Vapour Pressure over Water

[Zindin]

Dear all, my question is:
If I have a container that is filled with water and air, will the vapour pressure in the boundary layer over water surface (between water and air) be equal to the saturated vapour pressure at the boundary layer temperature??

Or does it keep changing till it reaches the vapour pressure at the boundary layer temperature?? If so, how could I calculate this change or in other words the vapour pressure??

Thanks in advance.

 

[mbeychok]

Zindin:

I'm not sure that I understand what you are asking, but here goes:

The partial pressure of the water vapor in the container's vapor space will be the saturation vapor pressure of the water at the water temperature. The partial pressure of the air in the vapor space will be the total pressure in the container minus the water vapor partial pressure.

In other words, the total pressure equals the partial pressure of the water vapor plus the partial pressure of the air ... and the partial pressure of the water vapor is the saturation pressure of the water (which can be found in any set of steam tables) at the water temperature.


Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[Zindin]

Hello Milton,

I think what you just described is the case, when the system reaches equilibrium, although i'm still not sure.

So let me describe my system in more detail. Say the tank is isolated and consists of 50% water and 50% air, and we want to simulate the temperature of both air and water starting from "t_start = 0" till "t_end = infinity". At some time between t_start and t_end, equilibrium happens (let us call it "t_equilib") that means the amount of vapour freed from the water surface (to air) is equal to the amount of vapour returning to the water surface (from air) and the partial pressure of vapour above the water surface at that time "t_equilib" is the saturated vapour pressure at the equilibrium temperature.

So my question would be: How could I calculate the vapour pressure above the water surface from t_start till t_equilib??
Note that at t_start, the temperature of air is a couple of degrees greater than the temperature of water.

What do you think?? I hope I was clear enough and really hope you could help..

Enjoy,
Tarek

 

[m777182]

If at t=0 Tair>Twater then you will come to a solution making heat and mass balance for an adiabatic system and iterating to an equilibrium point. It is a good exercise for loop programming: you should develop all relevant water and air properties that you normaly read from tables (Perry,...) into a functional relationship and iterate calculations until the difference between two iterations falls under deliberately chosen small value. Keep in mind that you do not measure T better then to +-0,01 degC so choosing iteration criteria at 10exp(-10)level would not be clever.
This calculation will not give you the rate of change.
m777182

 

[25362]

It is clear that m777182 is right concerning the rate of evaporation, since it would depend on a variety of factors such as the area of the interphase boundary layer, the initial humidity of the air in the insulated (not isolated) vessel, the original prevailing pressure, the air solubility in water, and, of course the temperature differences. I may have skipped other factors, too many even for just a thought process.