How long does it take water to cool to ambient temperature?

[Razzor7]

I would like to determine how long it would take a volume of water to cool from an initial temperature to a final temperature in a given ambient temperature. I don't know the volume, is this information important? If so, is there any way to come up with the time it would take as a function of the volume? Are there any other important details we need?

 

[dE_logics]

I don't know the volume, is this information important?

Yes, it has to do with the specific heat capacity of water.

Another info you will need is the area through which the heat dissipates.

You need to use Newtons law of cooling after that...with a bit of integration.

 

[mgb_phys]

Are there any other important details we need?

The shape of the container - cooling happens only on the surface of the water.
If it is open or closed
The insulation value of the container
The temperature of the room
The humidity if the water is warm enough that evaporation is going to matter.

The easy way is to measure the temperature drop in the 1st minute, 2nd minute etc for a few data points and plot a curve and then estimate where it crosses the final temperature you want.

 

[russ_watters]

The shape of the container - cooling happens only on the surface of the water.
If it is open or closed
The insulation value of the container
The temperature of the room
The humidity if the water is warm enough that evaporation is going to matter.

The easy way is to measure the temperature drop in the 1st minute, 2nd minute etc for a few data points and plot a curve and then estimate where it crosses the final temperature you want.

It is extrordinarily difficult (virtually impossible) to predict in advanced the heat transfer performance of a vessel, from scratch. Almost all real problems like this are solved via that second method: using experimental data as a baseline at least to give you the heat transfer coefficient. That curve, though, is Newton's law of cooling, so once you have a couple of data points, you aren't estimating anymore, you have all the information to plug into the equation and calculate the answer.

 

[mgb_phys]

Sorry should have said extrapolate not estimate