The partial molar heat capacity associated with a constant-pressure solvation process is extended to define a total of six generalized solvation heat capacities, each of which contain unique physical information. These arise from all the possible cross derivatives of the reversible heat of solvation (with respect to T and N), each evaluated at either constant pressure or constant volume. The resulting quantities may be interconverted using expressions that depend on the solvent equation of state and the solute partial molar volume. Moreover, contributions to each of the solvation heat capacities arising from the temperature dependence of the solute - solvent interaction energy and the solvent-reorganization energy (at either constant pressure or constant volume) are formally identified. For the self-solvation of a molecule in its own pure fluid, the latter quantities may be extracted directly from experimental data, while for more general solvation processes additional input is required, either from computer simulation or from theoretical approximations. The results are used to experimentally quantify the generalized heat capacities pertaining to the self-solvation of xenon, difluoromethane, n-hexane, and water, as well as the hydration of xenon, cyclohexane, and three hard sphere solutes (of about the same size as water, xenon, and cyclohexane).