  Based on the results obtained in a previous paper (S. Gaudio et al.,
cond-mat/0505309}, we derive the thermodynamic properties of a Fermi gas, deep
into the quantum degenerate regime. We show that, if Luttinger's theorem holds,
a first order phase transition occurs in the normal phase as a function of the
interaction strength, U. We also show that a volume change occurs at finite
temperatures from the BEC to the BCS side of a diverging s-wave scattering
length, in the normal phase. The transition has an end point above the BCS
critical temperature. Also we show that a paramagnetic system in equilibrium,
close to the divergence of the scattering length, on the negative side, screens
out any applied magnetic field.
