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Physics I: Thermal Expansion Worksheet
Class:
Section:
Lab Group:
Assignment Date:
Names:
answer key:
Copper
Steel
Aluminum
Length
(mm)
ΔL (mm)
701
701
701
.885
.500
.678
Table 1: Data and Calculations
Room
Resistance at
Resistance
Room Temp. when Heated Temperature
T rm ( C˚ )
R rm (Ω)
R hot (Ω)
116200
7780
22
114100
8870
22
113800
8900
22
Table 2: Results
Copper
Steel
Aluminum
Experimental
Thermal
Coefficient α
(1/C˚)
Accepted
Thermal
Coefficient α
(1/C˚)
% Error (%)
0.000018
0.000011
0.000015
0.0000176
0.0000113
0.0000215
2.3
2.6
30
Worksheet
numbers
data
Heated
Temperature
T hot ( C˚ )
90
86
86
Change in
Temperature
Δ T ( C˚ )
68
64
64
ons
Thermal Expansion Apparatus
012-04394C
Accepted Values for Coefficient of
Thermal Expansion
Material
a ( x10-6/∞C )
Copper
17.6
Steel
11.3 to 13.5
Aluminum
23.4
Replacement Parts
The following parts can be ordered from
PASCO scientific.
Item
Changing Tubes
➤ Caution:
Tube
When changing tubes be careful
not to pull the wires off the
thermistor. The thumbscrew must be completely removed
before the thermistor
can be lifted off the
threaded rod.
Thermistor
Thumbscrew
2
PASCO Part #
mod. Thermistor (100 kΩ)
150-03140
Al Tube Assy
003-04413
Cu Tube Assy
003-04412
Steel Tube Assy
003-04414
Foam Insulator
648-03100
Dial Gauge
620-050
012-04394C
Thermal Expansion Apparatus
Experiment: Measuring the Coefficient of Linear
Expansion for Copper, Steel, and Aluminum
Introduction
Most materials expand somewhat when heated through a temperature range that does not
produce a change in phase. 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 = αL ∆T;
where α is called the coefficient of linear expansion for the material.
For materials that are not isotropic, such as an asymmetric crystal for example, a can have a
different value depending on the axis along which the expansion is measured.
a can 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.
In this experiment, you will measure α for copper, aluminum, and steel. These metals are
isotropic so that a need only be measured along one dimension. Also, within the limits of
this experiment, a does not vary with temperature.
Procedure
➀ 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 1). Record your results in Table 1.
➁ Mount the copper tube in the expansion base as shown in Figure 2. 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.
➤ NOTE: Slide or push the tube to one side of
the slide support. Drive the thumbscrew
against the pin until the tube can no longer be
moved. Use this as your reference point.
➂ 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 2, so there is
maximum contact
L
Figure 1 Measuring Tube Length
Bracket on tube
Stainless steel pin
Dial Gauge Spring Arm
Slotted bracket
Figure 2 Equipment Setup (Top View)
3
Thumbscrew
Thermal Expansion Apparatus
012-04394C
between the lug and the tube.
➃ Place the foam insulator over the thermistor lug as shown in Figure 3.
➄ Plug the leads of your ohmmeter into the banana plug connectors labeled THERMISTOR in the center of the expansion base.
Copper Tube
Foam Insulator
➅ Measure and record Rrm, the resistance of the thermistor at room
temperature. Record this value in the table.
➆ Use tubing to attach your steam generator to the end of the
copper tube. Attach it to the end farthest from the dial gauge.
➇ 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.
Thermistor Lug
Banana Connectors
Figure 3 Thermistor Attachment
➈ 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.
➉ 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 betwen the dial gauge readings.
➤ Repeat the experiment for the steel and aluminum tubes.
Data and Calculations
TABLE 1 Data and Calculations
DATA
L (mm)
Rrm (Ω)
CALCULATIONS
∆L (mm)
Rhot (Ω)
Trm (C°)
Thot (C°)
Copper
Steel
Aluminum
➀ Use the Conversion Table at the end of this manual, or the one on the top of the expansion
base, to convert your thermistor resistance measurements, Rrm and Rhot, into temperature
measurements, Trm and Thot. Record your results in the table.
4
∆T (C°)
012-04394C
Thermal Expansion Apparatus
➁ Calculate ∆T = Thot – Trm. Record the result in the table.
➂ Using the equation ∆L = αL ∆T, calculate a for copper, steel, and aluminum.
αCu =
__________________
αsteel =
__________________
αAl =
__________________
Questions
➀ 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?
➁ On the basis of your answers in question 1, speculate on the possible sources of error in
your experiment. How might you improve the accuracy of the experiment?
➂ From your result, can you calculate the coefficients of volume expansion for copper,
aluminum, and steel? (i.e. ∆V = αvolV ∆T)
THERMISTOR CONVERSION TABLE:
Temperature versus Resistance
Res.
(Ω)
351,020
332,640
315,320
298,990
283,600
269,080
255,380
242,460
230,260
218,730
207,850
197,560
187,840
178,650
169,950
161,730
153,950
146,580
139,610
133,000
126,740
120,810
115,190
109,850
104,800
100,000
Temp.
(°C)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Res.
(Ω)
95,447
91,126
87,022
83,124
79,422
75,903
72,560
69,380
66,356
63,480
60,743
58,138
55,658
53,297
51,048
48,905
46,863
44,917
43,062
41,292
39,605
37,995
36,458
34,991
33,591
32,253
Temp.
(°C)
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
5
Res.
(Ω)
Temp.
(°C)
30,976
29,756
28,590
27,475
26,409
25,390
24,415
23,483
22,590
21,736
20,919
20,136
19,386
18,668
17,980
17,321
16,689
16,083
15,502
14,945
14,410
13,897
13,405
12,932
12,479
12,043
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
Res.
(Ω)
11,625
11,223
10,837
10,467
10,110
9,767.2
9,437.7
9,120.8
8,816.0
8,522.7
8,240.6
7,969.1
7,707.7
7,456.2
7,214.0
6,980.6
6,755.9
6,539.4
6,330.8
6,129.8
5,936.1
5,749.3
5,569.3
Temp.
(°C)
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100

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