We have measured the heat capacity of granular aluminum specimens with normalstate resistivities p N between 0.6xl0~3 and 40xl(T 3 fi cm. The specimens become superconducting with a heat-capacity transition which is BCS-like for the lowest p A , and then diminishes until it is no longer observable for the highest p Nm We conclude that the grains become decoupled such that, because of their small size, they do not exhibit bulk superconductivity when they are isolated.When aluminum is evaporated in the presence of oxygen it deposits in the form of metallic grains surrounded by insulating oxide. With increasing oxygen pressure the oxide barrier becomes thicker, the grains become increasingly decoupled, and the room-temperature normalstate resistivity p N of the specimen increases. For p N larger than 1(T 4 Q cm the grain size remains constant at about 30 A. 1 ' 2 We have made measurements on a series of granular aluminum films which show that the discontinuity in the heat capacity, which is characteristic of bulk superconductivity, is there to its full extent only in the specimen with the lowest value of p N (0.6 xlO" 3 £2 cm). In the specimens with greater p N the change in the heat capacity becomes smaller, and occurs at a lower temperature and over a wider temperature interval, until for the specimen with the highest value of p N (40 xlO" 3 £2 cm) it is no longer observable. We were thus able to show that when the grains are isolated they show no heat-capacity transition and that they are, therefore, smaller than the characteristic size below which bulk superconductivity cannot occur in isolated grains. 3 " 8 In addition, our results show that there is a rather narrow range of values of p N , corresponding to a small change in composition, 7 such that on one side of 316