  We perform a systematic study of the thermodynamics of quantum gases in the
unitarity limit. Our study makes use of a "Universality Hypothesis" for the
relevant energy scales of a many-body system at unitarity. This Hypothesis is
supported by recent experiments and can be proven in Boltzmann regime. It
implies a universal form for the grand potential which is characterized by only
a few universal numbers in degenerate limit. This universal form provides a
simple way to determine the density profile of a trapped fermion superfluid as
well as the second sound velocity of a homogeneous superfluid at unitarity.
