The heat capacity change associated with the hydration of benzene is a large and positive quantity, but it is significantly smaller than that associated with the hydration of an alkane having the same accessible surface area of benzene, the corresponding alkane. This large difference merits attention and should be rationalized. This task is performed by means of the two-state Muller's model for the reorganization of H-bonds. It results that: (a) the hydration shell of both hydrocarbons consists of H-bonds that are enthalpically stronger but slightly more broken than those in bulk water; (b) the hydration shell of benzene consists, on average, of enthalpically slightly weaker H-bonds with respect to the corresponding alkane. The latter feature, due to the presence of the weak benzene-water H-bonds, is the physical cause of the large difference in the hydration heat capacity change, according to the two-state Muller's model.