Physics Lab
The Coefficient of Linear Expansion
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INTRODUCTION
Most materials increase in size as the temperature is increased. Since this change in size appears
small to the eye, it is easy to think that it’s unimportant. However, as we’ve seen in class, this can
have extremely important effects, usually by causing very large pressures and forces.
For all of the materials we will be concerned with in this course, this expansion with temperature
is of the same type in all directions. For objects that are long and thin, it makes sense to pay
attention to the change in just one dimension – its length.
Although no material changes length perfectly linearly with tempeature, it is a good
approximation for many materials over a wide range of temperatures. As a result, we will use the
equation ΔL = αL0ΔT, where α is the coefficient of linear expansion. Also recall that a delta (Δ)
indicates the final value of a quantity, minus the initial value of that quantity. In this lab, we will
measure initial and final lengths, and initial and final temperatures, in order to calculate α for several
different metals.
PROCEDURE
IMPORTANT: Many of the items you will be using are extremely hot. Always think about
your actions before you do them. Any time you need to handle hot equipment, always use
gloves/pads.
1. Gather all the necessary materials: meter stick, metal rods, linear expansion apparatus,
temperature sensor or thermometer, steam generator, hotplate, and catch basin. Much of this
apparatus will already be at the lab stations (and hot!) when you arrive. Note: be sure to use a
temperature sensor that has blue plastic tubing at the end, to prevent steam from escaping.
Temperature Sensor
Steam Generator
Micrometer
Steam Jackets
Hotplate
Catch Basin
Plastic Tubing
Physics Lab
The Coefficient of Linear Expansion
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2. Measure the initial temperature of the room, and assign an appropriate uncertainty to this
measurement. You will use this as your initial temperature, for all of your rods. This
temperature should be very close to the temperature of the rods, and this temperature should not
change much over the course of the lab. If you would like to be more accurate, you may use a
second temperature sensor or thermometer, used only to measure the temperatures of the rods, at
the times you measure the lengths of the rods. Note: the fact that the room will likely get warmer
over the course of the lab should affect your uncertainty in the initial temperature.
3. Using the meter stick, measure the initial length of each metal rod (together with its uncertainty).
Do not handle the rods excessively while doing so, since the heat from your hands may increase
the temperatures of the rods. Note: once the first rod has been measured, one lab partner may
begin the following steps for that rod, while the other partner measures the rest of the rods.
4. Insert the rod into the aluminum steam jacket, then place the steam jacket into the linear
expansion apparatus. Make sure that one end of the rod rests firmly against the set screw, while
the other end is against the micrometer. Also, make sure that there is over 1 mm of “give” left
before the micrometer jams – if this is not the case, ask the instructor for assistance.
5. Record the initial micrometer setting with its uncertainty. Note:
the calculations will be easiest if you turn the outer dial of the
micrometer, so that its value is initially zero, though even this
value of zero should have some uncertainty. (And this
uncertainty will be different for each rod.)
Also: the
micrometer is correct in noting that each small division of the
dial is 0.01mm (the label printed on the expansion apparatus is
incorrect).
6. Connect the tubing from the steam generator to the steam jacket, and from the steam jacket to the
catch basin. The tubing should be secure, but you should not use too much force: you’ll need to
remove the tubing in just a few minutes. Then, place the temperature sensor or thermometer into
the hole at the center of the steam jacket. IMPORTANT: make sure that neither of the tubes nor
any part of the temperature sensor touches the hot plate or steam generator: they can melt!
7. Almost immediately, you should see the reading on the micrometer dial start to change. If it
does not, ask the instructor for assistance. Also: all parts of the steam jacket should get equally
hot. If one section is hot while the rest is cool to the touch, ask the instructor for assistance (and
see the note at the end of this handout).
8. Observe the micrometer dial. Once the needle has stopped moving, you may take your final
measurements. Record the final micrometer reading, and the final temperature (with
uncertainties). This should take a few minutes.
9. (Gloves/pads required.) CAREFULLY remove the temperature sensor/thermometer, and
disconnect both pieces of tubing from the steam jacket. (REMINDER: The steam jacket is
HOT.) Again, make sure that neither of the tubes nor any part of the temperature sensor touches
the hot plate or steam generator: they can melt! Then, CAREFULLY lift the steam jacket,
tilting the drain hole into the catch basin. Drain as much hot water as possible into the catch
basin.
Physics Lab
The Coefficient of Linear Expansion
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10. (Gloves/pads required.) Slide the heated rod out of the jacket, onto the table in the back of the
room. Then, take your steam jacket to the sink in either the front of the room or the back of the
room, and run it under cool water until it nears room temperature.
11. Set that steam jacket aside, and take a steam jacket that has been sitting at room temperature.
12. Repeat steps 4-11 for the other three rods (assuming you’ve already measured their lengths in
Step 4).
ANALYSIS
1. Calculate ΔL and ΔT for each case. Use these to calculate α for each case.
2. Using your uncertainties, calculate a worst-case maximum and minimum α for at least one case.
3. Calculate the % error between your calculated α and the accepted α (as found in your textbook)
for each case.
QUESTIONS
1. Do the measurements we made during this lab prove that the increase in length of these metal
rods is a linear function of their increase in temperature? Why or why not? (Make sure your
explanation is clear.)
2. Explain why the diameter of a hole in a metal plate increases when the plate is heated.
3. Based upon your observations, formulate an “order of magnitude” rule of thumb for linear
expansion of metals: “A meter length metal rod lengthens by about ____ mm for a temperature
rise of 100 °C.”
IF YOU HAVE PROBLEMS
Some students in prior semesters have had some difficulty with this experiment: steam appears to
enter the steam jacket and does not leave. After a few minutes, the end of the steam jacket where the
steam enters becomes extremely hot, while the other end remains cold.
This is due to a blockage in the steam jacket, most likely caused by condensed water. To prevent
this from occurring, you should make sure that your steam jacket is fully empty of condensed water
before attaching it to the steam generator, and that all of the tubing is also clear of condensed water.
(Dump any excess condensation in your catch basin before connecting.)
If this problem happens, you may just wait until the steam jacket becomes hot enough to boil this
water (this takes several minutes), then wait until the entire rod reaches the desired temperature. Or,
you may stop that trial and begin again, using a new, cleared out steam jacket.
If you encounter a different problem, please bring it to the instructor’s attention during class, and
mention it in your lab report, so that it may be explained for future students.