Question

How does a free electron gas differ from an ordinary gas?

Answer 1

An ordinary gas has pressure because it has temperature, an average velocity of the molecules bouncing around and bouncing off of each other and the walls of the container. This pressure is directly related to the temperature. Cool it enough, the pressure drops to zero when the gas becomes liquid.

You say “a” free electron. One electron or one molecule does not have pressure. Let’s assume you meant a lot of free electrons.

Electrons primarily repel each other by the electric field, which is independent of pressure/velocity and therefore temperature. There will be some small amount of pressure due to the average velocity and therefore temperature, but electric fields are VERY powerful so this will be pretty much the entire contribution to the outward pressure. Unless you get to really high temperatures.

So no matter how much you cool a gas of free electrons, they will exhibit tremendous pressure. They would be very difficult to store in a simple walled container, as the tendency will be for them to jump into the atoms/molecules of the container and by repelling each other, end up covering the outside of the container.

Answer 2

Answer:

Fermi presented the most basic metal model. The concepts of electron orbitals in atoms are translated into a macroscopic entity via this approach. Thus, the Pauli exclusion principle is where a metal's basic behavior originates.

Explanation:

Because of its temperature, average velocities of molecules bouncing off of one another, and the container's walls, an ordinary gas possesses pressure.

The relationship between this pressure and temperature is straightforward. If you cool it down sufficiently, the gas turns into liquid and the pressure goes away.

"A" free electron, you say. There is no pressure in an electron or a molecule. Assumedly, you meant a large number of free electrons.

Electric fields, which are independent of pressure/velocity and hence of temperature, are what essentially repel electrons from one another.

Although the average velocity and temperature will result in a modest amount of pressure, electric fields are VERY strong, therefore this will be very much the only factor in the pressure that is applied outside.

Hence, a free electron gas differs from an ordinary gas as explained above.

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