We study the problem of the relativistic free electron gas at arbitrary degenerate electronrngas. The speci_c heat at constant volume and particle number cv and the speci_c heatrnat constant pressure and particle number cp are calculated. The equation of state is alsornstudied. Non degenerate and degenerate electron limits are considered. We generalize thernformulas obtained in the non-relativistic and ultra-relativistic degenerate electron gas.rnNeutron stars are much denser than white dwarf stars, which, once again, causes therncore of the stars to collapse. The compression of neutrons in the contracting core, however,rncreates a neutron degenerate pressure. This pressure, analogous to the electron degeneraternpressure in white dwarf stars, combats the gravitational collapse of the star. If, however, thernneutron star is too massive (more than three solar masses), the neutron degenerate pressurernfails and the neutron star collapses into a black hole.rnWe now see that the role of both the neutron degenerate pressure, and the electronrndegenerate pressure is crucial to the maintained stability of a star The energy correspondingrnto this momentum, called the Fermi energy which we will discuss in the next section will alsornincrease. So, with a decreasing volume and an increasing particle momentum, we can sayrnthat a pressure formed inside of the core of the star, and continues to increase as long as thernvolume continues to increase, and that there are degenerate neutron energy states. Now thatrnwe know where the pressure comes from, we can _nally derive a mathematical expression forrnthe neutron degeneracy pressure by non-relativistic neutrons inside of a neutron star.