Temperature a la Galileo

i-6f07d4689fdcc04d488ad09d03ee8cb5-142px-Galileo_Thermometer.jpg

There's famously dozens of ways to measure the height of a building with a barometer. If you're sufficiently clever, you can think of many, many more ways to measure temperature with just about anything.

One of the most visually impressive ways to measure temperature is the Galilean thermometer, which is also sometimes called the Galileo thermometer. It consists of little fluid-filled glass bulbs immersed in another liquid. The suspending liquid is itself encased in a long glass tube. Hanging from each of the glass bulbs is a marker with a temperature label. Look at the temperature on the highest bulb which has sunk to the bottom and the temperature on the lowest bulb which has floated to the top and in between those numbers is the temperature. As the temperature rises, one bulb after another on the top will gradually sink to the bottom. As the temperature falls, one bulb after another on the bottom will rise to the top. In this way the temperature is reflected in which bulbs are floating and which are not. The tube itself is narrow enough to preserve the numerical order of the temperature markers, and the bulbs are too large to slide past each other.

To figure out how it works, let's examine the forces on a given bulb. There two of them. First there's the upward force of buoyancy. Second, there's the downward force of the bulb's weight.

According to Archimedes' principle, the buoyant force is equal to the weight of the liquid displaced. The mass is going to be equal to the volume of the fluid times the density of the fluid, and multiply that by g to get the weight. Let's call this force with the letter u to remind us that it's the upward force on a bulb:

i-d4bb9fe09d6b78eb832985821d8a307f-1.png

The downward force from the weight of the bulb itself is found in pretty much the same way. The weight is the mass of the bulb times g, but let's write the mass in terms of the density of the bulb itself, as the density of the bulb times the volume of the bulb:

i-88516ca505d84f969b7ab15a965c3fb3-2.png

And that's the upward force with the letter u. Subtract the downward force from the upward force and you'll get the total force on the bulb:

i-d18063683dcc0d42b9be45451a84d1e3-3.png

If the fluid density is greater than the bulb density the result will be a positive number, the force will be up, and the bulb will float. The the fluid density is less than the bulb density the result will be a negative number, the force will be down, and the bulb will sink.

Now you know that in general objects expand when heated and contract when cooled. The fluid itself is some hydrocarbon and its density changes in a comparatively large way with temperature. The fluid surrounding the bulbs will contract when it gets colder which means its density must increase. Denser fluid increases the upward force on each bulb. The bulb doesn't expand or contract very much at all because it is made of glass. Glass changes volume very little with temperature and so the density of each bulb is essentially constant with respect to the density of the fluid, and so the designers don't have to worry about the expansion of the glass bulb offsetting the expansion of the liquid. Pyrex glass, for instance, expands something like five hundred times less than ethanol per degree. This means the maker of these thermometers can carefully adjust the density of each bulb so that it will just exactly have the same density as the fluid when the fluid is at the particular temperature labeled on the bulb.

I have one of these on my desk, given to me by my lovely girlfriend for our anniversary. They're an elegant and useful demonstration of a rather interesting physical principle. And they're only about twenty or thirty bucks
depending on which size you're looking at.

Much more interesting than a boring old digital thermometer, I think.

More like this

The so-called "Galilean thermometer." The object known as the Galileo Thermometer is a vertical glass tube filled with a liquid in which are suspended a number of weighted glass balls. As the temperature of the liquid changes, so does the density. Since each glass ball is set to float at…
So Tony Soprano pitches ties a concrete block to Salvatore Bonpensiero and pitches him into the ocean, where he will inform the police no more. Being a big guy, Bonpensiero has a fairly low density compared to your average human being - say, 0.96 grams per cubic centimeter. That's less than water…
I want to say a word about what a proxyindicator is. And isn't. I noticed that the term is not in some, perhaps many, dictionaries, so I guess this leaves me free to do what I want with it! But wait, the term "proxy" is of course in the dictionary. It is an ancient short version of the word "…
Some months ago I made a (seemingly idle) threat to follow up my basic concepts posts on polar and non-polar molecules and intermolecular forces with a post on phase changes. Finally it's here! Since the discussion here will be leaning on a number of the concepts discusses in the earlier posts,…

I plan to buy one of those thermometers, as soon as they come out with one that works on the Kelvin scale. If you're going to go nerdy, you might as well go all the way ;)

By Max Fagin (not verified) on 20 Oct 2008 #permalink

I used to have one of these. I gave it away when I was trying to reduce my amount of stuff to be stored when I moved abroad. Maybe if I'm lucky I'll get a new one in the future. They are really nice.

It also demonstrated that glass and the air around it does not transfer heat energy so well. In the summer evenings, when I opened the windows to let in cool air and the temperature felt comfortable, my Galileo thermometer would still be showing 32 degrees for hours, which was probably the temperature of the walls in more or less thermal equilibrium (by radiation) with the thermometer.