Monday, October 03, 2005

Thermodynamics - on this and that

Many people find thermodynamics confusing... and why not. When the first law was propounded last, the second law first and the zeroeth law is not a law at all, you can blame people for finding thermo confusing.

On a more serious note, thermodynamically there has never been an energy crisis. As energy is always conserved, there can never be an energy cris. What we call an energy crisis is actaully an exergy crisis - in other words the useful work that can be produced is reducing, unable to meet demands. Exergy is not a conserved thermodynamic quantity.

9 comments:

Pentcho Valev said...

ENERGY CRISIS AND THE SECOND LAW OF THERMODYNAMICS

"If the second law of thermodynamics were false, a ship would be able to travel at the expense of the heat of the ocean." This argument is typical of the era of Postscientism in which science is just money. The argument is invalid: if the second law is false travelling would still be impossible since the ocean and the ship would be at almost the same temperature and in such almost isothermal conditions the heat exchange would be extremely slow.

In another era (or in a different world) the question would be: Are isothermal heat engines possible, although no money can be extracted from them? In our world the silent but unanimous answer is: Who cares. In the other world aliens would study isothermal heat engines diligently and may even find a way to resolve the slow-heat-exchange problem and ease the energy crisis.

Pentcho Valev
pvalev@yahoo.com

Pentcho Valev said...

NOBEL PRIZES IN THE ERA OF POSTSCIENTISM

For a closed system doing reversible work of expansion the first law of thermodynamics takes the form

dU = dQ - PdV /1/

where dU is the internal energy change, dQ is the heat absorbed, P is pressure and V is volume. Since the system is CLOSED and undergoes reversible changes the entropy change is, by definition, dS=dQ/T and /1/ becomes:

dU = TdS - PdV /2/

J. Gibbs managed to convince the world that, if the system is OPEN (substances are added to it), /2/ should be replaced by

dU = TdS - PdV + SUM mu_i dn_i /3/

where mu_i is the chemical potential and n_i is the amount of the ith component. However Gibbs failed to explain the meaning of the entropy change, dS, for an OPEN system. Was dS again equal to dQ/T, as for a closed system, or was dS equal to something else when substances were added to the system?

The fact that dS was not defined for open systems made the equation /3/ so fashionable (scientists adore equations with undefined terms) that in the end /3/ was called "the fundamental equation of thermodynamics". Yet scientists somehow felt that a new definition of dS would bring even more money. The quickest among them, Ilya Prigogine, simply combined /1/ and /3/ and obtained

dS = dQ/T - (1/T)SUM mu_i dn_i /4/

The Nobel Committee immediately gave him the money in the form of a Nobel Prize.

Pentcho Valev
pvalev@yahoo.com

Pentcho Valev said...

THE MOST MYSTERIOUS FORCE IN SCIENCE

If you insert a SOLID dielectric between two opposite charges, the polarization in the dielectric INCREASES the original force of attraction between the charges.

However if you insert a LIQUID dielectric (e.g. water) that wets the charges, the polarization in the dielectric generates a PRESSURE that pushes the charges apart and so DECREASES the original force of attraction between them. The decrease "cannot be explained by electrical forces alone", as Panofsky and Phillips put it in 1962. In my view, this pressure is the most mysterious force in science - see more in:

http://www.wbabin.net/valev/valev2.htm

Pentcho Valev
pvalev@yahoo.com

Pentcho Valev said...

HOW CLAUSIUS INTRODUCED THE SECOND LAW IN 1850

In 1850 Rudolf Clausius introduced the second law of thermodynamics in the following way:

http://web.lemoyne.edu/~giunta/Clausius.html "Ueber die bewegende Kraft der Warme":

"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."

If Clausius had been honest, he would have mentioned unavoidable changes in the operator that carries out the process, e.g. in the following way:

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. Changes will occur, on the one hand, 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, and on the other hand in the state of the operator that carries out the process. 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. However in "the other relations of heat" temperature differences can be equalized spontaneously, in the absence of an operator, whereas the process we consider is only possible in the presence of an operator unavoidably undergoing changes. Therefore we can draw no analogy between the process we consider and "other relations of heat" and always have to bear in mind the possible existence of "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".

The disciples of Clausius made the second law of thermodynamics both absolute and eternal by coining the curse "Perpetuum Mobile of the second kind" meaning that scientists trying to test the second law are just as mad as people trying to extract energy out of nothing.

Pentcho Valev
pvalev@yahoo.com

Pentcho Valev said...

LIFE AND THE SECOND LAW OF THERMODYNAMICS

The second law of thermodynamics emerged in a thought experiment involving two reversible heat engines which work in parallel but DO NOT INTERACT. That is, as the force F1 exerted by the first engine does work along the displacement X1, the force F2 exerted by the second engine remains unchanged. Vice versa, the second engine working along the displacement X2 leaves F1 unchanged. In mathematical terms, the partial derivatives dF2/dX1 and dF1/dX2 are both zero.

If the two reversible heat engines DO INTERACT, the partial derivatives dF2/dX1 and dF1/dX2 are not zero. However one could postulate that they remain equal under isothermal conditions:

dF2/dX1 = dF1/dX2 /1/

It can be shown that equation /1/ is a version of the second law: if /1/ is correct no work can be extracted from an isothermal cycle performed by the two heat engines. However if the inequality

dF2/dX1 > or < dF1/dX2 /2/

is correct, the second law is violated: the reversible isothermal cycle amounts to perpetual motion of the second kind.

The partial derivatives dF2/dX1 and dF1/dX2 can be determined experimentally. Equation /1/ is highly improbable and in this sense absurd whereas the inequality /2/ virtually characterizes all INTERACTING heat engines. Initially Life may have used perpetual motion machines of the second kind but their extreme slowness under isothermal conditions brought about sweeping changes: mechanisms exploiting external energy (e.g. that of the photons) were superimposed.

Pentcho Valev
pvalev@yahoo.com

Pentcho Valev said...

ZOMBIES AND HYPNOTISTS IN THERMODYNAMICS

If a relativist wholeheartedly believes that the speed of light is independent of the speed of the light source (Einstein's second postulate), he/she is a relativity zombie. Relativity hypnotists know Einstein's second postulate is false and work hard on various forms of camouflage - Very Special Relativity, Doubly Special Relativity, Deformed Special Relativity etc.

Similarly, if a thermodynamicist wholeheartedly believes that irreversible processes have reversible alternatives that join the same initial and final states (a falsehood introduced by Clausius), he/she is a thermodynamics zombie:

Peter Atkins, Physical Chemistry, 5th ed., p. 127: "Let the original change in the entropy of the system when the process of interest occurs be dS (this is the change we want to measure). The process need not be reversible, but we suppose that we can find a path that joins the same initial and final states and which is reversible."

Thermodynamics hypnotists (I. Prigogine) managed to camouflage Clausius falsehood 60-70 years ago but did not abandon it completely since this falsehood is essential for the derivation of the idiocy "Entropy always increases".

Pentcho Valev
pvalev@yahoo.com

Pentcho Valev said...

THE GUILTY CONSCIENCE OF RUDOLF CLAUSIUS

http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink, "Bluff your Way in the Second Law of Thermodynamics":

pp. 39-40: "On many occasions Clausius was criticised by his contemporaries. I do not know if, in his own time, he was criticised in particular for his famous formulation of the second law as the increase of the entropy of the universe. However, Kuhn (1978, pp.13-15, p. 260) has pointed out the remarkable fact that in the book (Clausius 1876) he eventually composed from his collected articles, every reference to the entropy of the universe and even to the idea that entropy never decreases in irreversible processes in adiabatically isolated systems is deleted! The most general formulation given to the second law in this book, which may be regarded as the mature presentation of Clausius’ ideas, is again the relation (10), where the system is supposed to undergo a cycle, and entropy increase is out of the question."

The relation (10) referred to by Uffink is a fundamental relation of thermodynamics, the so-called Clausius inequality:

Cyclic integral dQ/T =< 0 (10)

Clausius obtained it by using a proof described by Uffink on p. 34:

p. 34: "His argument is as follows: for an umkehrbar [reversible] cyclic process the result (9) [Cyclic integral dQ/T = 0] rests on the argument that according to the modified version of the second law the integral cannot be positive. The reversed cyclic process, where the integral has the opposite sign, must also satisfy this condition, and the integral is therefore also not negative.Therefore it must vanish. In the case of the nicht umkehrbar [irreversible] cyclic process the second part of this argument is not applicable, but the first part remains valid. Hence we obtain (10)."

Is Clausius proof correct? That is, is Clausius inequality true? The problem is difficult but those who wish to resolve it may find useful this:

http://www.chem.umd.edu/~devoe/thermo/3steps.pdf

Note that Clapeyron equation has been used in the calculations. Is this use legitimate?

Pentcho Valev
pvalev@yahoo.com

Pentcho Valev said...

SUBTLE FRAUD IN THE SECOND LAW OF THERMODYNAMICS

Initially Kelvin and Clausius offered the following equivalent versions of the second law of thermodynamics:

Kelvin: It is impossible for a self-acting machine, UNAIDED BY AN EXTERNAL AGENCY, to convey heat from one body to another at a higher temperature.

Clausius: Heat cannot of itself pass from a colder to a hotter body WITHOUT SOME OTHER CHANGE, connected herewith, occurring at the same time.

Both statements are true but trivial: no interesting conclusion can be deduced from them. So Kelvin and Clausius implicitly replaced them with and in fact used the following non-trivial but false versions:

It is impossible for a self-acting machine, EVEN AIDED BY AN EXTERNAL AGENCY, to convey heat from one body to another at a higher temperature.

Heat cannot of itself pass from a colder to a hotter body EVEN IN THE PRESENCE OF SOME OTHER CHANGE, connected herewith, occurring at the same time.

The false versions naturally produced a false conclusion:

False conclusion: All reversible heat engines working between the same two temperatures have the same efficiency.

The false conclusion was in fact the so-called Carnot theorem; Carnot had deduced it from the false premise:

Carnot false premise: Heat engines do work without any consumption of heat.

Pentcho Valev
pvalev@yahoo.com

Pentcho Valev said...

THE FUNDAMENTAL OXYMORON OF THERMODYNAMICS

The absurdity that entropy always increases would not hold "the supreme position among the laws of Nature" (A. Eddington, 1935) if Clausius had not deduced it gloriously from the fundamental oxymoron of thermodynamics:

THE FUNDAMENTAL OXYMORON OF THERMODYNAMICS: Any irreversible process is reversible; that is, any irreversible process can be closed by a reversible process to become a cycle.

Any textbook author who relishes deducing the supreme absurdity should initially introduce the fundamental oxymoron:

Peter Atkins, Physical Chemistry, 5th ed., p. 127: "Let the original change in the entropy of the system when the process of interest occurs be dS (this is the change we want to measure). The process need not be reversible, but we suppose that we can find a path that joins the same initial and final states and which is reversible."

For 140 years (Clausius deduced the supreme absurdity in 1865) the fundamental oxymoron of thermodynamics has been questioned once:

http://philsci-archive.pitt.edu/archive/00000313/ 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."

Pentcho Valev
pvalev@yahoo.com