• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Average energy of gas of fermions at T = 0

  • Thread starter Henk
  • Start date
22
0
Consider a system of N (>>1) particles with mass m in a (big) volume V. What is the average energy per particle if the particles are fermions.

I did some calculations and I came up with <E> = (2/3)*Fermi-energy.

Is this correct? I could post my calculations but my Latech-skills are very poor and the calculation involves some long integrals.
I used <E> = Etotal / N and calculated N and E by using the Fermi-Dirac distribution.

The other question is the same but then for bosons. In that case the average energie would be 0 right?
 

OlderDan

Science Advisor
Homework Helper
3,021
1
Henk said:
Consider a system of N (>>1) particles with mass m in a (big) volume V. What is the average energy per particle if the particles are fermions.

I did some calculations and I came up with <E> = (2/3)*Fermi-energy.

Is this correct? I could post my calculations but my Latech-skills are very poor and the calculation involves some long integrals.
I used <E> = Etotal / N and calculated N and E by using the Fermi-Dirac distribution.

The other question is the same but then for bosons. In that case the average energie would be 0 right?
Only you know exactly what you did, but I think your fermion result for <E> is OK. I got the same result using the Fermi-Dirac distribution with degeneracy proportional to the energy (spherically symmetric energy distribution in momentum space) without calculating a total energy or N. If you normalize the distrubtion for some assumed Fermi energy and do the expectation integral it comes out 2/3 of the assumed Fermi energy.

Why would the boson energy be zero. Isn't the minimum energy state for any confined particle greater than zero? The average energy for bosons should be the ground state energy, assuming no exitation.
 

Related Threads for: Average energy of gas of fermions at T = 0

Replies
1
Views
658
Replies
9
Views
3K
Replies
1
Views
1K
Replies
0
Views
876
Replies
1
Views
4K
Replies
1
Views
523
Replies
4
Views
1K
Replies
0
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top