  The thermodynamic potential is calculated for a uniform superfluid gas of
fermi atoms from the mean field BCS equations including corrections from
induced interactions, Hartree-Fock energies and quasiparticle selfenergies. The
entropy, specific heat and sound modes are calculated as function of
temperature, density and interaction strength from the BCS to the unitarity
limit and around the BCS-BEC crossover. The second sound speed is of particular
interest as it is a clear signal of a superfluid component and it determines
the critical temperature.
