CARNOT'S DIFFICULTY WITH THE SECOND LAW

In 1824 Sadi Carnot deduced the second law of thermodynamics from a
premise that went against the future law of conservation of energy
(the first law of thermodynamics). Here is an oversimplified but
consonant with the quotation below presentation of (part of) Carnot's
1824 argument:

Premise: Heat is an indestructible substance (caloric) that cannot be
converted into work by the heat engine.
Conclusion: A cold body accepting part of the heat taken from the warm
body NECESSARILY assist the heat engine.

Unpublished notes written in the period 1824-1832 reveal that, after
discovering the first law of thermodynamics (much earlier than the
official discovery), Carnot started to doubt the second:

http://www.nd.edu/~powers/ame.20231/carnot1897.pdf
p. 225: Sadi Carnot: "Heat is simply motive power, or rather motion
which has changed form. It is a movement among the particles of
bodies. Wherever there is destruction of motive power there is, at the
same time, production of heat in quantity exactly proportional to the
quantity of motive power destroyed. Reciprocally, wherever there is
destruction of heat, there is production of motive power."
p. 222: Sadi Carnot: "Could a motion (that of radiating heat) produce
matter (caloric)? No, undoubtedly; it can only produce a motion. Heat
is then the result of a motion. Then it is plain that it could be
produced by the consumption of motive power, and that it could produce
this power. All the other phenomena - composition and decomposition of
bodies, passage to the gaseous state, specific heat, equilibrium of
heat, its more or less easy transmission, its constancy in experiments
with the calorimeter - could be explained by this hypothesis. But it
would be DIFFICULT TO EXPLAIN WHY, IN THE DEVELOPMENT OF MOTIVE POWER
BY HEAT, A COLD BODY IS NECESSARY; why, in consuming the heat of a
warm body, motion cannot be produced."

I think that, almost 200 years later, Carnot's question is both
relevant and unanswered:

WHY, IN THE DEVELOPMENT OF MOTIVE POWER BY HEAT, A COLD BODY IS
NECESSARY; why, in consuming the heat of a warm body [in the absence
of a cold one], motion cannot be produced [in a cyclical process]?

Pentcho Valev

I made a mistake in presenting Carnot's 1824 argument: the conclusion,
as I formulated it, characterizes today's understanding of the second
law of thermodynamics whereas in 1824 Carnot would have subscribed to
the following (oversimplified) presentation of his argument:

Premise: Heat is an indestructible substance (caloric) that cannot be
converted into work by the heat engine.
Conclusion: A cold body accepting ALL THE HEAT taken from the warm
body NECESSARILY assists the heat engine.

Clearly, if the cold body is to accept ALL THE HEAT, its presence is
absolutely necessary - otherwise the heat released by the worm body
has nowhere to go. However if the premise is false and the heat
released by the warm body is converted into work by the heat engine,
then indeed "it would be DIFFICULT TO EXPLAIN WHY, IN THE DEVELOPMENT
OF MOTIVE POWER BY HEAT, A COLD BODY IS NECESSARY".

Pentcho Valev wrote:

In 1824 Sadi Carnot deduced the second law of thermodynamics from a
premise that went against the future law of conservation of energy
(the first law of thermodynamics). Here is an oversimplified but
consonant with the quotation below presentation of (part of) Carnot's
1824 argument:

Premise: Heat is an indestructible substance (caloric) that cannot be
converted into work by the heat engine.
Conclusion: A cold body accepting part of the heat taken from the warm
body NECESSARILY assist the heat engine.

Unpublished notes written in the period 1824-1832 reveal that, after
discovering the first law of thermodynamics (much earlier than the
official discovery), Carnot started to doubt the second:

http://www.nd.edu/~powers/ame.20231/carnot1897.pdf
p. 225: Sadi Carnot: "Heat is simply motive power, or rather motion
which has changed form. It is a movement among the particles of
bodies. Wherever there is destruction of motive power there is, at the
same time, production of heat in quantity exactly proportional to the
quantity of motive power destroyed. Reciprocally, wherever there is
destruction of heat, there is production of motive power."
p. 222: Sadi Carnot: "Could a motion (that of radiating heat) produce
matter (caloric)? No, undoubtedly; it can only produce a motion. Heat
is then the result of a motion. Then it is plain that it could be
produced by the consumption of motive power, and that it could produce
this power. All the other phenomena - composition and decomposition of
bodies, passage to the gaseous state, specific heat, equilibrium of
heat, its more or less easy transmission, its constancy in experiments
with the calorimeter - could be explained by this hypothesis. But it
would be DIFFICULT TO EXPLAIN WHY, IN THE DEVELOPMENT OF MOTIVE POWER
BY HEAT, A COLD BODY IS NECESSARY; why, in consuming the heat of a
warm body, motion cannot be produced."

I think that, almost 200 years later, Carnot's question is both
relevant and unanswered:

WHY, IN THE DEVELOPMENT OF MOTIVE POWER BY HEAT, A COLD BODY IS
NECESSARY; why, in consuming the heat of a warm body [in the absence
of a cold one], motion cannot be produced [in a cyclical process]?

Pentcho Valev

On Aug 31, 1:25*pm, Pentcho Valev wrote:
I made a mistake in presenting Carnot's 1824 argument: the conclusion,
as I formulated it, characterizes today's understanding of the second
law of thermodynamics whereas in 1824 Carnot would have subscribed to
the following (oversimplified) presentation of his argument:

Premise: Heat is an indestructible substance (caloric) that cannot be
converted into work by the heat engine.
Conclusion: A cold body accepting ALL THE HEAT taken from the warm
body NECESSARILY assists the heat engine.

Clearly, if the cold body is to accept ALL THE HEAT, its presence is
absolutely necessary - otherwise the heat released by the worm body
has nowhere to go. However if the premise is false and the heat
released by the warm body is converted into work by the heat engine,
then indeed "it would be DIFFICULT TO EXPLAIN WHY, IN THE DEVELOPMENT
OF MOTIVE POWER BY HEAT, A COLD BODY IS NECESSARY".

Pentcho Valev wrote:

In 1824 Sadi Carnot deduced the second law of thermodynamics from a
premise that went against the future law of conservation of energy
(the first law of thermodynamics). Here is an oversimplified but
consonant with the quotation below presentation of (part of) Carnot's
1824 argument:

Premise: Heat is an indestructible substance (caloric) that cannot be
converted into work by the heat engine.
Conclusion: A cold body accepting part of the heat taken from the warm
body NECESSARILY assist the heat engine.

Unpublished notes written in the period 1824-1832 reveal that, after
discovering the first law of thermodynamics (much earlier than the
official discovery), Carnot started to doubt the second:

http://www.nd.edu/~powers/ame.20231/carnot1897.pdf
p. 225: Sadi Carnot: "Heat is simply motive power, or rather motion
which has changed form. It is a movement among the particles of
bodies. Wherever there is destruction of motive power there is, at the
same time, production of heat in quantity exactly proportional to the
quantity of motive power destroyed. Reciprocally, wherever there is
destruction of heat, there is production of motive power."
p. 222: Sadi Carnot: "Could a motion (that of radiating heat) produce
matter (caloric)? No, undoubtedly; it can only produce a motion. Heat
is then the result of a motion. Then it is plain that it could be
produced by the consumption of motive power, and that it could produce
this power. All the other phenomena - composition and decomposition of
bodies, passage to the gaseous state, specific heat, equilibrium of
heat, its more or less easy transmission, its constancy in experiments
with the calorimeter - could be explained by this hypothesis. But it
would be DIFFICULT TO EXPLAIN WHY, IN THE DEVELOPMENT OF MOTIVE POWER
BY HEAT, A COLD BODY IS NECESSARY; why, in consuming the heat of a
warm body, motion cannot be produced."

I think that, almost 200 years later, Carnot's question is both
relevant and unanswered:

WHY, IN THE DEVELOPMENT OF MOTIVE POWER BY HEAT, A COLD BODY IS
NECESSARY; why, in consuming the heat of a warm body [in the absence
of a cold one], motion cannot be produced [in a cyclical process]?

Pentcho Valev




Hi

It is not so that cold body nessaserely contains less energi (heat)
than a warm body.

KON

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:

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.

The second law of thermodynamics is false but heat engines converting,
isothermally, heat into work are extremely slow and incommensurable
with human practice. See more in my 2004 paper:

http://www.wbabin.net/valev/valev2.pdf
BIASED THERMAL MOTION AND THE SECOND LAW OF THERMODYNAMICS

Pentcho Valev

http://www.math.utep.edu/Faculty/sewell/AML_3497.pdf
A second look at the second law
Granville Sewell, Mathematics Department, University of Texas, El
Paso, United States
"If an increase in order is extremely improbable when a system is
closed, it is still extremely improbable when the system is open,
unless something is entering which makes it not extremely improbable.
(...) Order can increase in an open system, not because the laws of
probability are suspended when the door is open, but simply because
order may walk in through the door.... If we found evidence that DNA,
auto parts, computer chips, and books entered through the Earth's
atmosphere at some time in the past, then perhaps the appearance of
humans, cars, computers, and encyclopedias on a previously barren
planet could be explained without postulating a violation of the
second law here.... But if all we see entering is radiation and
meteorite fragments, it seems clear that what is entering through the
boundary cannot explain the increase in order observed here."

Note that Clausius originally deduced "Entropy always increases" from
an assumption equivalent to "Any irreversible process can be
reversed":

http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink, Bluff your Way in the Second Law of Thermodynamics
p.39: "A more important objection, it seems to me, is that Clausius
bases his conclusion that the entropy increases in a nicht umkehrbar
[irreversible] process on the assumption that such a process can be
closed by an umkehrbar [reversible] process to become a cycle. This is
essential for the definition of the entropy difference between the
initial and final states. But the assumption is far from obvious for a
system more complex than an ideal gas, or for states far from
equilibrium, or for processes other than the simple exchange of heat
and work. Thus, the generalisation to all transformations occurring in
Nature is somewhat rash."

Pentcho Valev

On Aug 31, 3:59*am, Pentcho Valev wrote:
In 1824 Sadi Carnot deduced the second law of thermodynamics from a
premise that went against the future law of conservation of energy
(the first law of thermodynamics). Here is an oversimplified but
consonant with the quotation below presentation of (part of) Carnot's
1824 argument:

Premise: Heat is an indestructible substance (caloric) that cannot be
converted into work by the heat engine.
Conclusion: A cold body accepting part of the heat taken from the warm
body NECESSARILY assist the heat engine.

Unpublished notes written in the period 1824-1832 reveal that, after
discovering the first law of thermodynamics (much earlier than the
official discovery), Carnot started to doubt the second:

http://www.nd.edu/~powers/ame.20231/carnot1897.pdf
p. 225: Sadi Carnot: "Heat is simply motive power, or rather motion
which has changed form. It is a movement among the particles of
bodies. Wherever there is destruction of motive power there is, at the
same time, production of heat in quantity exactly proportional to the
quantity of motive power destroyed. Reciprocally, wherever there is
destruction of heat, there is production of motive power."
p. 222: Sadi Carnot: "Could a motion (that of radiating heat) produce
matter (caloric)? No, undoubtedly; it can only produce a motion. Heat
is then the result of a motion. Then it is plain that it could be
produced by the consumption of motive power, and that it could produce
this power. All the other phenomena - composition and decomposition of
bodies, passage to the gaseous state, specific heat, equilibrium of
heat, its more or less easy transmission, its constancy in experiments
with the calorimeter - could be explained by this hypothesis. But it
would be DIFFICULT TO EXPLAIN WHY, IN THE DEVELOPMENT OF MOTIVE POWER
BY HEAT, A COLD BODY IS NECESSARY; why, in consuming the heat of a
warm body, motion cannot be produced."

I think that, almost 200 years later, Carnot's question is both
relevant and unanswered:

WHY, IN THE DEVELOPMENT OF MOTIVE POWER BY HEAT, A COLD BODY IS
NECESSARY; why, in consuming the heat of a warm body [in the absence
of a cold one], motion cannot be produced [in a cyclical process]?

Pentcho Valev



I am a newbie in Thermodynamics, having only started learning about it
over the summer.

But all the books I read suggest that "laws" of thermodynamics are
really "principles." They are laws that are known to be true by
observation, rather than based upon some hard and fast theory. In
particular, I don't think anyone has proved thermodynamics from
Newton's laws of motion.

Part of the problem is that they apply to systems in equilibrium. And
there is no such thing as a system in equilibrium. So people adopt a
notion called quasi-equilibrium, which in essence seems to mean that
the systems change sufficiently slowly that the laws of thermodynamics
are an excellent approximation.

Which is to say - I think that Carnot's question is still unanswered.
And I don't think anyone is going to find a fully rigorous answer
anytime soon.

My personal guess is that if you wait long enough, that you can
produce motion from heat. Now that time will be very, very long - way
longer than, say, the expected life of the universe. I believe that
this is a consequence of Poincare's recurrence theorem for Hamiltonian
systems: http://en.wikipedia.org/wiki/Poincar...rrence_theorem.
So in my opinion, the second law that says entropy increases is not an
absolute, but only an extremely good approximation. But so good an
approximation that we haven't yet, nor are we likely, to devise an
experiment that violates it.

Stephen