View Single Post
  #6  
Old November 9th 11, 05:53 PM posted to sci.astro,sci.math
Radhakrishnamurty Padyala
external usenet poster
 
Posts: 1
Default VERSIONS OF THE SECOND LAW OF THERMODYNAMICS

On Nov 8, 12:02*am, Pentcho Valev wrote:
Carnot dealt with two reversible heat engines which DID NOT INTERACT.
In 1850 Clausius used NON-INTERACTING heat engines again:

http://www.mdpi.org/lin/clausius/clausius.htm
"Ueber die bewegende Kraft der Wärme", 1850, Rudolf Clausius: "Carnot
assumed, as has already been mentioned, that the equivalent of the
work done by heat is found in the mere transfer of heat from a hotter
to a colder body, while the quantity of heat remains undiminished. The
latter part of this assumption--namely, that the quantity of heat
remains undiminished--contradicts our former principle, and must
therefore be rejected... (...) It is this maximum of work which must
be compared with the heat transferred. When this is done it appears
that there is in fact ground for asserting, with Carnot, that it
depends only on the quantity of the heat transferred and on the
temperatures t and tau of the two bodies A and B, but not on the
nature of the substance by means of which the work is done. (...) If
we now suppose that there are two substances of which the one can
produce more work than the other by the transfer of a given amount of
heat, or, what comes to the same thing, needs to transfer less heat
from A to B to produce a given quantity of work, we may use these two
substances alternately by producing work with one of them in the above
process. At the end of the operations both bodies are in their
original condition; further, the work produced will have exactly
counterbalanced the work done, and therefore, by our former principle,
the quantity of heat can have neither increased nor diminished. The
only change will occur in the distribution of the heat, since more
heat will be transferred from B to A than from A to B, and so on the
whole heat will be transferred from B to A. By repeating these two
processes alternately it would be possible, without any expenditure of
force or any other change, to transfer as much heat as we please from
a cold to a hot body, and this is not in accord with the other
relations of heat, since it always shows a tendency to equalize
temperature differences and therefore to pass from hotter to colder
bodies."

NON-INTERACTION means that the work-producing force generated by the
first engine, F1, is independent of the displacement, X2, in the
second engine, and vice versa:

F1 = F1(X1, X2); F2 = F2(X1, X2)

dF1/dX2 = dF2/dX1 = 0

where "d" is the partial derivative symbol. It can be shown that, if
the two reversible heat engines DO INTERACT and the conditions are
isothermal, the equation:

dF1/dX2 = dF2/dX1

is a consequence of the second law of thermodynamics (Kelvin's
version). Accordingly, if the partial derivatives dF1/dX2 and dF2/dX1
are not equal, heat from a single reservoir CAN, cyclically, be
converted into work, in violation to the second law of thermodynamics.
Consider, for instance, 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 Fu0 and Fk0 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


The examples wherein heat is not converted into some other form of
energy in a cyclic process, do not come under the purview of second
law of thermodynamics. For example the polymer contraction - extension
reversible cycle, or the Capacitor between whose plates a dielectric
is introduced and withdrawn in a reversible cyclic process do not
concern with the second law; they concern with the first law only.
Since the aim is to show that second law of thermodynamics is false,
those examples do not serve the intended purpose.

I must mention, however, that the second law of thermodynamics suffers
from inconsistencies: The standard statements of the law due to
Caratheodory and Kelvin are not equivalent. See http://arxiv.org/abs/1102.4235.

Similarly, Clausius and Kelvin statements of the second law are not
equivalent.