- In equation (7.42), why is the total energy less than N*epsilonF?
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 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?
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.
- What is the physical origin of degeneracy pressure?
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.
- Give a definition for the density of states g(epsilon) in words. Hint: look around equation (7.50), not later.
The number of single-particle states per unit energy. So integrating over energy give the number of single-particle states.