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In AP Chem we did a lab investigating the relationship between vapor pressure and water temperature. The relationship is linear and as the vapor pressure approaches atmospheric pressure, it begins to boil. Obviously warm water will evaporate faster than cold water, so it made me wonder how do you calculate the evaporation rate of water? Is there a relation between the evaporation rate and temperature just like there is a relation of temperature to vapor pressure? Of course the surface area needs to be taken into account, but I'm more focused on the relationship between temperature and the rate of evaporation.

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  • $\begingroup$ Things get complicated. E.g. the rate might be zero if the gaseous phase is saturated with water. Then lowering the temperature will let condense water, not evaporate. $\endgroup$ – aventurin Jul 19 '16 at 20:33
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It gets complicated. A drop of water (30 mg) will evaporate completely in several hours under standard conditions. You need to consider these factors:

(1) Temperature
(2) Relative humidity
(3) Wind
(4) Surface area
(5) Thermal flux to water (container walls -> water heat flux)

By all means you can do it, but it is a question for physics forums. The main idea would be to write to equations:

(a) Heat flux +walls_to_water + air_to_water -heat_of_evaporation = 0
(b) Diffusion balance. Water pressure at its surface, vs water pressure at the top of the flask is governed by diffusion laws.
(c) Material balance: amount_of_water(t)=amount_of_water(t$_o$)-evaporated_water.

Those are differential equations, so it would be hard to work with them without a solid understanding of calculus.

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