  We report a model-independent measurement of the entropy, energy, and
critical temperature of a degenerate, strongly interacting Fermi gas of atoms.
The total energy is determined from the mean square cloud size in the strongly
interacting regime, where the gas exhibits universal behavior. The entropy is
measured by sweeping a bias magnetic field to adiabatically tune the gas from
the strongly interacting regime to a weakly interacting regime, where the
entropy is known from the cloud size after the sweep. The dependence of the
entropy on the total energy quantitatively tests predictions of the
finite-temperature thermodynamics.
