# Thermal expansion of water in a pool

I already talked about increasing the temperature of a pool. My father commented that he thought the pool level rose by like half an inch when the temperature increased (by about 10 degrees F). So, this leaves the question: Is my father crazy, or is this possible? Or are both true?

Does water expand when it warms up? Yes, except when it melts. Why does this happen? Liquids are actually very complicated, but here is a basic answer. Take a look at this PhET gas simulator, I know it is for gases not liquids. I think we can make it behave like a liquid if you increase the gravity to the maximum (in the simulator) and cool it down some so that it looks like this:

Now what happens if I increase the energy? Each particle has more energy and the result is an expansion.

I am really not sure if this is a valid comparison, but maybe it is enough for you to get the idea. The PhET simulator is awesome, by the way.

So, what about water? One way to model the expansion of water (or anything, really) is:

Where ? is the expansion coefficient, which is typically not constant with temperature. For the range of water temperature in this case, I will use (from hypertextbook.com)

Great. Now I can find the change in volume of the pool, but I want the change in the water level. Suppose the pool were a rectangular cube with a bottom of area A and depth of d. The initial volume of this pool will be:

And then when the volume increases, the final volume would be:

So, now I can re-write the thermal expansion stuff:

The best thing is that the bottom area of the pool cancels. I did make a guess that I can use the average depth of the pool, I am pretty sure this is ok (if not, the depth doesn't change that much). At this point, I am ready to plug in some stuff. I will assume an average depth of 1.5 meters and a 7 C change in temperature, then:

This is about 0.1 inches. So, yes. The water does expand when heated. 1/2 an inch change in the depth level seems a little high.

Tags

### More like this

##### Power source for a lightsaber
This one has been on my mind for quite some time. What kind of power source would you need to run a lightsaber? I was actually worried recently about this post when I saw the Discovery Channel show "Sci Fi Science". In that particular episode Michio Kaku talks about how you would actually build…
##### Energy in an exploding water heater
The more I think about the last MythBusters' exploding water heater, the more cool things I see. How about I look at the energy of the explosion. There are three things I can look at: How much energy went into the water heater from the electric source? How much kinetic energy did the water heater…
##### Ask a ScienceBlogger: Evaporating Water
Here is another question from Ask a ScienceBlogger. Reader Uday Panta asks: How does water evaporate in the seas? Doesn't water evaporate at 100 C? There were some very good responses in the comments where the question was, but I am going to answer it with some more details. Small Particle Model…
##### Temperature - weirder than you think
Temperature is a pretty weird thing if you think about it. How do you best define temperature? Let me go ahead and give you my favorite definition: Temperature is the thing that two objects have in common when they have been in contact for a long time. Yes, that is a good definition. Maybe now…