How long does it take air to heat up water?

[Drew]

I was hoping to find out how long it takes for 1000 ml water to heat up to air surrounding air temperature - is there a general equation that can be used to work this out? For example, 1000 ml of water = 14 deg C; surrounding air temperature = 18 deg C. In more detail the water container volume is 20cm*11cm*5cm.

Any help with this is most appreciated :)

 

[CWatters]

It's not an easy problem. What's the container made of? The amount of heat flowing into the container will depend on the thermal conductivity of the material it's made from and it's thickness.

It also depends on the thermal conductivity between the container and the surrounding air and the container and the water. You could probably assume this is zero if the air is moving and the water stirred. If not then it's even harder.

The amount of heat flowing into the container also depends on the temperature difference between the air and water and that's changing as the water warms up. As the temperature of the water approaches the temperature of the air the temperature difference and the amount of heat flowing in approaches zero... so technically it takes an infinite amount of time for them to become equal. A plot of water temperature vs time would be asymptotic to the air temperature. So you can only work out when it is within say 0.5 degrees of the air temperature.

If the container is open then evaporation will cool the water below air temperature.

 

[DaveC426913]

It might be simpler and more useful to simply perform the experiment. Get a clock, a thermometer and some graph paper.

I do this with my hot tub each autumn. :)

Don't forget it's asymptotic. The increase will level off as it nears completion, and, as CWatters points out, may never reach it if there's evaporation. You may have to decide how close to room temp. is acceptable for your purposes.

 

[Chestermiller]

I like DaveC's idea. It shouldn't take much time. I recommend plotting the log of the difference between the room temperature and the water temperature as a function of time. This should be pretty close to a straight line, which should help with accurately extrapolating into the asymptotic region at long times.

Chet