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Physics Lab The Coefficient of Linear Expansion 1

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 canhave 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 temperatureis 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 = α L0 ΔT , 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 aboutyour 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 thisapparatus 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.

Steam Generator 

Catch Basin

Temperature Sensor 

Steam Jackets

Micrometer 

Hotplate

Plastic Tubing

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Physics Lab The Coefficient of Linear Expansion 2

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. Thistemperature 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 increasethe 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, whilethe 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 themicrometer, 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 thedial 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 intothe 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 itdoes 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 finalmeasurements. 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, anddisconnect both pieces of tubing from the steam jacket. (REMINDER: The steam jacket isHOT.) 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 thecatch basin.

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Physics Lab The Coefficient of Linear Expansion 3

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 theroom, 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 inStep 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 toenter 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 preventthis 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, andmention it in your lab report, so that it may be explained for future students.