Our earlier-established thermodynamic solvate difference rule encompasses thermodynamic relationships for the quantities P = Delta H-f degrees, Delta(f)G degrees, Delta S-f degrees, S degrees, V-m, and U-POT for pairs of condensed-phase solvates (including hydrates) having n and m moles, respectively, of bound solvent (including water, i.e., L = H2O), and can be written as P{MpXq center dot nL,p} approximate to P{MpXq center dot mL,p} + (n-m)center dot theta(P){L,p-p} (with m = 0 for the corresponding thermodynamic quantity of the condensed-phase unsolvated parent, P{MpXq,p}), where theta(P){L,p-p} is the incremental contribution per mole of the bound solvent, L, to the property, P, of the solvate in condensed phase, p (where p = solid or liquid). We find that this rule can be extended to supercooled NaOH (and, probably, even more generally). Once established, the parameter theta p{L,p-p} provides approximate values of the thermodynamic property, P, for the remaining solvates (hydrates) for which data are unknown. The difference rule is here further extended to heat-capacity data, C-p, for both hydrates and other solvates. For solid-phase hydrates, theta c(p){H2O,S-S} is determined to be 42.8 J K-1 mol(-1). Further, the method is shown to apply also to the organic solvates, DMSO and DMF (the latter is based on a single example), leading to the (tentative) values theta(Cp){DMSO,S-S} approximate to 105 J K-1 mol(-1) (at 255 K); approximate to 161 J K-1 mol(-1) (at 350 K), illustrating typical temperature dependence of the theta(Cp) values. theta(Cp){DMF,S-S} approximate to 84 J K-1 mol(-1). For supercooled NaOH, theta(Cp){NaOH,I-I} = 77 J K-1 mol(-1). The values of the solvate difference rule parameters provide us with insight into the bonding condition of the solvent molecule, leading to the conclusion that bound solvent water in an ionic environment is ice-like. The situation is more complex within zeolites because water may enter the solvate in a variety of ways. These latter considerations are also briefly discussed with respect to fullerenes.