Do Electrons Lose Heat? Answers to Questions Explained

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Electrons do not possess heat as they are individual particles; heat is a bulk property of materials. In a cooled metal, electrons occupy lower energy levels, resulting in a decrease in their average speed. Electrons lose energy through interactions with their surroundings, primarily emitting energy as light or phonons. The application of electric or magnetic fields alters the energy states of bound electrons, affecting their orbits and energy levels. The dynamic behavior of electrons in metals can be modeled as a gas, which exhibits low heat capacity and quickly reaches thermal equilibrium with the surrounding material.
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Do electrons lose heat? If they do, how do they do it? Bremstrahlung for free electrons and going down to a lower energy level for bound electrons? If you had say a metal and cooled it down, would the electrons move slower or just jump to lower energy levels and lose photons?
 
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Do electrons lose heat?
Heat is a bulk-property - individual electrons don't have heat.

If you had say a metal and cooled it down, would the electrons move slower or just jump to lower energy levels and lose photons?
A cooler metal has more electrons in lower energy levels. This means that the electrons have a lower average speed.

The electrons in the metal lose energy by interaction with their surroundings... that means electromagnetic so, basically yes, they shed energy as light.
 
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What effect does an electric field have on a bound electron? Does it slow it down or affect its orbit in any other way? Does an electric field cause an electron to move to another energy level?

What effect does a magnetic field have on a bound electron? Does it slow it down or affect its orbit in any way?
 
An applied electric or magnetic field alters the Hamiltonian ... so the distribution of the energy states changes.
The effect depends on the exact situation.
 
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Within a metal, electrons can be treated as a gas; a kinetic model first developed by Drude ~1900.

Such a gas has a very low heat capacity (confirmed by experiment), and sheds kinetic energy quickly until the electron gas and the surrounding material reach equilibrium temperature.

Most of the shed energy is in the form of phonons (quantized sound). The moving ("free") electrons are not bound to individual atoms ... they are coupled to the bulk of the metal crystal, and move quite freely. These are your carrier electrons, which make up the conduction band.

This is most easily seen in far-from equilibrium systems as when an ultrafast laser pulse is absorbed by a thin metal film: the electrons, having a much smaller mass, are rapidly accelerated, and their thermal energy increases in less than a picosecond, resulting in a two-temperature system consisting of (1) the hot electron gas, and (2) the metallic ion cores. Depending upon the electron coupling constant for the metal ballistic (very hot) electrons may easily be emitted, or may be heavily suppressed.

You can find literature on this by searching Google Scholar for "electron two temperature model".

Note: I did my doctoral thesis on this topic, measuring the phonon distribution across different crystal directions. The cooling curve is the typical exponential thermal decay as the electron gas and the metal temperatures equilibrate. For a purely optical experiment one sees changes in optical reflectivity, which is a measure of the surface electron density.
 
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It may be shown from the equations of electromagnetism, by James Clerk Maxwell in the 1860’s, that the speed of light in the vacuum of free space is related to electric permittivity (ϵ) and magnetic permeability (μ) by the equation: c=1/√( μ ϵ ) . This value is a constant for the vacuum of free space and is independent of the motion of the observer. It was this fact, in part, that led Albert Einstein to Special Relativity.
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