1) Derive the equilibrium condition considering liquid-vapor interface in the isolated system where a sufficiently little amount vapor exists in bulky liquid. Note that the equilibrium condition of system is defined

in terms of total differentiation of its Helmholtz free energy. 2) Derive the pressure of the pre-existing vapor bubble in the cavity, using Clausius- Clapeyron equation. Here, the vapor density is lower enough than the liquid density. 3) Derive the curvature of the vapor bubbles in the cavity, 1/R, as a function of Tw, using the mechanical equilibrium condition. Here vapor pressure is approximated as saturated vapor pressure at vapor temperature. 4) 1. In case that <0 and 0