Relative permittivity, also known as static dielectric constant, is a key property of solvents in electrolyte solutions. It strongly influences the solubility of solutes and, therefore, it can be used as a predictive tool in chemical engineering processes. Relative permittivity also plays an essential role in the modeling of phase equilibria of electrolyte systems, since it is involved in the Debye-Hückel model and in the Mean Spherical Approximation, commonly used to represent long-range interactions between ions. In this paper, we propose a new temperature-dependent correlation for the relative permittivity of liquid water, methanol and ethanol, valid in a wide temperature range, including very high temperatures. Comparison with other literature equations evidenced that the main interest of the proposed correlation is to allow satisfactory predictions of the relative permittivity, not only in the range of validity of other literature models, but also in the high temperature domain, including supercritical temperatures for water. The new correlation is then used with the NRTL-PRA EoS to predict vapor pressure of water with several salts, including single electrolytes and two-salts mixtures; it must be noted that the modeling presented in this work is relevant for any GE/EoS model, since in this case (binary interactions between water and ions being equal to zero), the excess Gibbs energy reduces to the Long-Range term derived from the Pitzer-Debye-Hückel model. A temperature-dependent correction of the solvent relative permittivity is proposed to account for its dependence on ion mole fraction in this Long-Range term. Results thus obtained show that this correction leads to an accurate prediction both: for vapor pressures of aqueous electrolyte solutions in a very wide temperature domain and for the modeling of vapor-liquid equilibria of methanol-water and ethanol-water mixtures with several salts.