# Factors involved in water evaporation?

1. Dec 20, 2003

### draeken

Does anyone know the formula that describes the evaporation rate of water?
I'm assuming it involves temperature, dew point, relative humidity and other factors. Thanks in advance.

2. Dec 21, 2003

### Bystander

"The formula?" Depends on what you mean when you say "evaporation rate." "Rate" of evaporation equals rate of condensation when a liquid is in equilibrium with a vapor phase; that rate is a function of temperature ONLY --- there is zero net mass transfer between phases. If you're hunting for mass transfer rates in boilers, tea kettles, from goldfish ponds, you will start with vapor pressure (and Langmuir --- see Knudsen vapor pressure measurement), and add vapor volume exchange rates, vapor diffusion, surface area of the liquid-vapor phase boundary, and on, and on, in a nightmare transport problem.

3. Dec 21, 2003

### draeken

To be more precise, i'm looking for the net evaporation rate.
Since condensation and evaporation are both occuring simultaneously, i would like to know the net removal of water. Like i said before, this should depend on temperature and relative humidity.
If relative humidity is 100%, there should be no net evaporation of water since the the air would be saturated.

4. Dec 21, 2003

### Bystander

This is taking on a meteorological flavor --- there are no doubt ad hoc "models" for wind speed, air temp, water/snow pack surface temp, ground temp beneath the water/pack.

Are you looking for a "first principles" approach, or reviews of empirical correlations? Listing the first principles factors isn't too much trouble, but actually applying them to calculate rates that even agree in sign with what is actually measured can be a real b. Empirical approaches roll the known (but tough to handle factors) into fit parameters, and let you move on.

5. Dec 22, 2003

### draeken

both

i'm looking for both first principle amd empirical correlations answers. the latter is more important to me.
I would like to see the following graphs

1. net evaporation of water vs temp at 10%,30%,50%,70% relative humidity
2. net evaporation of water vs relative humidity at 10,13,16,20,23,26 degress celsius

the best would a 3-d graph
of relative humidity vs. temperature vs. net evaporation rate(mg/m2?)

a formula would be the best.

6. Dec 22, 2003

### Bystander

Can't help you with the empirical stuff --- hit chem or phys abstracts for "systems, water-air." For first principles, John Margrave, Characterization of High Temperature Vapors, 1967 --- this is tough to find --- but is available through interlibrary loan.

7. Jan 6, 2004

### GCT

I am assuming that you just want to see if it can be done, not actually find the answer yourself. There are a couple of ways to obtain the answer.

First of all the evaporation rate of water at a specific temperature is a constant. If you wish to find the net evaporation rate, you need to consider water in a closed container. In this case, the vapor pressure, at any temperature will always be the same regardless of the volume of the container; humidity should not be considered as it is not pertinent. Vapor pressure signifies the net evaporation rate. If you place water in a container at a specific temperature, the evaporation rate is constant. Nevertheless condensation rate increases until it has reached the evaporation rate. The reason that evaporation rate is a constant at specific temperature is applicable to the maxwell distribution of kinetic energy at a specific temperature.

If you wish to find the vapor pressures of water at different temperatures consider the following equation which is a derivation of the Clausius-Claperyron equation:

lnP1/P2 = (40790/R)((T1-T2)/T1T2)

Remember that at 373K the pressure is 1 atm.

One way is to look up the maxwell distribution curve for water at a particular temperature. I am sure that by now we have the actual data correlation between temperature and kinetic energy distribution and even rate of evaporation. Ask any chemistry teacher and I am sure they will be glad to help.

Here is a rather practical way using general chemistry:

Using the above equation you can find the vapor pressure at any temperature of water.

Using Henry's law-c=kP-you can find the solubility which is c in mol/L dissolved.

This will reflect the rate of evaporation. Think about it.

I will check back to make sure everything that I said is accurate, it certainly may not be.

Last edited: Jan 6, 2004