Includes
Teacher's Notes
and
Typical
Experiment Results
THERMAL EXPANSION
Instruction Manual and
Experiment Guide for
the PASCO scientific
Model TD-8558A
APPARATUS
012-04394C
5/94
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© 1990 PASCO scientific $2.00
012-04394C Thermal Expansion Apparatus
T able of Contents
Section Page
Copyright, Warranty and Equipment Return.................................................. ii
INTRODUCTION:
Equipment..................................................................................................1
Additional Equipment Required................................................................1
Notes on Temperature Measurement.........................................................1
Accepted Values for Coefficient of Thermal Expansion...........................2
Changing Tubes.........................................................................................2
Replacement Parts .....................................................................................2
EXPERIMENT:
Measuring the Coefficient of Linear Expansion for Copper, Steel, and
Aluminum:
Introduction .........................................................................................3
Procedure .............................................................................................3
Data and Calculations..........................................................................4
Questions .............................................................................................5
Thermistor Conversion Table:.............................................................5
Teacher’s Guide...............................................................................................1
Technical Support............................................................................................3
i
Thermal Expansion Apparatus 012-04394C
Copyright, Warranty and Equipment Return
Please—Feel free to duplicate this manual
subject to the copyright restrictions below.
Copyright Notice
The PASCO scientific Model TD-8558A Thermal
Expansion Apparatus manual is copyrighted and all
rights reserved. However, permission is granted to
non-profit educational institutions for reproduction of
any part of this manual providing the reproductions
are used only for their laboratories and are not sold for
profit. Reproduction under any other circumstances,
without the written consent of PASCO scientific, is
prohibited.
Limited Warranty
PASCO scientific warrants this product to be free
from defects in materials and workmanship for a
period of one year from the date of shipment to the
customer. PASCO will repair or replace, at its option,
any part of the product which is deemed to be defective in material or workmanship. This warranty does
not cover damage to the product caused by abuse or
improper use. Determination of whether a product
failure is the result of a manufacturing defect or
improper use by the customer shall be made solely by
PASCO scientific. Responsibility for the return of
equipment for warranty repair belongs to the customer. Equipment must be properly packed to prevent
damage and shipped postage or freight prepaid.
(Damage caused by improper packing of the equipment for return shipment will not be covered by the
warranty.) Shipping costs for returning the equipment,
after repair, will be paid by PASCO scientific.
Equipment Return
Should the product have to be returned to PASCO
scientific for any reason, notify PASCO scientific by
letter, phone, or fax BEFORE returning the product.
Upon notification, the return authorization and
shipping instructions will be promptly issued.
ä
NOTE: NO EQUIPMENT WILL BE
ACCEPTED FOR RETURN WITHOUT AN
AUTHORIZATION FROM PASCO.
When returning equipment for repair, the units
must be packed properly. Carriers will not accept
responsibility for damage caused by improper
packing. To be certain the unit will not be
damaged in shipment, observe the following rules:
➀ The packing carton must be strong enough for the
item shipped.
➁ Make certain there are at least two inches of
packing material between any point on the
apparatus and the inside walls of the carton.
➂ Make certain that the packing material cannot shift
in the box or become compressed, allowing the
instrument come in contact with the packing
carton.
Address: PASCO scientific
10101 Foothills Blvd.
Roseville, CA 95747-7100
Phone: (916) 786-3800
FAX: (916) 786-3292
email: techsupp@pasco.com
web: www.pasco.com
ii
012-04394C Thermal Expansion Apparatus
Introduction
Introduction
The PASCO Model TD-8558A Thermal Expansion
Apparatus provides easy and accurate measurements
of the coefficient of linear expansion for steel, copper,
and aluminum.
To make the measurement, the steel, copper, or
aluminum tube is placed on the expansion base. The
length of the tube is measured at room temperature,
then steam is passed through it. The expansion of the
metal is measured with 0.01 mm resolution using the
built-in dial-gauge. Temperatures are measured to
within 0.5 °C using a thermistor attached to the center
of the tube. If you wish to investigate the expansion of
the metals at additional temperatures, hot or cold water
can be passed through the tubes.
Complete step by step instructions and a data sheet for
results are provided on the following pages.
Equipment
Your TD-8558A Thermal Expansion Apparatus
includes:
• A 70 cm long expansion base with a built-in dial
gauge and thermistor.
➤ NOTE: The dial gauge can be removed or
repositioned by loosening the screw on the dial
gauge mounting block.
• Three metal tubes — steel, copper (99.5% Cu,
0.5% Te), and aluminum (98.9% Al, 0.7% Mg,
0.4% Si): 5/8-inch outside diameter with 1/4inch outside diameter connectors. Each tube has a
thumbscrew for attaching the thermistor lug.
• A foam insulator to avoid heat loss at the thermistor connection point.
Additional Equipment Required
In addition to the TD-8558A Thermal Expansion
Apparatus, the following items are needed to perform
the experiment:
➀ A source of steam or hot water, such as the PASCO
Model TD-8556 Steam Generator.
➁ A digital ohmmeter such as PASCO Model SE-
9589 to measure the thermistor resistance. Leads
should have banana plug connectors, such as
PASCO Model SE-9750 or SE-9751 Patch Cords.
➂ A small object to raise the end of the expansion
base approximately 2-inches and a container to
catch the water as it drains out of the tube.
If additional data points are desired you will also
➃
need: a source of hot or cold water.
Notes on Temperature Measurement
A thermistor's resistance varies reliably with temperature. The resistance can be measured with an ohmmeter, and converted to a temperature measurement using
the conversion table provided on the expansion base
and also on the back page of this manual. Although
the relationship between temperature and resistance is
not linear, a linear approximation can be accurately
used to interpolate between table data points with an
accuracy of approximately ±0.2 °C.
The thermistor used to measure the tube temperature is
embedded in the thermistor lug. Once thermal equilibrium has been reached, the heat is highly uniform
along the length of the tube. The foam insulator is
used to inhibit heat loss through the thermistor lug so
the lug temperature closely follows the tube temperature. The insulator does not have any appreciable
effect on the local temperature of the tube itself.
• Thermoplastic elastometer tubing with 1/4" I.D.
1
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
Changing Tubes
➤ Caution:
When changing tubes be careful
not to pull the wires off the
thermistor. The thumb-
screw must be completely removed
before the thermistor
can be lifted off the
threaded rod.
Thermistor
Tube
Thumbscrew
Replacement Parts
The following parts can be ordered from
PASCO scientific.
Item 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
2
012-04394C Thermal Expansion Apparatus
L
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
Bracket on tube
Dial Gauge Spring Arm
Figure 2 Equipment Setup (Top View)
Figure 1 Measuring Tube Length
Slotted bracket
Stainless steel pin
Thumbscrew
3
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 connec-
tors labeled THERMISTOR in the center of the expansion base.
Copper Tube
Foam Insulator
Measure and record R
➅
, the resistance of the thermistor at room
rm
temperature. Record this value in the table.
Use tubing to attach your steam generator to the end of the
➆
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
Thermistor Lug
Banana Connectors
base at which steam enters the tube—a few centimeters is
sufficient. This will allow any water that condenses in the tube
Figure 3 Thermistor Attachment
to drain out. Place a container under the other end of the tube to
catch the draining water.
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 (R
) in Table 1. Also record
hot
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 CALCULATIONS
L (mm) Rrm (Ω) ∆L (mm) Rhot (Ω) Trm (C°) Thot (C°) ∆T (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, R
measurements, Trm and T
. Record your results in the table.
hot
and R
rm
, into temperature
hot
4
012-04394C Thermal Expansion Apparatus
➁ Calculate ∆T = T
– Trm. Record the result in the table.
hot
➂ Using the equation ∆L = αL ∆T, calculate a for copper, steel, and aluminum.
αCu = __________________
α
= __________________
steel
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 = α
V ∆T)
vol
THERMISTOR CONVERSION TABLE:
Temperature versus Resistance
Res. Temp.
(Ω) (°C)
351,020 0
332,640 1
315,320 2
298,990 3
283,600 4
269,080 5
255,380 6
242,460 7
230,260 8
218,730 9
207,850 10
197,560 11
187,840 12
178,650 13
169,950 14
161,730 15
153,950 16
146,580 17
139,610 18
133,000 19
126,740 20
120,810 21
115,190 22
109,850 23
104,800 24
100,000 25
Res. Temp.
(Ω) (°C)
95,447 26
91,126 27
87,022 28
83,124 29
79,422 30
75,903 31
72,560 32
69,380 33
66,356 34
63,480 35
60,743 36
58,138 37
55,658 38
53,297 39
51,048 40
48,905 41
46,863 42
44,917 43
43,062 44
41,292 45
39,605 46
37,995 47
36,458 48
34,991 49
33,591 50
32,253 51
Res. Temp.
(Ω) (°C)
30,976 52
29,756 53
28,590 54
27,475 55
26,409 56
25,390 57
24,415 58
23,483 59
22,590 60
21,736 61
20,919 62
20,136 63
19,386 64
18,668 65
17,980 66
17,321 67
16,689 68
16,083 69
15,502 70
14,945 71
14,410 72
13,897 73
13,405 74
12,932 75
12,479 76
12,043 77
Res. Temp.
(Ω) (°C)
11,625 78
11,223 79
10,837 80
10,467 81
10,110 82
9,767.2 83
9,437.7 84
9,120.8 85
8,816.0 86
8,522.7 87
8,240.6 88
7,969.1 89
7,707.7 90
7,456.2 91
7,214.0 92
6,980.6 93
6,755.9 94
6,539.4 95
6,330.8 96
6,129.8 97
5,936.1 98
5,749.3 99
5,569.3 100
5
Thermal Expansion Apparatus 012-04394C
Notes
6
012-04394C Thermal Expansion Apparatus
T eacher’s Guide
Experiment: Measuring the Coefficient of Linear Expansion for Copper, Steel and Aluminum
Notes on Procedure
➉ If you allow too much time to elapse before making
your length measurement, the guage rod will absorb
heat, which will
thermistor takes longer to reach equilibrium than
the tube, though; so you must allow a fair amount
of time for your temperature measurement to stabilize. To get the best results despite these problems,
record the maximum change in length recorded by
the guage and the minimum resistance recorded by
the ohmmeter.
decrease the measurement. The
Notes on Questions
➀ The values for Copper and Aluminum are within
2% of the accepted values, and are both low. The
value for steel was within the accepted range. (Steel
has a wide range of linear expansion coefficients,
due to varying composition.)
➁ Answers will vary
➂ α
vol
≈ (α
linear
3
)
Data and Calculations
TABLE 1 Data and Calculations
DATA CALCULATIONS
L (mm) Rrm (Ω) ∆L (mm) Rhot (Ω) Trm (C°) Thot (C°) ∆T (C°)
Copper 700 99,100 0.88 5,910 25.1 98.0 72.9
Steel 700 99,300 0.61 5,970 25.1 97.9 72.8
Aluminum 700 102,000 1.19 5,880 24.5 98.5 74.0
αCu = 17.25 x 10-6 /C°
= 11.97 x 10-6 /C°
α
steel
α
= 23.1 x 10-6 /C°
Al
1
Thermal Expansion Apparatus 012-04394C
Notes
2
012-04394C Thermal Expansion Apparatus
T echnical Support
Feed-Back
If you have any comments about this product or this
manual please let us know. If you have any suggestions on alternate experiments or find a problem in the
manual please tell us. PASCO appreciates any customer feed-back. Your input helps us evaluate and
improve our product.
To Reach PASCO
For Technical Support call us at 1-800-772-8700 (tollfree within the U.S.) or (916) 786-3800.
Contacting Technical Support
Before you call the PASCO Technical Support staff it
would be helpful to prepare the following information:
• If your problem is computer/software related, note:
Title and Revision Date of software.
Type of Computer (Make, Model, Speed).
Type of external Cables/Peripherals.
• If your problem is with the PASCO apparatus, note:
Title and Model number (usually listed on the label).
Approximate age of apparatus.
A detailed description of the problem/sequence of
events. (In case you can't call PASCO right away,
you won't lose valuable data.)
If possible, have the apparatus within reach when
calling. This makes descriptions of individual parts
much easier.
• If your problem relates to the instruction manual,
note:
Part number and Revision (listed by month and year
on the front cover).
Have the manual at hand to discuss your questions.
3
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