How long does it take air to heat up water?

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Discussion Overview

The discussion revolves around estimating the time it takes for 1000 ml of water to heat up to the surrounding air temperature. Participants explore various factors influencing this process, including container material, thermal conductivity, and experimental approaches.

Discussion Character

  • Exploratory
  • Technical explanation
  • Experimental/applied

Main Points Raised

  • One participant inquires about a general equation to determine the heating time of water to match the surrounding air temperature, providing specific initial conditions.
  • Another participant emphasizes the complexity of the problem, noting that the container's material and thickness affect heat transfer, as well as the thermal conductivity between the container, air, and water.
  • It is suggested that if the air is moving and the water is stirred, the thermal conductivity assumptions might change, potentially simplifying the analysis.
  • A participant points out that as the water temperature approaches the air temperature, the rate of heat transfer decreases, leading to an asymptotic behavior where the temperatures may never fully equalize.
  • One participant proposes conducting an experiment to measure the heating time directly, highlighting the practical approach of using a thermometer and graphing the results.
  • Another participant agrees with the experimental approach and suggests plotting the logarithm of the temperature difference over time to analyze the asymptotic behavior more effectively.

Areas of Agreement / Disagreement

Participants express differing views on whether a theoretical equation can adequately describe the heating process, with some advocating for experimental measurement instead. The discussion remains unresolved regarding the best approach to estimate the heating time.

Contextual Notes

Factors such as container material, thermal conductivity, air movement, and evaporation are noted as significant variables that complicate the analysis. The discussion does not resolve how these factors quantitatively influence the heating time.

Drew
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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 :)
 
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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.
 
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.
 
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
 

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