Coefficient of Linear Expansion
Introduction: The objective of this experiment is to measure the coefficient of linear expansion
of copper, steel and aluminum by directly measuring the expansion in a length of tube (made of
copper, steel or aluminum) as the temperature of the tube is increased from room temperature.
Figure 1: Equipment for the Coefficient of Linear Expansion experiment showing the expansion tube
apparatus, metal tubs, steam generator, multimeter and condensation collection container.
Equipment: Expansion tube apparatus and steam generator, 2" elevation block, Digital
ohmmeter, rods of Steel, Cu and Al metal. A container to collect the condensed steam.
Theory:
Most materials expand somewhat when heated through a temperature range that does not
produce a change in phase (that is changing from a solid to a liquid or from a liquid to a gas).
The added heat increases the average amplitude of vibration of the atoms in the material which
increases the average separation between the atoms. Suppose an object of length L undergoes a
temperature change of magnitude ∆T. If ∆T is reasonably small, the change in length, ∆L, is
generally proportional to L and ∆T. Stated mathematically:
∆L = α .L∆T ,
(1)
where α is called the coefficient of linear expansion for the material. This, of course, assumes
that the material will have the same expansion in all directions for a given temperature change.
This is true for each of the materials we will be using, but not true for all materials (materials that
exhibit this type of behavior, same expansion in all directions, are called isotropic). Typically α
will also vary somewhat with temperature so that the degree of expansion depends not only on
the magnitude of the temperature change, but on the absolute temperature as well. That is, in
which temperature range is the expansion taking place. In this experiment, you will measure α
for copper, aluminum, and steel. These metals are isotropic (same expansion in all directions) so
that α need only be measured along one dimension. Also, within the limits of this experiment, α
does not vary with temperature.
(Hint: Fill in the open circles in front of the procedure steps to help you perform the experiment)
Procedure:
o Measure L, the length of the copper tube at room temperature. Measure from the inner edge
of the stainless steel pin on one end, to the inner edge of the angle bracket at the other end
(see Figure 2). Record your results in Table 1. NOTE: You will later use this measurement
of the length of the tube to calculate a value for α. Typical values of α are very small (on the
order of 10-6/°C). In order to determine a reasonably accurate value of α you will need to
measure L to a reasonable accuracy and precession. Try to accurately as possible measure L
to within 0.5mm. If you are concerned that you are not using the entire length of the tube to
measure the value of L, think about how L will be used to calculate α, and how Equation (1)
implies uniform expansion.
Figure 2: Proper measurement of length L of the metal tube.
o
Mount the copper tube in the expansion base as shown in Figure 3 and Figure 4. The stainless
steel pin on the tube fits into the slot on the slotted mounting block and the bracket on the
tube presses against the spring arm of the dial gauge.
Figure 3: Alignment and positioning of the metal tube in the expansion base.
Figure 4: Alignment of the stainless steel pin and slotted bracket.
o
o
Use one of the provided thumbscrews to attach the thermistor lug to the threaded hole in the
middle of the copper tube. The lug should be aligned with the axis of the tube, as shown in
Figure 5, so there is maximum contact between the lug and the tube.
Place the foam insulator over the thermistor lug as shown in Figure 5 and Figure 8.
Figure 5: Positioning of the foam insulation around the termistor lug.
o
o
o
o
o
Plug the leads of your ohmmeter into the banana plug connectors labeled “thermistor” in the
center of the expansion base.
Measure and record Rroom, the resistance of the thermistor at room temperature. Record this
value in the table.
Use tubing to attach your steam generator to the end of the copper tube. Attach it to the end
farthest from the dial gauge.
Use a book or a block of wood to raise the end of the expansion base at which steam enters
the tube—a few centimeters is sufficient. This will allow any water that condenses in the tube
to drain out. Place a container under the other end of the tube to catch the draining water.
Turn the outer casing of the dial gauge to align the zero point on the scale with the long
indicator needle. As the tube expands, the indicator needle will move in a counterclockwise
direction.
Figure 6: Manually turn the dial gauge to zero it. Note: Some models have a locking pin that
must be released prior to turning by pressing a release button.
o
Turn on the steam generator. As steam begins to flow, watch the dial gauge and the
ohmmeter. When the thermistor resistance stabilizes, record the resistance (Rhot) in Table 1.
Also record the expansion of the tube length (∆L) as indicated by the displacement of the
indicator on the dial gauge. (Each increment on the dial gauge is equivalent to 0.01 mm of
tube expansion.) Note that ∆L is the difference between the dial gauge readings.

Repeat the experiment for the steel and aluminum tubes. You will need to disconnect
and reconnect the thermistor. Exercise care when doing this so that the wires will not be
pulled off the thermistor. See Figure 7.
Figure 7: NOTE: Exercise caution when changing tubes.
Material
L(mm)
Data
Rroom(Ω)
ΔL(mm)
Rhot(Ω)
Temperature(conversion)
Troom(°C)
Thot(°C)
ΔT(°C)
Copper
Steel
Aluminum
Table 1: Measured data and temperatures from thermistor reference tables.
Figure 8: Be certain to properly position the foam insulation over the thermistor lug
otherwise a proper temperature reading may not be possible.
Analysis:
1. Use the Conversion Table supplied in the laboratory room to convert your thermistor resistance
measurements, Rroom and Rhot, into temperature measurements, Trm and Thot. Record your results in
the table.
2. Calculate ∆T = Thot – Troom. Record the result in the table.
3. Using the equation ∆L = αL ∆T, calculate α for copper, steel, and aluminum.
αCU = ________________
αsteel = ________________
αAl = ________________
1. Look up the accepted values for the linear expansion coefficient for copper, steel, and aluminum.
Compare these values with your experimental values. What is the percentage difference in each case?
Is your experimental error consistently high or low?
2. On the basis of your answers in question (1), speculate on the possible sources of error in your
experiment (the major sources, the ones that contribute the most to the error). How might you
improve the accuracy of the experiment?
3. From your result, can you calculate the coefficients of volume expansion for copper, aluminum, and
steel? (i.e. ∆V = αVolV ∆T). Note: We did not take enough data for you to answer this question
directly. What is being asked is given the materials we used are isotropic can you deduce the
change in volume of a cube of metal that initially was LxLxL, given the α you measured?
From that can you deduce αVol (typically called β). You may wish to consult your text book.