Stefan-Boltzmann and Freezing Water
Name: Steven H.
For some reason I do not understand, my e-mail has included several questions of
the form, "does hot water freeze faster than cold water". I posted a response to a "Marilyn
(vos Savant) is Wrong" some years ago and it must still be out there; I usually get about one
query a year. I looked over the answers turned up by searching the archive and I note that
opinion seems to be divided. One thing I did not notice, though, is the Stefan-Boltzmann law
(radiative energy transfer being proportional to the fourth power of temperature). I am not a
physicist and it has been a LONG time since my undergraduate physics days, but I do not know
if the Stefan-Boltzmann law applies at relatively low temperatures like boiling water or if it
only applies at stellar surface class temperatures. If it holds true across a wide range of
temperatures, for hot vs. cold water in containers that allow radiative cooling (I know; the
Stefan-Boltzmann law is for blackbody radiators) wouldn't hot water cool faster?
One of my favorite questions also. However, I KNOW the correct answer!!!
It was indelibly burned into my mind one incredibly embarrassing evening in a pool hall in my
home town when I was home from my studies as a physics major at the University of Chicago.
After I had pontificated a bit on the power of learning physics, Art, the pool hall proprietor,
asked me and my brother if we thought boiling water would freeze before cold water taken
directly from a faucet if both were placed in a freezer at the same time. I could see no
reason for hot water to freeze faster and so bet a dollar (big bet in those days!). Needless
to say, I lost the bet and had to admit that Art, who probably had not finished high school,
knew some physics better than this brash young physics major!
I am still not sure of the reason for this surprising phenomena, but I believe it is due to the
fact that boiling removes the air from the water and the air in the cold water slows the
freezing remarkably much.
As you say, radiation, being proportional to the fourth power of the absolute temperature,
cools the hot water more rapidly than the cold water at first. However, once the hot water
cools to the original temperature of the cold water, the cold water has cooled considerably
below that temperature and the cold water stays colder than the hot water. However, the
change of state to a solid is affected strongly by the dissolved air. Cooling is also caused
by convection and conduction, which are proportional roughly to the first power of the
difference between the water temperature and the surroundings cools the two pots more
Physics being an experimental science, the best way to check this is to actually do the
experiment. I would be delighted to hear of your results!
Best, Dick Plano...
You're thinking way harder than the answer I am going to give you. I also always have
students that ask the question about hot or cold water freezing faster. In "The Curious
Cook" by Harold McGee, beginning on p. 184,the question is answered in a most simple way.
After a simple empirical experiment he states (on p. 187), "My guess is that the hot water
needs to spend less time in the actual process of freezing because evaporation in the
initial descent to the freezing point has diminished its mass, so there is less water to
freeze." Makes sense considering evaporation can and does take place in the freezer.
Now what if you sealed those ice cubes off?....
Sounds like another experiment waiting to take place.
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Update: June 2012