# Kinetic theory for the molecular condensation flux

1. Oct 10, 2007

### Punchlinegirl

1. The problem statement, all variables and given/known data
Start with the kinetic theory formula for the molecular condensation flux, $$\Phi_cond$$ = 1/4 n_v*c_v, where n_v is the number density of vapor molecules just above a liquid water surface and c_v is the mean speed of the vapor molecules. Derive an expression for calculating the evaporation flux, $$\Phi_evap$$ in terms of the saturation vapor pressure of water e_s(T) at any given temperature T. The vapor may be treated as an ideal gas.

2. Relevant equations
see above

3. The attempt at a solution

I know that $$\Phi_cond$$=1/4 n_v *c_v = e/ (2$$\pi$$m_v*k_b*T)^1/2.
And that at equilibrium the evaporation flux and condensation flux are equal, but I know you can't say there equal here since it's for any time T. However, I have no idea how to get started. I would think you'd need to do a differential equation such as dn/dt is equal to the flux, but I'm not even sure how to get this set up. If someone could help, it would be greatly appreciated!