PHYS 317 - Reading Assignment #23
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N is the number of particles in the system. As they fill up the available states from lowest energy upwards, they take energies from 0 to epsilonF. Therefore the average energy per particle must be less than epsilonF.
- In equation (7.42), why is the total energy less than N*epsilonF?
Absolutely not. Only a fermions within an energy of kT of the Fermi energy can possibly go to an excited with a thermal energy of kT. This is a often tiny fraction of the actual fermions.
- In going from a T=0 fermion gas to a T>0 fermion gas, is it accurate to say that each fermion gains an energy of roughly kT?
Basically the Pauli exclusion principle. It forces an ideal electron gas to contain highly energetic electrons, and these provide a significant pressure even at absolute zero.
- What is the physical origin of degeneracy pressure?
The number of single-particle states per unit energy. So integrating over energy give the number of single-particle states.
- Give a definition for the density of states g(epsilon) in words. Hint: look around equation (7.50), not later.