In the case of nanosized systems, the free energy undergoes significant changes compared to its bulk counterpart. For bulk systems, properties such as free energy are extensive, meaning they depend on the amount of material present. However, as the size of the system approaches the nanometer scale, surface effects become more pronounced, and many properties that are extensive in bulk systems become intensive for nano-sized systems.
Specifically, free energy in nano-sized systems behaves differently from bulk systems and tends to no longer be extensive. This is because surface area-to-volume ratios increase significantly in nanosystems, altering their thermodynamic properties. The free energy per unit mass, for instance, becomes more dependent on surface characteristics and less on the total size of the system.
Thus, the correct answer is that the free energy of a nano-sized system is no longer extensive.