OPEN
(substances are added to it), /2/ should be replaced by

dU = TdS - PdV + SUM mu_i dn_i /3/

where mu_i is the chemical potential and n_i is the amount of the ith
component. However Gibbs failed to explain the meaning of the entropy
change, dS, for an OPEN system. Was dS again equal to dQ/T, as it is
for a closed system, or was dS equal to something else when substances
were added to the system?

The fact that dS was not defined for open systems made the equation /
3/ so fashionable (scientists adore equations with undefined terms)
that in the end /3/ was called "the fundamental equation of
thermodynamics":

L. McGlashan, Chemical thermodynamics, Academic Press, London (1979),
pp. 72-73: "For an infinitesimal change in the state of a phase alpha
we write
dU = T dS - p dV + SUM mu_B dn_B (1)
We regard equation (1) as an axiom and call it the fundamental
equation for a change of the state of a phase alpha. It is one half of
the second law of thermodynamics. We do not ask where it comes from.
Indeed we do not admit the existence of any more fundamental relations
from which it might have been derived. Nor shall we here enquire into
the history of its formulation, though that is a subject of great
interest to the historian of science. It is a starting point ; it must
be learnt by heart."

Yet scientists somehow felt that a new explicit definition of dS could
bring even more career and money. The quickest among them, Ilya
Prigogine, simply combined /1/ and /3/ and obtained

dS = dQ/T - (1/T)SUM mu_i dn_i /4/

That was a new incredible definition of the entropy change (the
scientific community had never seen anything like this) so the Nobel
Committee immediately gave Prigogine the Nobel Prize.

Pentcho Valev wrote:

http://web.mit.edu/keenansymposium/o...und/index.html
Arthur Eddington: "The law that entropy always increases, holds, I
think, the supreme position among the laws of Nature. If someone
points out to you that your pet theory of the universe is in
disagreement with Maxwell's equations - then so much the worse for
Maxwell's equations. If it is found to be contradicted by observation
- well, these experimentalists do bungle things sometimes. But if your
theory is found to be against the second law of thermodynamics, I can
give you no hope; there is nothing for it but to collapse in deepest
humiliation."

http://www.beilstein-institut.de/boz...nishBowden.htm
ATHEL CORNISH-BOWDEN: "The concept of entropy was introduced to
thermodynamics by Clausius, who deliberately chose an obscure term for
it, wanting a word based on Greek roots that would sound similar to
"energy". In this way he hoped to have a word that would mean the same
to everyone regardless of their language, and, as Cooper [2] remarked,
he succeeded in this way in finding a word that meant the same to
everyone: NOTHING. From the beginning it proved a very difficult
concept for other thermodynamicists, even including such accomplished
mathematicians as Kelvin and Maxwell; Kelvin, indeed, despite his own
major contributions to the subject, never appreciated the idea of
entropy [3]. The difficulties that Clausius created have continued to
the present day, with the result that a fundamental idea that is
absolutely necessary for understanding the theory of chemical
equilibria continues to give trouble, not only to students but also to
scientists who need the concept for their work."

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."

ftp://ftp.esat.kuleuven.ac.be/pub/SI...orts/06-46.pdf
"From the pedagogical point of view, thermodynamics is a disaster. As
the authors rightly state in the introduction, many aspects are
"riddled with inconsistencies". They quote V.I. Arnold, who concedes
that "every mathematician knows it is impossible to understand an
elementary course in thermodynamics". Nobody has eulogized this
confusion more colorfully than the late Clifford Truesdell. On page 6
of his book "The Tragicomical History of Thermodynamics" 1822-1854
(Springer Verlag, 1980), he calls thermodynamics "a dismal swamp of
obscurity". Elsewhere, in despair of trying to make sense of the
writings of some local heros as De Groot, Mazur, Casimir, and
Prigogine, Truesdell suspects that there is "something rotten in the
(thermodynamic) state of the Low Countries" (see page 134 of Rational
Thermodynamics, McGraw-Hill, 1969)."

Pentcho Valev