Thermodynamics, Statistical Physics, and Quantum Mechanics

(^174) SOLUTIONS
law is linear: The number of quantum states is the same as for the
nonrelativistic case considered in Problem 4.66:
However, the Fermi energy now is different since and
Hence,
The total energy is
After substituting from (S.4.67.1), we obtain
So, the pressure is
Hence, for an ultrarelativistic gas we have the same as for mass-
less particles(e.g., photons), which is not surprising since the dispersion law
is the same.
4.68 Quantum Corrections to Equation of State
(MIT, Princeton, Stony Brook)
a) Start with the particle distribution over the absolute value of momentum: