  We study the energy conservation for the weak solutions to the compressible
Primitive Equations (CPE) system with degenerate viscosity. We give sufficient
conditions on the regularity of weak solutions for the energy equality to hold,
even for solutions that may include a vacuum. In this paper, we give two
theorems, the first one gives regularity in the classical isotropic Sobolev and
Besov spaces. The second one state result in anisotropic spaces. We get new
regularity results in the second theorem because of the special structure of
the CPE system, which is in contrast to compressible Navier-Stokes equations.
