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Q & A: Boiling times

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Most recent answer: 10/22/2007
What fraction of the time would cold water boil faster than hot water and why?
- Ruben (age 13)
Isaac Middle School, Pheonix,AZ
Hello Ruben,

This is a fun question. Perhaps you have heard of the "Mpemba effect", an observation that sometimes a bucket of hot water left out in the cold ends up frozen before a similar bucket of colder water. You can search our Questions and Answers site for the word "Mpemba" and get some interesting information about it. One of our replies states that there is no such effect for boiling.

One word about the reproducibility of physical experiments. If quantum effects do not play a role, then identically prepared experiments should produce identical results. Of course, even small changes to the preparation of the system can produce large changes in the results. If the world were only governed by classical physical laws, then if we knew its state precisely enough, we could predict what would happen in the future. (of course both of these we know to be false. The world is not governed by classical physical laws, and it is impossible to know the current state precisely enough).

James provides a classical boiling time calculation below. I must amend it to include a few other observations, some of which may even cause the cold water to boil sooner than the hot water, if enough other things are different between the pot of hot water and the pot of cold water.

One thing you can do to make cold water boil is to put a very hot item in it (say a glowing-red-hot metal rod). While there may not be enough heat to get the whole pot of water boiling, it may briefly make all the water in close proximity to it vaporize, that is, until it cools off. If you put one of these in the cold water and vaporize a small amount of the water but put the hot water pot on a different heat source, you might claim the cold water boiled sooner. But this would be an "uncontrolled experiment" -- something would be different in the way the two pots were treated.

Hereís another thing you can do: you can reduce the air pressure over the cold water. Water will boil at room temperature if the pressure is low enough. "Boiling" just means that the vapor pressure is the same as the ambient air pressure. Then bubbles of vapor will spontaneously form). If you put the cold water in a bell jar in a vacuum, you can get it to boil sooner. But to control the experiment properly, youíd have to put the hot water also in a vacuum, and then it would boil sooner.

Hereís something else: If the hot water is very pure and its container is very smooth, you can superheat it past the boiling point without actually setting off the boiling process. Bubbles need to "nucleate", that is, form around litte defects and impurities. Remove all the impurities and you can superheat the water. Hereís a tragic example of someone getting hurt by superheated water:


You can imagine heating hot water past its boiling point, and even though it got to the boiling point first, if it superheats, it could start boiling (or exploding) after a similarly prepared cooler pot of water with a little stuff dissolved in it to help bubble nucleation, but the cooler water starts boiling first. But then again you have changed something -- the dissolved stuff.

On the subject of solutes, the dissolved stuff raises the boiling point a bit. So you have to check whether the hot and cold water have the same things dissolved in them.

You can also put a layer of oil on top of one of the pots of water while heating it to keep it from evaporating during the heating process, thus biasing the race in favor of the one you want to win. This is also not a controlled experiment.

Here is a calculation done by one of our answer team, to see just how much longer it takes to boil water if itís cold than if itís hot.

This is a very interesting question. Lets start off by making some assumptions. First lets assume that the cold water is very cold - almost frozen so its temperature is about 0 Celcius (32 degrees F). Next lets assume that the hot water is very hot - almost to the boiling temperature of 100 C (212 degrees F). The third and final assumption is that we have some kind of heating coil that is placed directly in the water so we we are going to ignore the effects of the pot the water is sitting in.
The big difference between the two situation is that we have to first heat and then boil the cold water where as the hot water just needs to boil. The change in temperature of the cold water will obviously require some energy. But what is boiling? When water boils it changing phases. It starts in the liquid phase and then transitions into the gas phase. This transition requires a lot of energy that we call the latent energy of vaporization. Now lets actually do the calculation. Start with 1 liter of water (same as 1 kilogram of water).
dT = the change in temperature
m = mass of water
J = joules, a unit of energy
Kg = kilograms, a unit of mass
K = Kelvin, a unit of temperature
Lv = Latent heat of vaporization of water = 2,260,000 J/Kg
C = Specific heat of water = 4186 J/Kg.K
The total heat (energy) we need to put into the cold water to make it boil is:
Q_cold = m C dT + m L .
And the total heat (energy) needed to make the hot water boil is:
Q_hot = mL .
A-HA. Now we see the difference. The cold water has the extra term of (m C dT) because it has to go through a temperature change of dT = 100 degrees Kelvin.
Q_cold = (1Kg)(4186 J/Kg.K)(100K) + (1Kg)(2,260,000 J/Kg)
= 2,678,600 J of energy
Q_hot = (1Kg)(2,260,000 J/Kg)
= 2,260,000 J of energy

Since we have a water heater that supplies a constant output of energy then the boiling time is just proportional to the total heat. Dividing Q_cold by Q_hot gives us 1.1852 as the fraction of time. Putting it in simpler terms: "Very cold water takes about 18.5% more time to boil than very hot water".
Thanks for your question,

(published on 10/22/2007)

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