CAPACITOR IN WATER VIOLATES THE SECOND LAW OF THERMODYNAMICS

[Pentcho Valev]

Consider the additional hydrostatic pressure emerging between and PUSHING APART the plates of a constant-charge capacitor immersed in water:

http://www.amazon.com/Introduction-Electromagnetic-Theory-Modern-Perspective/dp/0763738271
Introduction to Electromagnetic Theory: A Modern Perspective, Tai Chow, p. 267: "Calculations of the forces between charged conductors immersed in a liquid dielectric always show that the force is reduced by the factor K. There is a tendency to think of this as representing a reduction in the electrical forces between the charges on the conductors, as though Coulomb's law for the interaction of two charges should have the dielectric constant included in its denominator. This is incorrect, however. The strictly electric forces between charges on the conductors are not influenced by the presence of the dielectric medium. The medium is polarized, however, and the interaction of the electric field with the polarized medium results in an INCREASED FLUID PRESSURE ON THE CONDUCTORS that reduces the net forces acting on them."

http://farside.ph.utexas.edu/teaching/jk1/lectures/node44.html
"However, in experiments in which a capacitor is submerged in a dielectric liquid the force per unit area exerted by one plate on another is observed to decrease... (...) This apparent paradox can be explained by taking into account the difference in liquid pressure in the field filled space between the plates and the field free region outside the capacitor."

When the capacitor is only partially immersed, the additional pressure forces the water between the plates to rise above the surface of the pool:

http://iopscience.iop.org/1367-2630/12/5/053020/fulltext/
New J. Phys. 12 (2010) 053020, Microscopic derivation of electromagnetic force density in magnetic dielectric media, A Shevchenko and B J Hoenders: "As a first example, we consider the well-known experiment on raising a dielectric liquid within a parallel-plate capacitor. The capacitor is partially immersed in the liquid, and the liquid rises when a horizontal static electric field E is applied between the plates."

http://www.amazon.com/Classical-Electricity-Magnetism-Second-Physics/dp/0486439240
Classical Electricity and Magnetism: Second Edition (Dover Books on Physics), 1962, Wolfgang K. H. Panofsky, Melba Phillips, p. 112: "Fig. 6-7. Two capacitor plates dipping into a liquid dielectric."

http://www.youtube.com/watch?v=T6KAH1JpdPg
"Liquid Dielectric Capacitor"

In 2002 I suggested that the pressure difference between the interior and exterior of the capacitor will constantly pump water through a small hole punched in one of the plates, in violation of the second law of thermodynamics:

http://proceedings.aip.org/resource/2/apcpcs/643/1/430_1
AIP Conf. Proc. 643, pp. 430-435, Pentcho Valev 2002: "...as two vertical constant-charge capacitor plates partially dip into a pool of a liquid dielectric (e.g. water), the liquid between them rises high above the surface of the rest of the liquid in the pool. Evidently, if one punches a macroscopic hole in one of the plates, nothing could prevent the liquid between the plates from leaking out through the hole and generating an eternal waterfall outside the capacitor. This hypothesis has been discussed on many occasions but so far no serious counter-argument has been raised."

Here (Fig. 2) can be seen a picture of the "eternal waterfall" (although the author seems to suggest, wrongly in my view, a violation of the FIRST law of thermodynamics):

http://energythic.com/view.php?node=208
"However we may try to go around this difficulty by not expecting the liquid to flow out at the edges, where the retarding forces are strong (sealing the edges), but through a hole drilled into the middle of the grounded plate, as shown in fig. 2."

A tentative explanation of the effect. Consider an oversimplified picture of the arrangement of water dipoles between the (vertical) plates of the capacitor:

P+ (-)(+) (-)(+) (-)(+)..........(-)(+) -P

where P+ and -P are the positive and negative plate respectively. This arrangement has the lowest potential energy so any disturbance caused by thermal motion can only increase the potential energy, at the expense of heat absorbed from the surroundings. For instance, if the second dipole on the left receives a thermal stroke and undergoes rotation, the picture changes:

P+ (-)(+) !!(+)(-)!! (-)(+)..........(-)(+) -P

As a result, the electrostatic repulsion increases and the string tends to stretch. Macroscopically, this is expressed as an additional hydrostatic pressure emerging between the plates and forcing the water there to rise above the surface of the pool. This pressure is non-conservative and can do work at the expense of heat absorbed from the surroundings.

Pentcho Valev
pva...@yahoo.com

[Pentcho Valev]

The suggested violation of the second law of thermodynamics finds its justification in the experimental fact that, when a constant-charge parallel-plate capacitor is immersed in water, some additional hydrostatic pressure emerges between the plates. Roughly speaking, water presses against the inner surface of the capacitor plate more than against the outer surface. So it is not at all crazy to infer that, if a small hole is punched in the plate, water will flow through the hole down the pressure gradient. The hole could be drilled at the level of points 3 and 5 in FIG. 1 below (the hydrostatic pressure variation from point 1 to point 5 is shown in FIG. 2):

http://pages.csam.montclair.edu/~yecko/ferro/papers/Fundamentals/Brevik_ElecMagnFluids.pdf
Can. J . Phys., 60. 449 (1982), Fluids in electric and magnetic fields: Pressure variation and stability, I. BREVIK: "FIG. 1. Two charged condenser plates partly immersed in a dielectric liquid. (...) FIG. 2. The hydrostatic pressure variation from point 1 to point 5 in Fig. 1."

Pentcho Valev
pva...@yahoo.com

[Pentcho Valev]

http://iopscience.iop.org/1367-2630/12/5/053020/fulltext/
New J. Phys. 12 (2010) 053020, Microscopic derivation of electromagnetic force density in magnetic dielectric media, A Shevchenko and B J Hoenders: "As a first example, we consider the well-known experiment on raising a dielectric liquid within a parallel-plate capacitor. The capacitor is partially immersed in the liquid, and the liquid rises when a horizontal static electric field E is applied between the plates."

http://arxiv.org/ftp/arxiv/papers/0812/0812.4845.pdf
"The fluid will rise between the capacitor plates..."

And if a small hole is punched in one of the plates, will the liquid constantly flow through it, in violation to the second law of thermodynamics? Yes - there is a hydrostatic pressure difference between the interior and the exterior of the capacitor. The hole could be drilled at the level of points 3 and 5 in FIG. 1 below (the hydrostatic pressure variation from point 1 to point 5 is shown in FIG. 2):

http://pages.csam.montclair.edu/~yecko/ferro/papers/Fundamentals/Brevik_ElecMagnFluids.pdf
Can. J . Phys., 60. 449 (1982), Fluids in electric and magnetic fields, I. BREVIK: "FIG. 1. Two charged condenser plates partly immersed in a dielectric liquid. (...) FIG. 2. The hydrostatic pressure variation from point 1 to point 5 in Fig. 1."

Pentcho Valev
pva...@yahoo.com

[Pentcho Valev]

The force of attraction between two opposite charges (or between the plates of a constant-charge capacitor) immersed in water substantially decreases. The reason is that an additional hydrostatic pressure between the charges (plates) emerges; this pressure pushes the charges (plates) apart and so counteracts the original electrical force of attraction. In characterizing the situation Panofsky and Phillips use expressions such as "somewhat mysterious", "lacks a physical explanation", "cannot be explained by electrical forces alone":

http://www.amazon.com/Classical-Electricity-Magnetism-Second-Physics/dp/0486439240
Classical Electricity and Magnetism: Second Edition (Dover Books on Physics), Wolfgang K. H. Panofsky, Melba Phillips, p. 114: "This means that if a system maintained at constant charge is totally surrounded by a dielectric liquid all mechanical forces will drop in the ratio 1/k. A factor 1/k is frequently included in the expression for Coulomb's law to indicate this decrease in force. The physical significance of this reduction of force, which is required by energy considerations, is often somewhat mysterious. It is difficult to see on the basis of a field theory why the interaction between two charges should be dependent upon the nature or condition of the intervening material, and therefore the inclusion of an extra factor 1/k in Coulomb's law lacks a physical explanation." p.115: "Therefore the decrease in force... cannot be explained by electrical forces alone." pp.115-116: "Thus the decrease in force that is experienced between two charges when they are immersed in a dielectric liquid can be understood only by considering the effect of the pressure of the liquid on the charges themselves. In accordance with the philosophy of the action-at-a-distance theory, no change in the purely electrical interaction between the charges takes place."

Two problems:

1. If the additional hydrostatic pressure between the charges (plates) "cannot be explained by electrical forces alone", then one must conclude that a NON-CONSERVATIVE force (one which can do work in isothermal conditions at the expense of heat absorbed from the surroundings) is present in the system. This undermines the deductive edifice of classical electrostatics built on the assumption that only conservative (electrical) forces are present.

2. Since there is a hydrostatic pressure difference between the interior and the exterior of the capacitor, water will constantly flow through a small hole punched in one of the plates, down the pressure gradient and in violation to the second law of thermodynamics.

Pentcho Valev
pva...@yahoo.com