# Q & A: evaporation rate

Q:
How does one compute the rate of evaporation from a surface of water knowing the temperature and vapor pressure?
- Robert Krakowski (age 67)
Santa Fe, New Mexico
A:
The answer is going to be it depends on other conditions, but bear with me as we get there. We can calculate pretty well how many molecules leave the surface per area per time from the temperature and vapor pressure. The reason is that in equilibrium the number entering the liquid from that vapor equals the number leaving. Since the gas is nearly ideal, simple rules describe how the molecules in it move around at some temperature, and we also know the density that gives that vapor pressure. The problem is that this calculation gives an enormous rate, because the molecules are moving at something like the speed of sound, around 300m/s. (To learn how to get the exact distribution of speeds, look up any beginning text on the kinetic theory of gases.) A little below the boilng point of water, the vapor pressure is close to 1 atmosphere, which means over 40 moles/m^3 of vapor, or around 700 gm/m^3. Now in practical situations theres no way that 210,000 gm/m^2-s is evaporating away.

Where did we go wrong? We assumed that the molecules that left didnt return. Actually, they will bounce off air molecules and diffuse around, with a high chance of returning to the liquid. The actual net rate at which water leaves the surface then depends not only on the simple factors that we could calculate from the kinetic theory of gases, but also on what sorts of winds are blowing, since they determine how far the vapor must diffuse (and thus how many chances it has to return) before blowing away.

Mike W.

The ambient humidity far away from the surface also affects the evaporation rate since water molecules diffuse along concentration gradients, and if the ambient humidity is such that the air is already saturated with water, the water will not evaporate.  Air pressure and temperature affect the diffusion rate too.  Water, when it evaporates, takes 540 calories per gram to do so, and this will reduce the temperature at least in the vicinity of the evaporating surface.  Often the heat transfer rate from either the air to the water or the rest of the bulk of the water to the surface can be the limiting factor in how fast the water will evaporate.  A thin layer of oil will also stop the evaporation.

Tom

Tom maks a good point. If the water starts off at some temperature, it wont stay at that temperature, because of evaporative cooling. Even if the bottom surface of the water had a controlled temperature, the top surface will be cooled. So the evaporation rate depends both on how well mixed the molecules are above the water and in a very similar way on how well mixed the thermal energy is in the water. mw

(published on 10/22/2007)

## Follow-Up #1: Does water evaporate quicker at 6000 feet

Q:
The answers you have given seem to say that air pressure is inversly related to diffusion rate of evaporating water. My question is very direct: Does water evaporate quicker at 6000 feet elevation than at, say, 500 feet (other factors being equal, though that isn't likely outside the lab)?
- Bob Carleton (age 65)
Albuquerque, NM, USA
A:
Yes

LeeH

(published on 07/31/2008)