Equation of state of an ideal Fermi gas

Exact formulas for the thermodynamic variables of an arbitrarily degenerate and relativistic ideal Fermi gas are applied to the adiabatic expansion of an ideal Fermi gas from extreme relativistic down to nonrelativistic temperatures. Approximations to the Fermi integrals are developed for a degeneracy parameter of the order of unity and used to calculate the rate of electron capture on free nucleons and the neutrino energy losses. The loss rates obtained are as much as 8 times greater than those previously calculated and employed in current stellar-collapse calculations. A neutral mixture of equal numbers of ideal fermions and antifermions is studied. The adiabatic expansion of such neutral matter is followed, showing elevated temperature when kT is less than mc-squared.