Why is there zero resistivity in superconductors when there is non-zero entropy?

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Discussion Overview

The discussion centers around the phenomenon of zero resistivity in superconductors and its relationship with entropy. Participants explore the implications of non-zero entropy in the context of superconductivity, questioning how conducting electrons can move freely in a state of zero resistivity when there is still disorder present in the material.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants assert that resistivity is not just "almost zero" but zero in superconductors below the critical temperature.
  • There is a question regarding how Cooper pairs can move freely if the entropy is not zero, as this suggests some level of disorder in the system.
  • One participant emphasizes that not all electrons in the superconductor contribute to superconductivity, indicating that there are normal-state electrons present.
  • Another participant points out that superconductivity can occur at temperatures above absolute zero, where lattice vibrations and thus entropy can still be significant.
  • Concerns are raised about the assumption that zero resistance must imply zero entropy, with calls for clarification on this connection.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between zero resistivity and non-zero entropy, with no consensus reached on how these concepts interact within superconductors.

Contextual Notes

The discussion highlights the complexity of superconductivity, including the role of temperature, electron participation, and the nature of entropy in the material. There are unresolved questions regarding the assumptions made about the implications of zero resistivity.

anuraj.b
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According to theory of superconductivity, resistivity almost zero. Below critical temperature the entropy decreases markedly with cooling .
why resistivity zero when entropy not equal to zero?
my doubt is when there is an entropy there is a disorder. then how can move conducting electron freely and zero resistivity occur ? if you know please replay
 

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resistivity almost zero
Exactly, not almost.

why resistivity zero when entropy not equal to zero?
Where is the issue? Note that not all particles in the material contribute to superconductivity.
 
you know when resistivity is zero then cooper electrons move freely. but the problem is the entropy not equal to zero , the atoms in the superconductor vibrate its mean position. then how can cooper electron move freely?
 
I still don't see the issue.
 
anuraj.b said:
you know when resistivity is zero then cooper electrons move freely. but the problem is the entropy not equal to zero , the atoms in the superconductor vibrate its mean position. then how can cooper electron move freely?

You do know that the "entropy" here is the entropy of the whole material? mfb has indicated that NOT ALL ELECTRONS PARTICIPATE IN SUPERCONDUCTIVITY (sorry, I had to bold it and cap it since you appear to have missed it the first time around). So there are normal-state electrons in the material that are not part of the supercurrent.

Furthermore, superconductivity does NOT occur just at 0 K. In fact, in high-Tc superconductors, the transition temperatures can be as high as 100-130 K! The lattice still has considerable vibrations at those temperatures. So why would entropy be zero when there is a non-zero finite temperature?

You haven't made much attempt to try and connect why "zero resistance" MUST somehow imply "zero entropy". On the other hands, you'll notice that I've had to type quite a bit (more than all of your posts combined so far) in explaining to you why it can't be zero.

Zz.
 

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