  We model cuprate superconductors as an infinite layered lattice structure
which contains a fluid of paired and unpaired fermions. Paired fermions, which
are the superconducting carriers, are considered as noninteracting zero spin
bosons with a linear energy-momentum dispersion relation, which coexist with
the unpaired fermions in a series of almost two dimensional slabs stacked in
their perpendicular direction. The inter-slab penetrable planes are simulated
by a Dirac comb potential in the direction in which the slabs are stacked,
while paired and unpaired electrons (or holes) are free to move parallel to the
planes. Paired fermions condense at a BEC critical temperature at which a jump
in their specific heat is exhibited, whose values are assumed equal to the
superconducting critical temperature and the specific heat jump experimentally
reported for YBaCuO_(7-x) to fix our model parameters: the plane
impenetrability and the fraction of superconducting charge carrier. We
straightforwardly obtain, near and under the superconducting temperature Tc,
the linear (\gamma_e T) and the quadratic (\alpha T^2) electronic specific heat
terms, with \gamma_e and \alpha, of the order of the latest experimental values
reported. After calculating the lattice specific heat (phonons) Cl from the
phonon spectrum data obtained from inelastic neutron scattering experiments,
and added to the electronic (paired plus unpaired) Ce component, we
qualitatively reproduce the total specific heat below Tc, whose curve lies
close to the experimental one, reproducing its exact value at Tc.
