# I have 1 litre of water at 45 °C. How long would it take to evaporate when ambient temperature is 25 °C?

Assume that the water is 2 cm deep in a flat pan (if that is relevant).

EDIT: As a fun experiment, I'm trying to evaporate a mixture of powdered root and water in my kitchen. I've heated the mixture to 45 °C, and I'm wondering how long it might take to completely evaporate and leave behind a dry powder.

• My guess is that we are speaking about days. Just pour the solution into something shallow and leave for several days in place with strong ventilation, I used this scheme for evaporation of solutions of some salts. – permeakra Sep 8 '15 at 4:41
• Might also depend on ambient humidity. If the relative humidity in the air is 100%, then the air is already saturated with water vapor and the water will never evaporate. – chipbuster Sep 8 '15 at 6:26
• Why, if the relative humidity in the air is 100%, but the air is at 25 °C, and your water is heated to 45 °C, then it will evaporate. Though of course that would not be as fast as it could be in a less humid air, and you'll get moisture all over the place, too. – Ivan Neretin Sep 8 '15 at 10:32

The evaporation rate $E_r$ can be approximated by: $$E_r = C \times A \times (x_s - x) = 0.013$$ kg/h

$C$... evaporation coefficient $= 25 + 19 \times v$

$A$... water surface $= 0.03$ m$^2$

$x_s$... saturation humidity $= 0.027$ kg/kg (at 30 °C)

$x$... absolute humidity $= 0.011$ kg/kg (at 30 °C and 40 % rel. humidity)

$v$... air speed above water surface $= 0.08$ m/s

If you mesure the air temperature above the water surface - which I approximated with 30 °C - you can get a way better approximation for your case. Also having the rel. humidity you can then find the values for $x_s$ and $x$ in a Mollier diagram (h,x-diagram).

PS: You will waste a lot of energy when you want to obtain the water temperature at 45 °C. Heating the air instead should be more effective.