A complete set of thermodynamic fundamental equations for heterogeneous systems with curved interfaces in an external electric field has been derived recognizing the difference between the mechanical surface tension, γ, and the thermodynamic surface tension, a. Equations have been obtained for the dependence of γ, σ, the phase transition temperature, chemical potentials, and pressure on the surface curvature and an electric field. Extensions of Kelvin's and J. J. Thomson's equations have been given. Calculation of the work of nucleation on charged particles and the phase transition activation energy has been carried out. When applied to water condensation, the result obtained shows that negative condensation centers are more active than positive ones.