Dear Jerry,
The foundational logic of thermodynamics (see Josiah Willard Gibbs "On
the Equilibrium of Heterogeneous Substances", 1875–1878) does not depend
on equation of state at all. The ideal gas law as such has nothing to do
with the foundational logic in thermodynamics.
As for chemical reaction, the chemical variable solves perfectly the
problem you describe. Chemical reactions are successfully treated in
chemical thermodynamics for ages. Please just open for example Peter
Atkins, Physical Chemistry.
By the way, above I am not talking about philosophy of science. I am
talking about thermodynamics as it is employed in science.
Best wishes,
Evgenii
On 28.06.2014 20:11 Jerry LR Chandler said the following:
Evgenii, List:
On Jun 28, 2014, at 3:01 AM, Evgenii Rudnyi wrote:
On 27.06.2014 19:26 Jerry LR Chandler said the following:
The concept of entropy as a scientific concept is a rigorous
mathematic concept. It is an abstract concept, strictly limited
to the flow of HEAT (not matter) in a closed system AT
EQUILIBRIUM.
I would not agree.
Then, you do not accept the foundational logic of thermodynamics,
which is derived and "validated" by the so-called "perfect gas
laws".
The foundational equation is:
Pressure x Volume is equal to a number x constant x temperature
(where the term number refers to any positive real number, "constant"
is called the Ideal Gas Constant (a fixed value) and the symbol x
represents the mathematical concept of multiplication.)
In the symbol system of real numbers and variables, the same equation
is expressed with a different set of symbols:
PV=nRT.
It is critical to note that the critical notion behind this equation
is that with a changes in volume, pressure often result in the
changes of temperature. The concept of time is introduced as a
continuous variable of differentiation in the relating the
relationships among temperature, volume and pressure. The temperature
changes are mathematically related to energy changes and and a new
concept, entropy, is introduced as relation between heat and
temperature. Essentially, the concept of entropy is much like the
notion of a very complicated parameter that is a property of the
closed system in its totality. (A crude way of stating that the
thermodynamic variables form a "bilinear group.")
While the mathematics of thermodynamics is well established, the
application of the mathematical system is severely bounded by the
concept of the ideality of gases being treated as point particles
(aka Aristotelian atoms.) In fact, atoms of a gas condense to form a
finite volume of liquid, that is, pragmatically, real gases are not
ideal gases. (Invisible steam can be condensed into drinking
water!)
You write:
First, I would place 'entropy' at the same shelf with for example
'gravitational force'.
Based, in part, on the above discussion, I would argue that entropy
is, at best, a third order and highly ARTIFICIAL concept, that plays
a unique scientific role in relating the symbols of mathematics to
the symbolic representation of ideal gases as physical particles.
The logical symbol system of chemistry and changes in chemical
bonding are not expressed in this frame work of continuous
mathematics. Atomic numbers ( as representamen of electrical
particles) are NOT real numbers and are not part of the systems of
differential equations.
You write:
The change of the number of moles (dn_i) is in any textbook on
thermodynamics.
I agree. But what does it mean? The mathematical term, "d(n-i)"
merely expresses a change in number, NOT a chemical change which must
be expressed in terms of the chemical symbol system. Thus the term
d(n_i) is chemically meaningless except that the concept of mole
expresses an approximate number. It does NOT express the quantity of
electricity as in atomic numbers.
In fact, this discussion has far deeper scientific origins than you
might suspect. That is, the "System International" which grounds the
relationships among representamen of physics, excludes the
representation of chemical symbols.
So, Evgenii, I understand your arguments and the metaphysics which
motivate them. I disagree for many reasons which can be summarized as
follows:
Pragmatic application of thermodynamic equations to life (and
chemistry) require the creation of unique relations among five
different symbol systems - ordinary rhetoric, mathematics, physic (SI
units), chemistry and genetics.
The broad pragmatic utility of the thermodynamics discipline is not a
basis for generalization to universal meanings in all systems at all
times and all places. The scientific relations among multiple symbol
systems is an open problem.
Many if not most philosophers of science will find my views as
heretical. So be it, but it is simply not so! I accept the
pragmatic utility of the discipline and its sound mathematical
principles. The simple question wrt to the meaning of thermodynamic
"Laws" is a pragmatic one. When are thermodynamic laws useful and
when are they pragmatically virtually useless?
Cheers
Jerry
(Please note that it has required nearly two hours to draft this
email. It is an expensive undertaking from a temporal perspective,
one that I can seldom afford.)
Evgenii
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