Although a number of analyses have been presented on the size effects on transport properties like the thermal conductivity, very few studies have focused on size effects on thermodynamic properties like the heat capacity. The present analysis considers the effect of size on thermodynamic properties when the dimension in one, two or all three directions is extremely small, leading to a reduction in the number of phonon wave vectors. The results are presented in a novel non-dimensional form, so that the effect of dimension on the thermal properties of any material can be easily obtained once the bulk properties are known.