Exploring Fermi Pressure in Relativistic Conditions

In summary, the conversation discusses the derivation of Fermi pressure and the assumptions made by the author. At low temperatures, all low energy states are filled and only high energy states near the Fermi energy are available for interaction, leading to relativistic conditions. The Pauli principle prevents collapse of the Fermi gas even at zero Kelvin and maintains pressure in the electron or fermion gas. The energy levels of nuclei are much larger than atomic energy levels and the Pauli principle plays a similar role in both cases.
  • #1
Silviu
624
11
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!
 
Physics news on Phys.org
  • #2
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.
 
  • #3
phyzguy said:
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?
 
  • #4
Silviu said:
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.
 
  • #5
Silviu said:
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.
 
  • #6
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?
Please correct if my understanding is inadequate.
 

1. What is Fermi pressure?

Fermi pressure is a type of pressure that arises when a large number of fermions (particles with half-integer spin) are confined in a small space. It is caused by the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state at the same time.

2. What are relativistic conditions?

Relativistic conditions refer to situations where objects are moving at speeds close to the speed of light. This can also refer to situations where the effects of gravity are significant, such as near massive objects like black holes.

3. How is Fermi pressure related to relativistic conditions?

In relativistic conditions, fermions can reach extremely high speeds and energies. This causes the particles to become more tightly packed, resulting in an increase in Fermi pressure. Additionally, the effects of relativity on the particles' mass can also contribute to changes in Fermi pressure.

4. What are some real-world applications of studying Fermi pressure in relativistic conditions?

Understanding Fermi pressure in relativistic conditions is crucial for many fields of study, including astrophysics, nuclear physics, and material science. It can help us better understand the behavior of matter in extreme environments, such as inside stars or during high-energy collisions.

5. How do scientists study Fermi pressure in relativistic conditions?

Scientists use a variety of experimental and theoretical methods to study Fermi pressure in relativistic conditions. These include high-energy particle accelerators, astrophysical observations, and computer simulations. By studying the behavior of fermions in these extreme conditions, scientists can gain insight into the fundamental properties of matter.

Similar threads

I Fermi gas in relativistic limit
    • Quantum Physics
Replies
7
Views
1K
I Determining the Number of Points in the n-Space
    • Quantum Physics
Replies
16
Views
1K
I Solving the Quantum Mechanics of a Hydrogen Atom
    • Quantum Physics
Replies
3
Views
1K
I Uncertainty Principle in QFT & Early Universe Conditions
    • Quantum Physics
Replies
1
Views
806
I The general structure of relativistic QFTs
    • Quantum Physics
3
Replies
87
Views
5K
A Thermal Properties of the Free Electron Gas: Fermi-Dirac Distribution
    • Atomic and Condensed Matter
Replies
1
Views
2K
I Calculating Relativistic Phase and Group Velocity
    • Quantum Physics
Replies
10
Views
3K
I How does diffusion of high energy electrons shift band structure?
    • Atomic and Condensed Matter
Replies
1
Views
1K
Can a turbo expander convert more heat to work than a piston expander?
    • Mechanical Engineering
Replies
2
Views
472
A Model the pressure of a zero-gravity simple fluid system
    • Classical Physics
Replies
6
Views
692

Hot Threads

Recent Insights

Back
Top