🚀 go-pugleaf

Originally, the second law of thermodynamics appeared in 1824 as the
conclusion in an argument advanced by Carnot:

Premise 1: Heat is an indestructible substance (cannot be converted
into work in the heat engine).
Premise 2: Perpetuum mobile of the first kind is impossible.
Conclusion: All heat engines working reversibly between the same two
temperatures have the same efficiency.

Carnot's 1824 argument was valid but Premise 1 turned out to be false
in the end (in fact, heat IS converted into work in the heat engine).
The crucial question:

How can a FALSE premise be indispensable in the deduction of a TRUE
conclusion?

has never been asked. (Those who would think that Premise 1 was not
indispensable for Carnot's argument should try to deduce the
conclusion from Premise 2 alone).

Let me advance a hypothesis: If the crucial question had been both
asked and answered, the following sad texts would never have been
written:

http://www.guardian.co.uk/science/2005/nov/22/schools.g2
"We are nearing the end of the "World Year of Physics", otherwise
known as Einstein Year, as it is the centenary of his annus mirabilis
in which he made three incredible breakthroughs, including special
relativity. In fact, it was 100 years ago yesterday that he published
the most famous equation in the history of physics: E=mc2. But instead
of celebrating, physicists are in mourning after a report showed a
dramatic decline in the number of pupils studying physics at school.
The number taking A-level physics has dropped by 38% over the past 15
years, a catastrophic meltdown that is set to continue over the next
few years. The report warns that a shortage of physics teachers and a
lack of interest from pupils could mean the end of physics in state
schools. Thereafter, physics would be restricted to only those
students who could afford to go to posh schools. Britain was the home
of Isaac Newton, Michael Faraday and Paul Dirac, and Brits made world-
class contributions to understanding gravity, quantum physics and
electromagnetism - and yet the British physicist is now facing
extinction. But so what? Physicists are not as cuddly as pandas, so
who cares if we disappear?"

http://www.guardian.co.uk/science/2007/may/22/highereducation.education
Harry Kroto: "The wrecking of British science....The scientific method
is based on what I prefer to call the inquiring mindset. It includes
all areas of human thoughtful activity that categorically eschew
"belief", the enemy of rationality. This mindset is a nebulous mixture
of doubt, questioning, observation, experiment and, above all,
curiosity, which small children possess in spades. I would argue that
it is the most important, intrinsically human quality we possess, and
it is responsible for the creation of the modern, enlightened portion
of the world that some of us are fortunate to inhabit. Curiously, for
the majority of our youth, the educational system magically causes
this capacity to disappear by adolescence.....Do I think there is any
hope for UK? I am really not sure."

Pentcho Valev wrote:

Kelvin's version of the second law of thermodynamics: It is impossible
to perform a cyclic process with no other result than that heat is
absorbed from a reservoir, and work is performed.

THEOREM: Kelvin's version of the second law is true if and only if,
whenever two INTERACTING heat engines absorb heat from a reservoir
(the surroundings) and perform reversible work, the following equality
of partial derivatives holds:

(dF1 / dX2)_X1 = (dF2 / dX1)_X2

where "d" is the sign for partial derivative, F1 and F2 are work-
producing forces and X1 and X2 are the respective displacements. If
the two partial derivatives are not equal, the second law is false.

Consider INTERACTING "chemical springs". There are two types of
macroscopic contractile polymers which on acidification (decreasing
the pH of the system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
Dan W. Urry, "Physical Chemistry of Biological Free Energy
Transduction As Demonstrated by Elastic Protein-Based Polymers"

Polymers designed by Urry (U) absorb protons on stretching (as their
length, Lu, increases), whereas polymers designed by Katchalsky (K)
release protons on stretching (as their length, Lk, increases). (See
discussion on p. 11020 in Urry's paper).

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, if the
second law is true, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu>0 and Fk>0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can be
assessed from experimental results reported on p. 11020 in Urry's
paper. As K is being stretched (Lk increases), it releases protons,
the pH decreases and, accordingly, Fu must increase. Therefore, (dFu/
dLk)_Lu is positive. In contrast, as U is being stretched (Lu
increases), it absorbs protons, the pH increases and Fk must decrease.
Therefore, (dFk/dLu)_Lk is negative.

One partial derivative is positive, the other negative: this proves
that the second law of thermodynamics is false.

Pentcho Valev
pvalev@yahoo.com