Sadi Carnot Questions the Second Law of Thermodynamics

The Conversation: "The next scientific breakthrough could come from the history books. New perspectives on old investigations might turn out to be promising routes to radical research. Most current research programmes represent attempts to make incremental advances, nurtured and supported by a conservative system of peer review. But the generation of really fresh ideas requires methods that don't just rely on linear progression." https://theconversation.com/the-next...ry-books-73553

My comment in The Conversation:

A revolution in science involving the refutation of the second law of thermodynamics can be triggered by the works of the founder, Sadi Carnot. The simplest and most precise formulation of the second law was given by Sadi Carnot himself:

"A cold body is necessary"

That is, heat cannot be cyclically converted into work unless there is some temperature gradient (a hot body, source of heat, and a cold body, receiver of heat, must be available). The problem is that in 1824 Carnot deduced "A cold body is necessary" from a postulate that eventually turned out to be false:

Carnot's (false) postulate: Heat is an indestructible substance (caloric) that cannot be converted into work by the heat engine.

Unpublished notes written in the period 1824-1832 reveal that, after realizing that his postulate was false, Carnot found "A cold body is necessary" implausible:

http://www.nd.edu/~powers/ame.20231/carnot1897.pdf
Sadi Carnot, REFLECTIONS ON THE MOTIVE POWER OF HEAT, p. 225: "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: "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."

Generally, a cold body is not necessary, that is, the second law of thermodynamics is false. The cold body is only TECHNOLOGICALLY necessary as it makes heat engines fast-working. Heat engines working under isothermal conditions (in the absence of a cold body) are commonplace but are too slow and impuissant to be of any technological importance. Yet they do violate the second law of thermodynamics.

Pentcho Valev

Unless the working substance is ideal gas-like, all isothermal heat engines are essentially perpetual-motion machines of the second kind. For instance, there are macroscopic contractile polymers which, on adding acid (H+) to the system, develop a huge work-producing force, contract and lift a weight:

http://www.gsjournal.net/old/valev/val3.gif

http://www.google.com/patents/US5520672
"When the pH is lowered (that is, on raising the chemical potential, μ, of the protons present) at the isothermal condition of 37°C, these matrices can exert forces, f, sufficient to lift weights that are a thousand times their dry weight."

See Figure 4 he

http://www.ncbi.nlm.nih.gov/pmc/arti...00645-0017.pdf
A. KATCHALSKY, POLYELECTROLYTES AND THEIR BIOLOGICAL INTERACTIONS, p. 15, Figure 4: "Polyacid gel in sodium hydroxide solution: expanded. Polyacid gel in acid solution: contracted; weight is lifted."

Mineral acid (hydrogen ions, H+) is added to the system and "the polymolecule contracts and lifts the attached weight through a distance ΔL". Then the acid can be removed and the macromolecule resumes its initial stretched state, ready to lift another weight. The work involved in adding and removing (electrochemically) hydrogen ions, if performed very slowly, almost reversibly, is virtually zero, while the net work extracted from contracting and stretching is obviously positive - the system is cyclically lifting weights at the expense of heat absorbed from the surroundings, in violation of the second law of thermodynamics.

There are also macroscopic polymers which contract and lift a weight as H+ is removed, not added:

https://www.youtube.com/watch?v=JGn2a21FvLM
"Here we see a pH-responsive polyacrylic acid hydrogel contained within an unbound carbon fibre braid. The artificial muscle (McKibben style) actuates when placed in a solution with high pH..."

Pentcho Valev

The second law of thermodynamics is invincible in its not-even-wrong formulation "Entropy always increases":

http://web.mit.edu/keenansymposium/o...und/index.html
Arthur Eddington: "The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics, I can give you no hope; there is nothing for it but to collapse in deepest humiliation."

"Entropy always increases" is in fact a theorem deduced by Clausius in 1865:

http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink, Bluff your Way in the Second Law of Thermodynamics, p. 37: "Hence we obtain: THE ENTROPY PRINCIPLE (Clausius' version) For every nicht umkehrbar [irreversible] process in an adiabatically isolated system which begins and ends in an equilibrium state, the entropy of the final state is greater than or equal to that of the initial state. For every umkehrbar [reversible] process in an adiabatical system, the entropy of the final state is equal to that of the initial state."

Clausius' deduction was based on three postulates:

Postulate 1 (implicit): The entropy is a state function.

Postulate 2: Clausius' inequality (formula 10 on p. 33 in Uffink's paper) is correct.

Postulate 3: Any irreversible process can be closed by a reversible process to become a cycle.

All the three postulates are totally unjustified - clever scientists are well aware of that:

Uffink, 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."

The original sin of the entropy concept is that the entropy is not a state function. This means that any statement involving the term "entropy" is not even wrong. If you define the entropy S as a quantity that obeys the equation dS=dQrev/T, you will find that, so defined, the entropy is a STATE FUNCTION FOR AN IDEAL GAS. Clausius was very impressed by this statefunctionness and decided to prove that the entropy (so defined) is a state function for ANY system. So "Entropy is a state function" became a fundamental theorem in thermodynamics. Clausius deduced it from the assumption that any cycle can be disintegrated into small Carnot cycles, and nowadays this deduction remains the only justification of "Entropy is a state function":

http://mutuslab.cs.uwindsor.ca/schur...es/240_l10.pdf
"Carnot Cycles: S is a State Function. Any reversible cycle can be thought of as a collection of Carnot cycles - this approximation becomes exact as cycles become infinitesimal. Entropy change around an individual cycle is zero. Sum of entropy changes over all cycles is zero."

http://ronispc.chem.mcgill.ca/ronis/chem213/hnd8.pdf
"Entropy Changes in Arbitrary Cycles. What if we have a process which occurs in a cycle other than the Carnot cycle, e.g., the cycle depicted in Fig. 3. If entropy is a state function, cyclic integral of dS = 0, no matter what the nature of the cycle. In order to see that this is true, break up the cycle into sub-cycles, each of which is a Carnot cycle, as shown in Fig. 3. If we apply Eq. (7) to each piece, and add the results, we get zero for the sum."

The assumption on which "Entropy is a state function" is based - that any cycle can be subdivided into small Carnot cycles - is obviously false. An isothermal cycle CANNOT be subdivided into small Carnot cycles. A cycle involving the action of conservative forces CANNOT be subdivided into small Carnot cycles.

Conclusion: The belief that the entropy is a state function is totally unjustified. The part of thermodynamics based on the entropy concept is not even wrong.

https://en.wikipedia.org/wiki/History_of_entropy
"My greatest concern was what to call it. I thought of calling it 'information', but the word was overly used, so I decided to call it 'uncertainty'. When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, 'You should call it entropy, for two reasons: In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage."

Pentcho Valev

It seems that isothermal heat engines (violating the second law of thermodynamics) are now not only under scientific scrutiny but also gone into the phase of technological development. Yet the scientific community finds it judicious to completely ignore the reports, even when they are published in prestigious journals:

http://www.azocleantech.com/article.aspx?ArticleID=610
"A graphene battery has been developed that has the potential to convert ambient heat into electric current. This invention increases the prospect of green, clean batteries powered by ambient heat, and represents a significant progress in the research of self-powered technology."

http://arxiv.org/abs/1203.0161
Self-Charged Graphene Battery Harvests Electricity from Thermal Energy of the Environment, Zihan Xu et al: "Moreover, the thermal velocity of ions can be maintained by the external environment, which means it is unlimited. However, little study has been reported on converting the ionic thermal energy into electricity. Here we present a graphene device with asymmetric electrodes configuration to capture such ionic thermal energy and convert it into electricity. [...] To exclude the possibility of chemical reaction, we performed control experiments... [...] In conclusion, we could not find any evidences that support the opinion that the induced voltage came from chemical reaction. The mechanism for electricity generation by graphene in solution is a pure physical process..."

http://scitation.aip.org/content/aip...1063/1.4825269
Electricity generated from ambient heat across a silicon surface, Guoan Tai, Zihan Xu, and Jinsong Liu, Appl. Phys. Lett. 103, 163902 (2013): "We report generation of electricity from the limitless thermal motion of ions across a two-dimensional (2D) silicon (Si) surface at room temperature. [...] ....limitless ambient heat, which is universally present in the form of kinetic energy from molecular, particle, and ion sources, has not yet been reported to generate electricity. [...] This study provides insights into the development of self-charging technologies to harvest energy from ambient heat, and the power output is comparable to several environmental energy harvesting techniques such as ZnO nanogenerator, liquid and gas flow-induced electricity generation across carbon nanotube thin films and graphene, although this remains a challenge to the second law of thermodynamics..."

https://www.youtube.com/watch?v=RVUf7-tTLXo
The Super Supercapacitor. Note the "real exciting discovery" ("The world changed at that point") demonstrated by UCLA scientists at 1:09.

Pentcho Valev