- #1

Frank Einstein

- 170

- 1

## Homework Statement

Hi everybody. I am currently trinyg to solve the first exercice of the fifth chapter of R.R. Rogers book about cloud physics.

"Show that the vapor pressure in equilibrium over a pure water drop of radius r decreases with T if r<2σ/Lρ

_{L}.

## Homework Equations

e

_{s}(r)=e

_{s}(r=infinite)*(2σ/rR

_{v}ρ

_{L}T).

This equation relates the vapor pressure of saturation of a drop of radius r and the one from a plain surface.

e

_{s}is the vapor pressure, r is radius, σ is surface tension, R

_{v}is the gas constant, ρ

_{L}is density and T is temperature.

3. The Attempt at a Solution

As far as I understand, I have to derivate e

_{s}(r) respect to T and see if the result is similar to the crtical radius which value is 2σ/R

_{v}ρ

_{L}TlnS.

If I have understood correctly, none of the values in the expression of es depends on T, therefore d/dT=∂/∂T. If I derivate exp(a/T) I obtain -a*exp(a/T)/T

^{2}. This expression doesn't look like the one expressed in the upper paragraph.

Note: a=2σ/rR

_{v}ρ

_{L}

If someone could give me some guidance I would be extremley grateful.