Metals Conduct Electricity Faster Than Heat – Discover Why

electricityelectromagnetismquantum mechanicsthermodynamics

I have read this question:

https://physics.stackexchange.com/a/561125/132371

where cuevobat says:

You will note if you examine the tables on conductors that some metals that are good electrical conductors also conduct heat well for the same reason – heat is also a vibration of electrons and depends on free electrons to easily transmit heat.

This says that (the conduction of) both heat and electricity depend on free electrons.

But we know that metals conduct electricity close to the speed of light.

Now if I have a metal wire, and heat one end of the wire (various ways, for example put it into hot water), the other end will heat up very slowly. Yet if you connect one end of the wire to electricity (outlet), electricity will flow through it and reach the other end (if you connect something to it, like you touch it) with speeds close to the speed of light.

What causes this difference between the speeds of the propagation of those two phenomena (electricity and heat) in metals?

Just to clarify, both depend on free electrons, so why don't both propagate at comparable speeds?

So far, I have two very interesting answers, and we got so far to the point where I see that in the case of:

  1. electricity, the electrons "push" each other, and this transfer of momentum propagates close to the speed of light

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  1. heat, the electrons transfer energy (hot electrons colliding with cold electrons), and this is much slower

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So now basically, the question comes down to why is transfer of momentum faster then transfer of energy between the free electrons?

Question:

  1. Why do metals conduct electricity faster than heat?

Best Answer

In the case of heat transfer, the wire stays electrically neutral, so one electron can only interact with other electrons in it's close vicinity by collisions, but has no effect on electrons far away. So the signal about the increased temperature (i.e. higher thermal velocity) travels by collisions from one electron to the next. In the best case scenario the random collsions happen such that the next electron always travels in the right direction. Then the information about the increased temperature can travel at most with a speed equivalent to the electrons thermal velocity, which is about 100 km/s or 0.3% of the speed of light.

In the case of electricity, you push additional electrons in one side of the wire. This charge surplus will cause an electric field to form which travels at the speed of light. So this electric field can almost instantaneously affect all electrons in the wire, even electrons far away on the other end of the wire. All electrons will start moving in the same direction driven by this electric field.

So in short, heat transfer is analogous to sending a message through a relay race, while electricity transfer is equivalent to cheating in that race by calling the person on the end of the line with your phone and telling him the message.

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