johanfprins wrote:Giorgio wrote:
As for defining a superconducting wire:
A piece of material (in the shape of a wire) that will transport a given current from its start to its end without heat generation.
A much better definition than one usually finds in text books; but it is still flawed. Assume that the charge-carriers in a metal have an average free pathlength L and you have a wire of length smaller than L: There will then be no heat generation even though the wire is NOT a superconductor.
No, even with an average free path length >> length, you will see measurable resistivity; because the mean path is a mean, with path lengths above and below. Those that fall within the length will generate resistivity.
This applies even when you are getting into the realm of quantum effects, its been observed in the 20 nm research parts, where the uncertainty principle contributes significant leakage in FETs.
johanfprins wrote: From a mathematical point of view it must satisfy the following criteria:
electrical resistivity equal to zero : ro=0
or Joule Effect equal to zero : P=RI^2=0
i.e.: No power dissipation generated from the current flowing into the wire.
Another problem: By defining a superconductor as a material with zero resistivity, you are defining one unknown in terms of another unknown. Zero resistivity has NEVER been defined in physics EVER. Thus to define a superconductor in terms of zero resistivity you must first give an independent definition for zero resistivity.
R=0 implies I(in) = I(out) and V(in) = V(out).
However, it allows one to call a vacuum tube "zero resistivity" and a "superconductor" for the vacuum travel portion, which is somewhat absurd...
A superconductor is a conductor that exhibits no voltage differential across its entirety. Which, of course, merely adds "conductor" to the zero resistivity definition.
And, of course, the model for resistivity is NOT unknown.
Theoretically, the voltage pulls outer electrons from all the atoms in the conductor and they jump from atom to atom. In this model, the resistivity occurs because there is a resistance to the loss of an electron that must be overcome for every atom in the conductor, over and over again.
In the band gap theory, a superconductor is a conductor in which the electrons continue to be excited above the valence energy of the material, and so don't undergo the resistivity mechanism.