🚀 go-pugleaf

The MAGICIAN'S HAT model of science in action. Initially, an idiotic
"axiom" is advanced; then magicians are free to extract career, money,
Nobel prizes etc. from it; all along believers should sing dithyrambs,
"until any single one of the host of equations that can be derived
from it....has been shown experimentally to be false":

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. It may be allowed to stand as an axiom until any
single one of the host of equations that can be derived from it (with
the help of other axioms of thermodynamics) has been shown
experimentally to be false."

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 the equation:

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". 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. Believers do not
know how /4/ can be "shown experimentally to be false". Similarly,
they do not know how the statement "The greenness of the crocodile
exceeds its length" can be shown experimentally to be false.

Pentcho Valev
pvalev@yahoo.com