Comment on Temperature-Pressure Equilibrium Between Dispersed and Continuous Phases of a Material

This memo calls attention to the fact that the relationship between equilibrium temperature and the pressures in two phases of a material is {Delta}sdT = {Delta}(vdP) , and not, as now routinely assumed by bubble investigators, the Clausius-Clapeyron equation {Delta}sdT = {Delta}vdP . If one phase is discontinuous (subscript "d") and consists of spheres of radius r in a continuous phase (subscript "c") whose pressure is held constant, then the equilibrium temperature will be above the saturation temperature of the continuous phase by an amount ({Delta}T{sub sup}){sub c} = 2 {integral}{sub 0}{sup ({sigma}/r){sub e}}(v{sub d}/{delta}s)d({sigma}/r) and above the saturation temperature of the discontinuous phase by an amount ({Delta}T{sub sup}){sub d} = 2 {integral}{sub 0}{sup ({sigma}/r){sub e}}(v{sub c}/{delta}s)d({sigma}/r