The thermodynamic properties such as the specific heat are uniquely determined by the second moments of the energy distribution for a given ensemble averaging. However for small particle numbers the results depend on the ensemble chosen. We calculated the specific heat for both the canonical and the microcanonical ensemble for the same van der Waals clusters. The differences of the resulting thermodynamic observables for the two ensembles are calculated. We demonstrate how for increasing particle number these terms vanish for bulk material. For the calculation of the specific heat within the microcanonical ensemble we give a new method based on an analysis of histograms.