Nonpolar solutes have a large positive heat capacity of hydration (Delta C-p), while polar groups have a smaller, negative Delta C-p of hydration. The physical origin of these quite different heat capacity behaviors remains a major gap in our understanding of aqueous solvation. The heat capacities of hydration of simple nonpolar and polar solutes, argon (Ar) and potassium ion (K+), were calculated by a combination of Monte Carlo simulations and the random network model of water. The calculated hydration heat capacities of Ar and K+ were positive and negative, respectively, in agreement with experimental behavior. Contributions to Delta C-p from solute-solvent interactions and the first shell of hydration accounted for about 80% of the observed changes. The approximately 20% remaining discrepancy with experimental values probably comes from heat capacity contributions from more distant waters. In the case of Ar the major contribution comes from the reorganization of water in the first hydration shell with a smaller contribution from the solute-solvent interaction. In the case of K+ there is also a significant effect from the reorganization of water in the first hydration shell and also from a combination of solvent-solvent and solute-solvent interactions beyond the first two shells. Unlike Ar though, the contribution of solute-solvent interaction from the first two shells is subject to large numerical noise and could not be determined with precision in these simulations. Changes in C-p due to reorganization of water in the first hydration shell of Ar and K+ are largely due to changes in the distribution of hydrogen bond (H-bond) angles and lengths compared to bulk water. Argon produces a narrower, more "ice-like" H-bond angle distribution and a smaller mean H-bond length, while K+ produces a broader, less "ice-like" angle distribution and a longer mean H-bond length.