An extension of the classical thermodynamics to nanometer scale has been conducted to elucidate information regarding size dependence of phase transition functions and binary phase diagrams. The theoretical basis of the extension is Lindemanns criterion for solid melting, Motts expression for vibrational melting entropy, and Shis model for size dependent melting temperature. These models are combined into a unified one without adjustable parameters for melting temperatures of nanocrystals. It is shown that the melting temperature of nanocrystals may drop or rise depending on interface conditions and dimensions. The model has been extended and applied to size dependences of melting enthalpy, melting entropy, atomic cohesive energy. Moreover, the above modeling has been utilized to determine the size-dependent continuous binary solution phase diagrams. These thermodynamic approachs have extended the capability of the classical thermodynamics to the thermodynamic phenomena in the nanometer regime.