# Does water do work as it freezes? Where does the energy come from?

I saw this interesting question in “The Last Word”, a column in the British science mag New Scientist quite similar to “The Straight Dope”, but focusing on science.

Paraphrased:

If water expands when it freezes, and is able to do things like burst pipes, then it is doing work as it freezes. Where does this energy come from? Isn’t energy being taken away from it in order to freeze it?

WAG: Perhaps some of the energy being taken from the water to freeze it is used instead towards the work involved in bursting pipes and eroding rocks.

That’s an interesting WAG. If it’s true, then water that would do work, like burst pipes, might freeze quicker that water that’s “just sitting there”.

Or maybe not, since it’s always doing the work of displacing air. So, perhaps work is always done (or almost always, at least in the atmosphere).

Been a while since I did fluid mechanics, so where to begin to explain your question? Hmmm…

Let’s start with dimensional analysis. If you multiply pressure times volume, what units do you get? Pressure is force over area, or N/m^2. Volume is m^3, and the product of pressure and volume is N*m which is the same units as work!

In fact, chemists often write work done as the pressure times the change in volume for a liquid. Engineers know better and correctly write the change in work as the pressure times the change in volume multiplied by the volume times the change in pressure.

In fact, a fluid does work whenever it changes volume and/or pressure. Is this related to temperature change? Of course. We know for gases that pressure is proportional to temperature, for example, and all that stuff about Boyle’s Law and Charles’ Law etc. applies. But there is also a relation for liquids and ice as well which can be interpreted from the appropriate “phase diagrams” (graphs of V vs. T, P vs. V, P vs. T, or all three) for the given subject, i.e. ice and water.

As for energy, heat loss with a change in temperature when not at the freezing point is given by E=mc(dT) where c is the specific heat cvapacity and dT is the change in temperature for an object of mass m. At the actual freezing point, the temperature of ice stays at 0 degC but there is energy needed to change the liquid into a solid by making stronger bonds and closer molecules. This is given by E=K*m where K is a coeeficient of freezing in J/kg.

Work is nothing more than a change in energy over a certain time, i.e. W=dE/dt. Both of these factors change, so work must be done. It comes from all of the changing things: pressure, volume, temperature… does ice expand when it freezes? IIRC, I think the answer is yes to about -4 degC but only because water is different from most other liquids. Like I say, it’s been a while since I’ve dealt with this stuff… years even.

Wow, Dr_Paprika, great reply there, although a little hard for neophytes like myself to understand.

Just to throw another twist on this thing…

The freezing temperature of water drops about one degree for every 75 atmospheres, right?

So, wouldn’t water under pressure, about to burt a pipe or crack a rock, or displace something take longer to freeze? Maybe that’s where the extra work/energy comes into the equation.

Sorry, that may have been unclear. What I was trying to say was:

Perhaps the greater temperature drop required to freeze water under pressure is directly related to the energy it requires for that ice to do the work of bursting a pipe.

What do you think?

It’s been forever since I’ve done this stuff. I’m glad I went to a really good engineering school where they taught me how to recover anything I ever learned from first principles (at least in theory) :). Let me try and think this through.

Pressure, molecularly, is the number of collisions the atoms make with side of the container. If you increase the temperature, a direct measurement of the average kinetic energy of the substance, you increase the temperature too since atoms which move faster collide with the container more often.

So water under pressure has a higher temperature to begin with (though not necessarily much) and a smaller volume too. The smaller volume makes it harder to expand, the higher temperature means more energy is needed to cool it and bring the temperature down.

Where this gets complicated beyond my ability to explain it to you is that there are many kinds of ice, more than seven, that have different molecular structures and are formed depending on the pressure on the water. I have no idea whether this affects your problem or not since it is asked in general terms.

The pipe bursts because the ice continues to expand. When the ice has filled the pipe and it tries to expand, it pushes circumferrentially against the pipe. The pipe resists this with a normal force for as long as it can, eventually the outward expansion force exceeds the pipes ability to provide resistance and it needs to deform in order to rebalance the forces.

Conceptually there is an energy cost. It took heat energy to take water from a solid to a liquid. Maintaining water in a liquid form is akin to it having potential energy. When freezing occurs this potential energy is released and does “work” as kinetic energy as the phase state changes back to a solid.

No…that’s not right, it’s too simple. Jeez I hate these kinds of problems.

What are all you SMDB Physics mavens doing… knitting Afghans? A Dr. had to answer the physics of this question!

I invoke the Great Cecil to weigh in on this one. It’s very tiresome (although sincerely appreciated) to wade through someone’s attempt to figure out something they know only a little about. The Great Cecil has the ability to do the research and then reduce it to lay-speak. I don’t know how to contact Him, but if there’s a special horn or whistle or signal that the moderator can flash, I request it. Do we shine a Cecil signal on a nearby building or cloud? Does someone have to call Bruce Wayne-Zotti on the Cece-phone? It’s a darn good question and one we might expect to see in a column, so how about a little professional help here?

Rev, are you sure New Scientist doesn’t answer that? Is there a newscientist.com?

" There is a latent heat in liquid water that must be released and removed before that liquid can become
solid ice. The latent heat is essentially a chemical potential energy associated with the tighter bonding of the
water molecules in ice than in liquid water."

Therefore, Heat=energy to do work (Pipe expands)

The reason that water expands upon freezing is because of the strong hydrogen bonding between the water molecules. Water is
polar having a positive e3nd nearest the Hydrogens and a negative end nearest the Oxygen atom. Therefore The positive ends
of some water molecules attract the negative ends of other water molecules. When water reaches 4 degrees Celsius the
molecules have been pushed as close to one another as they will be. Below 4 degrees the water molecules begin to align
themselves into the crystal structure of ice. This requires the water molecules to widen the angle between the Oxygen Hydrogen
single bonds from the usual 104.5 degrees Celsius. When this happens the water molecules take up more space hence
expansion. "

Hmmmn… response is topical and contains useful information and links.

Alright DAMMIT!! What have you done with Handy! Give him back un-hurt and we won’t call the authorities!

Interesting.

So, water -under pressure- would probably have a lower freezing point than water at, say, 1 atmosphere?

Then there’s that non-compressibility thing about water.

(Well, you try to make sense of it while taking Nyquil for the flu.)

Water has a higher potential energy than ice. As water turns to ice this potential energy is given off as heat. If the ice is constrained under the pressure of a container part of the energy is given off as heat and part is used to do work against the container. So it doesn’t turn to ice as fast. This effect is also what makes skating possible - the pressure turns the ice under the blade back into water which allows the blade to slide.

Liquid water at the freezing temperature has more internal energy than ice at the freezing temperature. The combination of heat removed and work done by the expanding ice against a pressure will equal this change in energy. Look up the first law of thermodynamics for more info.

I see Ring just said about the same thing…

The way the “Last Word” works is that people send in questions, and scientists reading the mag send in their answers. It will be a week or so before the answers start coming in. I was just impatient, and thought it might be an interesting subject for a thread here.

There is in fact a newscientist.com. I don’t go to it often, because I subscribe the the mag and there’s little more than a subset of the print mag on the site.

It’s my favorite science magazine, it suites me better than Scientific American and Discover.

To All: thanks for your replies. I’m kind of under the weather right now; I’ll wait till my mind is working better before I ask some specific questions.