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The entropy and kinetic, potential, and interaction energies of an atomicFermi gas in a trap are studied under the assumption of thermal equilibrium forfinite temperature. A Feshbach resonance can cause the fermions to pair intodiatomic molecules. The entropy and energies of mixtures of such molecules withunpaired atoms are calculated, in relation to recent experiments on molecularBose-Einstein condensates produced in this manner. It is shown that, startingwith a Fermi gas of temperature $T= 0.1 T_F^0$, where $T_F^0$ is thenon-interacting Fermi temperature, an extremely cold degenerate Fermi gas oftemperature $T \lesssim 0.01 T_F^0$ may be produced without further evaporativecooling. This requires adiabatic passage of the resonance, subsequent suddenremoval of unpaired atoms, and adiabatic return. We also calculate the ratio ofthe interaction energy to the kinetic energy, a straightforward experimentalsignal which may be used to determine the temperature of the atoms and indicatecondensation of the molecules.Comment: 12 pages, 5 figure

End-point thermodynamics of an atomic Fermi gas subject to a Feshbach resonance