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

 

[sardar]

The time it takes for air to heat up water depends on various factors such as the volume and temperature of the water, the temperature of the surrounding air, and the heat source used. There is no general equation that can accurately determine the exact time it would take for 1000 ml of water to reach the surrounding air temperature of 18 degrees Celsius, as it would vary depending on the specific conditions and variables involved.

However, we can make an estimation using the specific heat capacity of water, which is 4.186 joules/gram-degree Celsius. This means that it takes 4.186 joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius. In your example, the water container has a volume of 20cm x 11cm x 5cm, which is equivalent to 1100 ml. Assuming the density of water is 1 gram/ml, this means that the water has a mass of 1100 grams.

To calculate the amount of energy needed to raise the temperature of 1000 ml of water from 14 degrees Celsius to 18 degrees Celsius, we can use the formula:

Q = m x c x ΔT

Where:
Q = amount of energy (in joules)
m = mass of water (in grams)
c = specific heat capacity of water (in joules/gram-degree Celsius)
ΔT = change in temperature (in degrees Celsius)

Substituting the values from your example, we get:

Q = 1100 g x 4.186 J/g-°C x (18°C - 14°C)
Q = 18308.8 joules

Now, assuming the heat source used has a power output of 1000 watts (which is equivalent to 1000 joules/second), we can estimate the time it would take for the water to heat up by dividing the amount of energy needed by the power output of the heat source:

Time = Q / Power output
Time = 18308.8 J / 1000 J/s
Time = 18.3 seconds

Please note that this is only an estimation and the actual time may vary depending on other factors such as heat loss to the surrounding environment. I hope this information helps.