  In this work, corrections for the Weyl law and Weyl conjecture in d
dimensions are obtained and effects related to the polarization and area term
are analyzed. The derived formalism is applied on the quasithermodynamics of
the electromagnetic field in a finite $d$-dimensional box within a
semi-classical treatment. In this context, corrections to the Stefan-Boltzmann
law are obtained. Special attention is given to the two-dimensional scenario,
since it can be used in the characterization of experimental setups. Another
application concerns acoustic perturbations in a quasithermodynamic
generalization of Debye model for a finite solid in d dimensions. Extensions
and corrections for known results and usual formulas, such as the Debye
frequency and Dulong-Petit law, are calculated.
