I’m looking for an answer from someone in the know; I’ve done quite a bit of web searching and have yet to see an informative discussion of the topic.
Are electrical superconductors also thermal superconductors?
Are there any limits on the ability of real, physical thermal superconductors (if there are any such things) to transfer heat? If I have a length of thermal superconducting wire, which is initially above its critical temperature for superconductivity, and plunge one end into a bath of fluid that is below that critical temperature, what governs the heat transfer along the wire?
The short answer is no. Heat is transferred by 3 main methods - conduction, convection, and radiation. A typical piece of superconducting wire on a block transfers heat via all three methods. Put it in air, and it can still transfer heat by convection and radiation. Put it in a vacuum, and it will still transfer heat via radiation. Put it in a theoretical perfectly reflecting chamber, in a perfect vacuum, and with the surroundings all at the same temperature, and you may end up with a thermal superconductor.
But the two are not related at all, and one does not really influence the other. A very simple basic way to look at it is superconductivity is a feature of the relationships between the electrons and their shells, while thermal energy is a feature of the overall movement or vibration of the entire atoms themselves.
I know, oversimplified, but it works for a quick explanation.
If you stick one end of your wire in a cold source, heat is transferred out of the wire by conduction and convection between the wire’s surface and the fluid. The thermal energy of the motion and vibration of the atoms in the wire is transferred to the slower moving/vibrating cold fluid, thus heating it while the wire cools. Is there perhaps something else that you are asking when you ask “what governs” the heat transfer?
One quick example: Helium II (superfluid Helium) is a thermal superconductor - its thermal conductivity is about 3x10[sup]6[/sup] times greater than “normal” Helium. However, it is not an electrical superconductor.
Conversely, mercury is an electrical superconductor near absolute zero, but it is not a thermal superconductor.
But the phenomena certainly are related, in fact this is an area of intense study. Obvious parallels include:
[ul]
[li]Both are very-low-temperature phenomena, appearing only below some critical temperature[/li][li]Both exhibit anisotropy (different behaviors when measured along different directions)[/li][li]Both are associated with the behavior of electrons in various states of excitation[/li][li]Electrical superconductors do exhibit changes in thermal conductivity as they approach their critical temperature[/li][li]Both phenomena have something to do with the interaction between electrons and phonons (vibrations, essentially)[/li][/ul]
Anthracite-
Point well taken about the radiation and convection boundary condition issues.
I was thinking however, that in addition to temperature manifesting itself via vibrational energy in the lattice, it also is carried by free electrons in the material. Any temperature gradient, it follows, should result in a gradient in electrical potential. I’m pretty sure this is how a thermocouple works. It seems like an electrical superconductor shouldn’t be able to withstand an induced voltage; it should respond with a large restorative current. Wouldn’t this result in an always isothermal superconducting body?
To take your augmentation of my original example, if you have various wires with different thermal conductivities, the steady-state temperature gradient in the wire is a strong function of the wire’s thermal conductivity. As the thermal conductivity increases, the gradient decreases (all other conditions (radiation, convection) being the same). In the limit of infinite thermal conductivity, the wire is isothermal, even though heat is constantly being exchanged between the wire and the environment and the wire and the cold bath.
I’ll have to think a bit about m’s point about Hg…
Does this mean that at least for some superconductors the electrons and phonons are isolated? They don’t communicate at all? Does this apply to the high temperature superconducting ceramics?
Okay, in talking around about this with some other folks, the distinction between Type 1 and Type 2 superconductors came up. Does this govern the communication between electrons and phonons? No solid state physicists here?
I’m a little confused as to how you are defining thermal superconductivity. You are only considering conduction then? And would not a thermal conductive superconductor require an infinite conductivity?
What I am trying to say is - I don’t know if the term thermal superconductor is really analagous at all to electrical superconductivity.
Yes, in a conductor the translational motion of the free electrons contributes as well. In a nonconductor it is entirely lattice vibrations.
Ah, I see now. Well, from what I know the thermal conductivity is an additive effect - where the total conductivity is equal to the lattice wave conductivity plus the free electron conductivity. Or k = k[sub]l[/sub]+k[sub]e[/sub]. Is what you are asking this - does k[sub]e[/sub] go to infininty as electrical superconductivity occurs, thus making k approach infinity?
You got it, Anthracite, that’s my question exactly.
In the question of thermal superconductivity, temperature plays the same role as voltage does in an electrical superconductor. The electrical superconductor doesn’t really care what voltage it’s at, but it can’t support any kind of internal potential difference. Similarly, a thermal superconductor has to be isothermal; any temperature difference is very quickly restored by an arbitrarily large heat flux. k -> infinity.
This topic is right up my husband’s alley, so I linked him to it thinking he’d want to contribute. (His thesis was on this stuff…and by thesis I mean a bound paper about the size of a phone book.)
Here’s the response he sent me. Bear in mind that I have no idea what any of you are talking about, so I don’t know if this helps or not.
Hope that helps…I can forward an email to him if you’d like.
Is condition 2 truly part of the definition, or merely a property all superconductors (that we know of) have? The reason I ask is that condition 2 doesn’t seem necessary for the applications of superconductors we normally hear of (i.e. conducting electricity with zero ohmic losses).
It’s on its way…I was hoping he’d just register and answer, lol. Oh well, he’s sorta busy building a space probe and all. Your tax dollars wouldn’t be well spent on SDMB addiction.
Now, I’m not going to argue with voguefox (rule of thumb: Never argue with a specialist in his field, unless you’ve got equal or greater qualifications in the same field), but perhaps I can clarify a tad. Isn’t it impossible to produce any electromagnetic fields in a perfect conductor? If you attempted to create such a field, the unimpeded electrons (or other charge carriers) would instantly react in such a way as to cancel out that field. Correct?
(I asked him yesterday if he was looking this up or if it was all in his head; he claimed it was all in his head and part of his right arm – haha. A little physicist humor for you, there.)
OK, the change in B is zero in a hypothetical perfect conductor (available from the same catalog that sells the massless strings and frictionless tables). I should have realized that… I guess that some of my E&M hasn’t been sinking in properly.
And of course he was joking about the right arm part. Everyone knows it’s actually the left arm.
voguefoxen: Can you add to the above info a little discussion of the distinction between type 1 and type 2 superconductors, and what effect that distinction might have on thermal conductivity?
Mr.Vixen is behind on his gyroscope testing, so I’ll attempt to field this from his paper. Note that (Hc) and (Hc1) are actually H subscript C and H subscript C1, etc.
T=temperature, H=external magnetic field, and J=current density, if I understand the charts and graphs correctly.
Two of the books cited are High Temperature Superconductivity - An Introduction by Burns (1992) and Introduction to Superconductivity by Rose-Innes and Rhoderick, 1978, if you’re looking for some good sources.