Combining Kelvin’s Equation with Jennings’ Equation for Snow Formation

Winter snow is necessary for countries to maintain their crops. Here we combine two equations, one the Kelvin equation (Young, 1993, page 30) [1], and an equation derived by (Jennings, 2025) [2], by eliminating kT between them. T is the temperature of supercooling in the cloud. Here is the Kelvin equation for prssure of a raindrop over a curved surface.

ln (P / Psat) = (2 σ) / (NL k T r)

Then we present the Jennings equation for undercooling in snow formation.

T = (D (7.14 x 107)) / (k ns a (To - T)0.69)

By taking kT out of both the result becomes.

(2 σ) / (ln (P / Psat) r) = (D (7.785 x 107)) / (a (To – T)0.69)

To > T and D is a function of T and P. D, the self-diffusion coefficient, is obtained by consulting Krynicki, et al (1978) [3]. Since a snow forming cloud can form at 0°C, it is instructive to get D near there. For σ, water surface tension, this is found in (Hacker, 1951) [4].