conductivity of metals at 0 kelvin?
What is the conductivity of metals at 0 kelvin? i think it will be zero because at 0 k entropy is zero. Every motion is cease.

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plz tell me hypothetically it will zero or not?

Re: conductivity
If you measure conductivity, you apply a voltage that moves electrons. No need for entropy.
Beyond this, experimental data exists for very low temperature. 
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Re: conductivity of metals at 0 kelvin?
It depends on how pure the metal is. If there are scattering centers, the conductivity will remain finite. For very pure metals, the conductivity becomes very high and will ultimately only be limited by scattering from the surfaces.

Re: conductivity of metals at 0 kelvin?
For non superconducting metals the resistance at 0K is not zero in practice: http://en.wikipedia.org/wiki/Residual_resistance_ratio

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thank's

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Vidar 
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I doubt that you can apply a voltage without changing the entropy. 
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Re: conductivity of metals at 0 kelvin?
I don't think zero entropy is any proper world because uncertainty relation really matters when one deals with subatomic things.

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Entropy is defined via the states of the system  and those states already take the uncertainty relation into account. 
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Re: conductivity of metals at 0 kelvin?
$$S=k_B \sum_i P_i \ln(P_i)$$
If the ground state is not degenerate, ##P_i=0## everywhere apart from the ground state, where ##P_g=1##. Take the limit to avoid ln(0), and you get ##S=k_B (1 ln(1)+0)=0##. Who needs volumes of anything? This is a general result, you can apply it to all thermodynamical systems  spins, gases, crystals, whatever. If the ground state is degenerate, you get some tiny amount of entropy. 
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The answer you get depends very much on how complex and at what level you wish to receive: 1. High School. The conductivity is infinite, meaning the resistivity approaches zero. This is imply based on extrapolating what we know from looking at the dependence of conductivity with temperature. 2. Undergraduate level. The conductivity is expected to be infinite, i.e. resistivity approaches zero. This is because the predominant source of resistivity (lattice vibrations) diminishes to zero (theoretically) at T=0. 3. Graduate/professional level. The answer has two forms: theoretical and experimental. Theoretically, the properties of a "typical" metal can be accurately described by Landau's Fermi Liquid theory. Here, one can employ the Drude model and arrive at a description of the scattering rate of the charge carrier (quasiparticles) in a metal that depends on (i) electronphonon scattering (ii) electronelectron scattering (ii) electronimpurity/defect scattering. Scattering rate of (i) and (ii) are temperature dependent and can approach zero as T approaches zero. However, scattring rate (iii) does not. It is almost a constant. Thus, one needs to look if one is asking about our ordinary, REAL metals, or some idolized, perfect, singlecrystal, no impurity/defect metal. Any metal of any considerable size will have impurity and defect (i.e. grain boundaries, etc. even without impurities). Thus, what will happen here is that there will be something called "residual resistivity" at T=0. And this is where the experiment comes in, because such a study has been done a long time ago, showing not only such resistivity at very low temperatures, but also the T^2 dependence of the electronelectron scattering (as predicted by the Fermi liquid theory). So there! Zz. 
Re: conductivity of metals at 0 kelvin?
classical calculation does not apply as I already said.It is pointed out in feynman lectures vol. 1 that uncertainty principle must be invoked for non zero entropy.see some early chapter,it is written there.

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