Where does the heat come from?

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When two conductors are electrically connected, electrons flow from the conductor with a higher Fermi level, where they are less bound, to the one with a lower Fermi level, where they are more bound. This movement continues until the electrostatic potential, known as contact potential, equalizes the Fermi levels of both conductors. The flow of current across this junction can create either forward or reverse bias, leading to a temperature gradient. The heat generated during this process arises from the energy lost by electrons as they move to lower energy states, causing them to collide with the atoms in the conductor, which increases atomic vibrations and produces heat.
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When two conductors are placed in electric contact, electrons flow out of the one in which the electrons are less bound, into the one where the electrons are more bound.

The reason for this is a difference in the so-called Fermi level between the two conductors. The Fermi level represents the demarcation in energy within the conduction band of a metal, between the energy levels occupied by electrons and those that are unoccupied.

When two conductors with different Fermi levels make contact, electrons flow from the conductor with the higher level, until the change in electrostatic potential brings the two Fermi levels to the same value. (This electrostatic potential is called the contact potential.)

Current passing across the junction results in either a forward or reverse bias, resulting in a temperature gradient.
Where does the heat come from? The current going through results in heat how? The electrons moving give off heat as going to a lower energy?
 
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The fast moving electrons collide with the conductor's atoms which start to vibrate (heat).
 
Thanks, that was a good explination.
 
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