Thermodynamics of interface is extended for small fluid nuclei including those that do not possess homogeneous bulk properties even at their centers. Employing a mathematical boundary to define the system, interaction between the molecules in the system and in the surroundings is taken into account. It is found that the formula for macroscopic systems are rigorously valid for small nuclei without limitation of the size. The meaning of the bulk and the interface terms in the reversible work of forming a critical nucleus is clarified by employing the thought pocess due to Gibbs.
