Pressure, Temperature, and Freezing Water
Country: United States
Date: June 2007
My 12 year old son asked the following question to which
we're having a difficult time getting a conclusive (and consistent)
answer from our scientist friends: If you take a 1 ft x 1 ft x 1 ft
infinitely strong and rigid cube and fill it completely with water
such that absolutely no additional space exists in the cube, and
then place the cube in a deep freeze (as low as almost 0 K), will
the water ever freeze since it cannot expand at all?
The short answer is yes, it will be a solid at nearly zero Kelvin,
regardless of pressure.
Water's expansion during freezing at atmospheric pressure is well known, but
water is still compressible. If you have sufficiently high pressure or very
low temperature, water will be solid.
Reference this water phase diagram for more information:
That is a bit oversimplified, though. The simple phases (solid, liquid, etc)
lose their distinctions at these extreme conditions. Our common-sense
knowledge of how things works tends to break down. We cannot actually achieve
0K experimentally anyway, and even if we could, the thermodynamics would
make things act really squirrely. At massive pressures, the terms solid and
liquid start to lose meaning. You have a system so highly constrained that
it is no longer hydrogen bonding or van der Waals forces, but nuclear
repulsive forces that dominate the structure. The fact that molecules cannot
jump around as readily is what makes a solid a solid, although technically
molecules can jump around, just at a much slower rate. But I digress...
And, for all you ever wanted to know about water, here is the terrific site
from which I got the phase diagram:
Hope this helps,
The reason your "scientist friends" are having a problem is that this "simple"
question is not at all simple. Ice is a very complicated substance -- possibly
not more complicated than other substances, but certainly the most thoroughly
studied. What you are "really" asking for is the "phase diagram of ice", which
term you can use to search the topic in as much detail and complexity as you
can stand. A rather inclusive site is:
If you refer to the insert figure on that site you will see that at temperatures
just below 0 C. and hold the temperature fixed but increase the pressure several
different transitions from one crystal structure to another will occur. This is a
bit different than the "experimental setup" you proposed, but it ends up doing
the same "experiment". As you can see, below 0 C. and - 60 C. and pressures
less than 1000 MPa there are 5 different arrangements of water molecules that
can occur in solid ice. In total there are between 11 and 13 structures of ice
known (depending upon whose data you believe). Yes the water will freeze, but the
water molecules will rearrange themselves in different shapes depending upon the
specific temperature and pressure.
Yes, the water will indeed freeze, but determining the exact temperatures and
pressures where this happens is for an expert familiar with the properties of
ice. I will explain.
There are at least 12 different forms of ice. Each form has a different arrangement
f atoms and can exist at different pressures and temperatures. There are "phase
diagrams" easily available on the Internet that show the stability of water, ice,
steam, and fluid for various pressures and temperatures. Ordinary ice is Ice 1 -
Water stays liquid at temperatures below 0C when subjected to high pressures.
But there comes a limit to this, and this limit is about –20C and a pressure of
200 megapascals. At higher pressures, the trend reverses and the high pressures
tend to make the water solid. At really high pressures, water is solid up to many
hundreds of degrees.
The diagrams show that solid ice is ALWAYS the stable phase of water below –20C,
regardless of how much pressure there is. So, if you cool your box to –20C or so,
you are guaranteed to have solid ice (assuming no nucleation problems).
But let us do a little calculation, because you are worrying that the pressure
will suppress the freezing.
As a first approximation, suppose you pour water into the container and seal it at
room temperature. As the water is cooled, the water will become more dense and the
water will exert a pulling force on the container. (yes, fluids can "pull" on the
container that they are inside of).
At 0C and below, ice will start to form. Water expands about 9% when it freezes, and
so the water-ice mixture will start to experience pressure as the first bits of ice
form. As more and more ice freezes, there will be more and more pressure in the box.
Let us do a simple calculation. Then we will find out why the simple calculation is
not quite right.
The bulk modulus of ice is about 8.8E9 pascals. That means that if you completely froze
the ice cube (let us say, pretty cold), and tried to stuff it back into the box, you
would need to squeeze with a pressure of about 790 megapascals of force to compress 9%
to make it fit. That is about 114,000 pounds per square inch, so you would need a
strong box. But during the process of compressing it into the box, the pressures would
be high enough for the ice to transform to types 3 and 5 and maybe even 6. It is
difficult to determine what the compressibility of these ice forms are. So, as the
ice is squeezed into the box (or as it is made cooler and cooler), it takes a real
expert to figure out what the pressures are. But, solid ice is ALWAYS the stable
phase of water at about –20C and below, so that the water in the infinitely strong
and rigid cube will indeed freeze.
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Update: June 2012