| MadSci Network: Engineering |
Most thermometers depend on the differential thermal expansion rates of
materials to measure temperatures. That is, we all know that materials
expand in heat and contract in the cold; what's less obvious is that
different materials do so at different rates. The rate is called
"coefficient of thermal expansion".
I describe three different designs below that reflect this principle and
classic thermometer designs. My recommendation is to go with design #3 as
being the simplest in concept and construction.
Thermometer #1
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The difference in expansion rates of different metals is the
principle is used in mechanical dial thermometers. Consider two long strips
of dissimilar metals are welded together along their lengths. As the
temperature increases, one of the metal strips want to expand more than the
other, so the assembly bends towards the side that isn't expanding as fast.
In a dial thermometer, the bimetal strip is coiled into a spring that
expands as the temperature rises and contracts as the temperature falls.
One end of the sprig is fixed to the thermometer's case, and the other to
the pointer.
If you were to find two long, thin strips of dissimilar metal (say, brass
and aluminum), these could be fastened together along their lengths using
screws and nuts every few inches, or perhaps by gluing them with a strong
glue such as epoxy. One would take note of the amount of curvature in the
strips to detect temperature changes.
Thermometer #2
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Another approach is to take advantage of the different expansion rates of a
liquid and solid. Galileo used this idea and Archimede's principle to
invent his thermometer, the aptly named "Galileo's thermometer". Liquids
such as water often expand much more than solids such as glass or metal.
Objects float in water if the weight of water they displace is more than
their own weight; if the weight of water displaced is less than the
object's weight, it will sink. The weight of an object does not change
with temperature. The density (weight per unit volume) of a liquid changes
with temperature because although the total weight is constant, the total
volume changes. For water above 4 deg C, but below boiling, water expands
at the rate of about 0.2 cc per kg per deg C. That is, 1.000 liter of
water at 25 deg C will occupy about 1.002 liters (that is, one liter plus 2
cc more) at 35 deg C.
An object that just *barely* floated at 25 deg C will sink at 35 deg C, if
it doesn't expand very much (its temperature is increasing, too). But
glass doesn't expand very much compared to water. What Galileo did is have
a glass blower make some sealed, air-filled glass balls. Galileo then
carefully added weights to these balls so that each had a specific
temperature at which could no longer float. That is, balls with a lot of
weight would sink when the temperature was low, while balls with less
weight would float until the temperature got higher. The balls were marked
with the target temperature at which they would sink.
Galileo's thermometers can often be found in scientific gift shops (search
the Web for "Galileo +thermometer" to see illustrations). I have one at
home and it works quite nicely.
You could try reproducing this invention using water and any kind of rigid
floating object. For example, small bottles in which you put a little sand
(but mostly air) might work. If you have access to a chemistry lab (or
better yet, the chemist!) with accurate scales and volume measuring
equipment (you need to measure the displacement volume of the bottles
accurately), you could assemble the weighted bottles in fairly
straightforward fashion. One would need to reference a table of water
density versus temperature, with the objective to weighting the different
bottles to get to the same average densities for different water
temperatures. The scales would be used to measure the mass
of each bottle and deterrmining how much sand to add. Alternatively, one
could get there experimentally (as did Galileo) by floating the bottles in
tubs of water at different temperatures until just the right amount of sand
is in each (and checking that there's not too much or too little by seeing
if they float or sink in tubs colder or hotter than the target temperature
of each bottle).
This design (#2) is probably the fussiest of the three to get working
right.
Thermometer #3
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The simplest approach of all (sorry I made you wait 'til the end) is to
reproduce the bulb thermometer on a grand scale. The bulb thermometer has
a reservoir of liquid (alcohol or mercury, typically) that feeds a very
narrow channel inside a glass column. As the liquid expands with
temperature, the level inside the columns rises; as the temperature
decreases, the level sinks.
Why not do this with a glass jug, a stopper, some clear, thin plastic
tubing, a funnel, a long thin stick, a small stick to plug a hole in the
stopper (see below), and some duct tape? (No good science experiment can be
done without duct tape; however, any kind of reasonably waterproof adhesive
tape will do for your purposes). Make two holes in the stopper that snugly
fit the plastic tubing. Fill the jug with colored water, and insert the
stopper. Use some of the plastic tubing to connect the funnel's outlet to
the jug (via the hole in the stopper). Insert a different piece of plastic
tubing in the other hold in the stopper part way into the jug. Use the
tape to affix the stick to the jug so that the stick stands vertically,
then tape the second piece of tubing to the stick.
The glass jug is the reservoir of your thermometer and the tubing taped to
the stick is the "glass column".
All that's left to do is to use the funnel to force in a bit more liquid to
the jug to force out all air and to get some liquid partway up the other
tube (the one taped to the stick). Remember that "water seeks its own
level". Once you've done that, remove pull out the tubing connected to the
funnel and plug its hole through the stopper (this is where the "plug
stick" comes in). This will take some practice and deft application of
fingers, as the water partway up the column will want to come spurting out
of the hole formerly occupied by the filling tube.
You need to use a glass jug, as opposed to plastic, to ensure rigidity, so
that as the water expands and contracts it must rise and fall up and down
the thermometer's column. The other trick to making this work is to force
out all the air bubbles. Again, you want to make sure that the water has
no place to go when it expands except up the column.
A gallon jug (about 4 liters) will work nicely if thin tubing (say, 1/8" to
1/4" diameter, that is, 3 to 6 mm diameter) can be procured. I'm thinking
of the clear plastic tubing that's often used by hobbyists who keep
aquariums to supply air to their water filters from an external air pump.
A pet shop or well stocked hardware store should also be able to fix you up
with some of this tubing (it's quite inexpensive).
With a 4 liter reservoir and 5 mm diameter tubing, you should get a rise of
about 2 cm of liquid per deg C temperature rise. But remember, it will take
time for this amount of water to change temperature, so don't expect rapid
response times. You should easily see temperature changes through the
course of a day, though.
This apparatus will be a bit messy to set up, but probably the easiest and
most accessible to your students in terms of concept and materials.
Have fun!
Steve Czarnecki
P.S. A simple "dinner table" experiment to demonstrate the thermal
expansion of gasses: Take an empty glass soda bottle ("a Coke bottle" or a
wine bottle), wet the top of the rim with saliva, and place a small coin
over the opening. A U.S. dime works well with one of the old 16 oz.
returnable Coke bottles. The saliva acts to help seal the air inside the
bottle.
Carefully wrap your hands around the bottle as it stands on a table top.
Continue holding the bottle, being careful not to shake or move it. Watch
the coin over the opening very carefully.
After five minutes or so, you should see it pop up a bit and come back to
rest, with the cycle repeating a few times over the next few minutes.
What's happening is that your hands are warming the air inside the bottle,
which expands, forcing the coin to flip up a bit and allow the excess
pressure to escape.
It takes time to get this going because you have to warm up the glass
bottle and then the air inside.
Note that a glass bottle is essential to making this work (the air must
have no where to go except to dislodge the coin). Use the smallest (i.e.,
lightest) coin that will just cover the bottle opening.
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