  We study the specific dependence of the periodic Anderson Model (PAM) in the
limit of $U=\infty$ employing the X-boson treatment in two fifferent regimes of
the PAM: the heavy fermion Kondo (HF-K) and the heavy fermion local magnetic
regime (HF-LMM). We obtain a multiple peak structure for the specific heat in
agreement with experimental results as well as the increase of the electronic
effective mass at low temperatures associated with the HF-K regime. The entropy
per site at low T tends to zero in the HF-K regime, corresponding to a singlet
ground state, and it tends to $k_{B}ln(2)$ in the HF-LMM, corresponding to a
doublet ground state at each site. The linear coefficient $\gamma(T)=C_{v}/T$
of the specific heat qualitatively agrees with the experimental results
obtained for differents materials in the two regimes considered here.
