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Joule heating happens every time when the conduction electrons transfer kinetic energy to the conductor's atoms through collisions, causing these conductor's atoms to increase their kinetic and vibrational energy which manifests as heat. Then, why wouldn't it happen when no current is flowing through the conductor? When there is no current, the electrons are still moving randomly at a speed of $\mathrm{~10^5\ m/s}$, but at a zero average velocity.

Then, why don't these electrons collide with the atomic ions making up the system and transfer energy to them causing them to heat up even when no net current is flowing?

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When no current is flowing, the system is in thermal equilibrium. The electrons do transfer kinetic energy to the atoms through collisions, but the atoms also transfer kinetic energy to the electrons, and these two processes happen at the same rate, so there's no net energy transfer and the system neither heats up nor cools down. This is just the same as any other case of thermal equilibrium: effectively, the electrons and the atoms are at the same temperature, and that's why there's no heat flow.

However, when you switch the voltage on there is an electric current accelerating the electrons, which increases their kinetic energy. Now they have, on average, more kinetic energy to give to the atoms than the atoms have to give to them. This means that there is a net transfer of energy from the electrons to the atoms. Moving an electron in an electric field changes its potential energy, and this is where the energy for the heating ultimately comes from.

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Because at room temperature and in a zero electric field the lower energy levels are mostly occupied by electrons, so most electrons cannot lose energy due to the Pauli principle.

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From a classical perspective, "heat" is a measure of the average velocity of a microscopic system. In a conductor at zero potential, all of the particles in the system - electrons and nuclei alike - are moving randomly with no new energy entering the system. An increase in the temperature of the conductor would imply an increase in the total energy of the conductor system, which would contradict the claim that the system is at zero potential.

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  • $\begingroup$ "'heat' is a measure of the average velocity of a macroscopic system" - this is not correct. Temperature can, in certain idealised circumstances, be seen as a measure of the average kinetic energy of the particles in a system, but heat is nothing like that at all. $\endgroup$
    – N. Virgo
    Commented Sep 21, 2013 at 1:50
  • $\begingroup$ Ah, yes, sorry. The distinction slipped my mind - thanks for the correction. By "measure of the average velocity", I actually meant that the "heat" (read temperature now) is proportional to some degree to the average velocity of the system, according to the ideal gas law. $\endgroup$
    – Ebnor_Eqvine
    Commented Sep 21, 2013 at 11:03
  • $\begingroup$ Ok, but temperature is proportional to the average kinetic energy of the particles in the system, not their velocity. Unless the system as a whole is moving, the average velocity is zero. $\endgroup$
    – N. Virgo
    Commented Sep 21, 2013 at 11:15

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