The following UNREALISTIC scenario will make important features of the next, realistic, scenario clearer. Assume that, somewhere in an isolated system in equilibrium, a temperature difference between the two sides of a thin thermoinsulating plate is somehow maintained. Two questions are relevant:

(1) Does this violate the second law of thermodynamics?

(2) Can the fact that no real thin plate is a perfect insulator prevent us from answering "yes" to the first question?

Those who are inclined to answer (1)Yes and (2)No may wish to consider the following REALISTIC scenario:

If a constant-charge parallel-plate capacitor is immersed in water, a pressure develops between the plates that greatly exceeds the pressure outside the capacitor plates. (W. Panofsky, M. Phillips, Classical Electricity and Magnetism, Addison-Wesley, Reading, Massachusetts, 1962, pp. 112-116). If the capacitor plate is very thin, we can imagine a sharp drop in pressure across it; then the following conclusion is unavoidable:

Punching a small hole in the plate will result in an eternal water flow through the hole, from inside to the outside of the capacitor, in violation of the second law of thermodynamics.

An objection against the above conclusion could be based on the fact that, in an isolated system, the capacitor will discharge sooner or later. The unrealistic scenario may help one to overcome this objection.

A few years ago, at the 2002 First International Conference on Quantum Limits to the Second Law, I called the effect "dynamic equilibrium":

link.aip.org/link/?APCPCS/643/430/1
"Two testable paradigms - the system performing two types of reversible work and the system in dynamical equilibrium - suggest that perpetuum mobile of the second kind in the presence of an operator is possible."

The scientific community remained silent and hostile but still from time to time Panofsky-Phillips pressure leaves scientists speechless:

www.physorg.com/news110191847.html
"When exposed to a high-voltage electric field, water in two beakers climbs out of the beakers and crosses empty space to meet, forming the water bridge. The liquid bridge, hovering in space, appears to the human eye to defy gravity."

Pentcho Valev
pvalev@yahoo.com

You can get around the amazingly false axiom by the way if you dispose the Axiomatic approach to Knowing Energetic equations to development such as of Gibb's, of Boltzmann's distribution, and so forth to the forms of extensive Being in space and time.

Mechanical energy changes into Thermal energy by the balance of relations worded with facts; arguments are grounding of the phenomena in Nature, not filling out the universal concrete space and time (which by the way Strawson was critical of for an idea of what IS a universal). Mathematics can just be used for tests and experiments in these thermodynamical judgments of materialized energy.


I think these days they are teaching set theory applied to thermodynamics in grade eight. I slept too well last night to follow the morning's ideas on the web. Miss your point.

In his 1824 memoire Carnot dealt with two reversible heat engines which DID NOT INTERACT. In 1850 Clausius used NON-INTERACTING heat engines again:

web.lemoyne.edu/~giunta/Clausius.html
"Ueber die bewegende Kraft der Warme" 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). That is, 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. This is the first testable paradigm - "the system performing two types of reversible work" - referred to below (the second one is "the system in dynamic equilibrium"). See more in:

www.wbabin.net/valev/valev2.pdf

Pentcho Valev
pvalev@yahoo.com

Pentcho wrote:
The following UNREALISTIC scenario will make important features of the next, realistic, scenario clearer. Assume that, somewhere in an isolated system in equilibrium, a temperature difference between the two sides of a thin thermoinsulating plate is somehow maintained. Two questions are relevant:

(1) Does this violate the second law of thermodynamics?

(2) Can the fact that no real thin plate is a perfect insulator prevent us from answering "yes" to the first question?

Those who are inclined to answer (1)Yes and (2)No may wish to consider the following REALISTIC scenario:

If a constant-charge parallel-plate capacitor is immersed in water, a pressure develops between the plates that greatly exceeds the pressure outside the capacitor plates. (W. Panofsky, M. Phillips, Classical Electricity and Magnetism, Addison-Wesley, Reading, Massachusetts, 1962, pp. 112-116). If the capacitor plate is very thin, we can imagine a sharp drop in pressure across it; then the following conclusion is unavoidable:

Punching a small hole in the plate will result in an eternal water flow through the hole, from inside to the outside of the capacitor, in violation of the second law of thermodynamics.

An objection against the above conclusion could be based on the fact that, in an isolated system, the capacitor will discharge sooner or later. The unrealistic scenario may help one to overcome this objection.

A few years ago, at the 2002 First International Conference on Quantum Limits to the Second Law, I called the effect "dynamic equilibrium":

link.aip.org/link/?APCPCS/643/430/1
"Two testable paradigms - the system performing two types of reversible work and the system in dynamical equilibrium - suggest that perpetuum mobile of the second kind in the presence of an operator is possible."

The scientific community remained silent and hostile but still from time to time Panofsky-Phillips pressure leaves scientists speechless:

www.physorg.com/news110191847.html
"When exposed to a high-voltage electric field, water in two beakers climbs out of the beakers and crosses empty space to meet, forming the water bridge. The liquid bridge, hovering in space, appears to the human eye to defy gravity."

The supposition that an isolated system in equilibrium has two regions at different temperatures separated by an ideal thermal insulator, is invalid. Such a system does not qualify to be a system in equilibrium. See Feynman's Lectures in Physics for a definition of equilibrium.Even otherwise, the temperature difference between the two regions could be exploited to obtain useful work, showing that the system is not in a state of equilibrium. Therefore, the second law in equilibrium/Classical Thermodynamics has no answers to questions concerning processes that connect ill defined states (states not in equilibrium).

So is the case with the charged capacitor. It is a system not in equilibrium; You can use it to do work for you!

Regarding the 'Panofsky-Phillips pressure' the experiment deals with a electro-mechanical process. It is a thermodynamically reversible process, in principle.

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