Surface area vs rate of evaporation

[rezaxis]

Two vessels of the same volume, in the same location and open to the atmosphere. One is tall and of a small diameter, the other is short and is of a larger diameter.

Each vessel supplied with an identical heat source. Each vessel filled with an equal volume of an identical liquid.

The goal is to reduce the volume of the liquid in both vessels by 1/2.

I know it will take exactly the same amount of energy to bring each vessel to the boil.

The question is will the vessel with the larger surface area evaporate the liquid faster than the smaller one?

Is there a formula or known and named relationship the would allow me to say "If I doubled the area available to evaporation, I would see an X increase in the rate of evaporation."?

 

[Topher925]

If the same amount of heat is going into both fluids at the same rates, then both containers will have the same rate of evaporation. Surface tension might play a small role but I would presume it to be negligible.

 

[russ_watters]

Important clarification, though: boiling and evaporation are not quite the same thing. Boiling is specifically the internal vaporization of a liquid due to adding heat to bring the vapor pressure above atmospheric pressure. Evaporation, typically, is a surface effect where water is vaporized due to the vapor pressure at the surface's temperature being above the vapor pressure of water in the air.

So since the two concepts were mixed and matched, I'm going to proivde two answers:
-Water will boil (roughly) equally fast in two different shaped vessels given the same heat input.
-Water will evaporate faster from a vessel with more surface area exosed to the atmosphere than from one with less surface area exposed to the atmosphere.

This also means that if you heat the water up to slightly less than the boiling point, the one with more surface area will evaporate faster and as a result, keeping the temperature steady will require more heat input.

 

[rezaxis]

Thanks for the clarifications. I appreciate it, and I think I got it.

Now, does this evaporation rate vs surface area relationship have a name or a formula?

 

[HallsofIvy]

Simply that evaporation is proportional to surface area. The proportionality depends upon things such as the properties of the specific liquid and the temperature.

 

[Bystander]

See "Langmuir."