Consider a gas of N non-interacting, spin fermions of mass M, initially in a volume Vi

Question:

Consider a gas of N non-interacting, spin ½ fermions of mass M, initially in a volume Vi at temperature τi = 0. Let the gas expand irreversibly into a vacuum, without doing work, to a final volume Vf. What is the temperature of the gas after expansion if Vf is sufficiently large for the classical limit to apply? Estimate the factor by which the gas could be expanded for its temperature to settle to a constant final value. Give numerical values for the final temperature in Kelvin for two cases:
(a) A particle mass equal to the electron mass, and N/V = 1022cm-3,as in metals;
(b) A particle mass equal to a nucleon, and N/V = 1030, as in white dwarf stars.