The thermodynamic properties such as the specific heat are uniquely de
termined by the second moments of the energy distribution for a given
ensemble averaging. However for small particle numbers the results dep
end on the ensemble chosen. We calculated the specific heat for both t
he canonical and the microcanonical ensemble for the same van der Waal
s clusters. The differences of the resulting thermodynamic observables
for the two ensembles are calculated. We demonstrate how for increasi
ng particle number these terms vanish for bulk material. For the calcu
lation of the specific heat within the microcanonical ensemble we give
a new method based on an analysis of histograms.