The heat capacities of hydration (Delta C-p,) of the first four of the linear alkane series, methane, ethane, propane, and butane, were calculated by a combination of Monte Carlo simulations and the random network model (RNM) of water. The contribution from the water-water interaction and the solute-water interaction accounted for about 45% and 20%, respectively, of the experimental values. The water-water contribution to Delta C-p, arises from distortions in the water structure in the hydration shell. The hydrogen bonds between the water molecules in the first hydration shell were shorter and less bent (had a smaller root-mean-square angle, theta) compared to those in pure water. In the case of propane and butane, the greatest decrease in theta was for waters hydrating the methyl groups, with a somewhat smaller decrease for waters hydrating the methylene groups. Thus the contribution to Delta C-p, per hydrogen bond from water around the methyl groups is a little larger than from water around the methylene groups. This also implies that the hydrogen bonds around the former are slightly stronger than those around the latter. The calculated Delta C-p, for the four hydrocarbons depends nearly linearly on the number of hydrogen bonds participating in the first hydration shell of each solute, which in turn depends linearly on the total accessible surface area of the molecule or the number of carbon atoms in the hydrocarbon. It is evident, however, that the number of hydrogen bonds in the first shell characterizes the hydration heat capacity better than the total accessible surface area of the solute does. This is so because the number of hydrogen bonds with their RNM parameters not only gives a good estimate for the hydration heat capacities but also provides an insight to the mechanism for such an effect.