# Fermi Pressure

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## Main Question or Discussion Point

Hello! I am reading a derivation for Fermi pressure and the author assumes that the electrons in a box are cooled so much that they occupy all the states in the momentum space from p=0 up to a maximum value of p. Then after he obtains a formula for the pressure, he simplifies the formula further, by assuming a very relativistic gas. I am not sure I understand how can we make both assumptions. If we reduce it as much as we can (basically close to 0K), it means that the velocities are very small (the temperature is given by the speed of the particles, so small temperature means small speed). So if the velocities are small, how can one assume "very relativistic" conditions? Thank you!

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phyzguy
At low temperature, all of the low energy states are filled. The only states available for interaction are the high energy states, which have an energy near the Fermi energy. This can lead to the particles being relativistic, even at low temperature.

At low temperature, all of the low energy states are filled. The only states available for interaction are the high energy states, which have an energy near the Fermi energy. This can lead to the particles being relativistic, even at low temperature.
So you mean that if you have a big enough number of electrons in the volume, the ones with the highest momentum, will be relativistic, just because all the lower velocity states have been occupied?

phyzguy
So you mean that if you have a big enough number of electrons in the volume, the ones with the highest momentum, will be relativistic, just because all the lower velocity states have been occupied?
Yes, exactly. At least, that is my understanding.

PeterDonis
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the temperature is given by the speed of the particles
The temperature is given by the average speed of the particles. Not all particles will have the average speed.

Is there a non interactive fermi gas?
Pauli principle saves the fermi gas from collapsing even at zero kelvin.There is cobditioned degeneracy pressure.
So separatedness of energy levels is only upto the conditoon that star is not big enough to overcome degeneracy pressure .Energy levels of nuclei are enormously big in comparison to atomic energy levels.
Does Pauli principle similarly maintains pressure in electron gas or fermion gas? How?