A Reexamination of the Derivation of the Equilibrium Supersaturation Curve for Soluble Particles

K. C. Young Institute of Atmospheric Physics, The University of Arizona, Tucson, Arizona

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A. J. Warren Institute of Atmospheric Physics, The University of Arizona, Tucson, Arizona

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Abstract

In this derivation of the equilibrium supersaturation curve for soluble particles, Köhler treated the van't Hoff factor as a constant. McDonald points out that this factor is actually a function of the droplet molality. In this paper, we have rederived equilibrium supersaturation relation following Köhler's approach, except that the van't Hoff factor is treated as a variable in the derivation. The resulting equation is considerably more complicated than the result obtained by Köhler. A simple substitution of a variable van't Hoff factor into Köhler's familiar equation that was derived assuming a constant van't Hoff factor results in a fairly significant error.

Abstract

In this derivation of the equilibrium supersaturation curve for soluble particles, Köhler treated the van't Hoff factor as a constant. McDonald points out that this factor is actually a function of the droplet molality. In this paper, we have rederived equilibrium supersaturation relation following Köhler's approach, except that the van't Hoff factor is treated as a variable in the derivation. The resulting equation is considerably more complicated than the result obtained by Köhler. A simple substitution of a variable van't Hoff factor into Köhler's familiar equation that was derived assuming a constant van't Hoff factor results in a fairly significant error.

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