Instruction Manual and
Experiment Guide for the
PASCO scientific
Model TD-8578
THERMAL EXPANSION
APPARATUS
012-07114D
© 1999 PASCO scientific
012-07114D Thermal Expansion Apparatus
Table 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, Brass, and
Aluminum:
Introduction .........................................................................................3
Procedure .............................................................................................3
Data and Calculations .......................................................................... 4
Questions ............................................................................................. 5
Thermistor Conversion Table: ............................................................. 5
Technical Support ............................................................................................ 7
i
Thermal Expansion Apparatus 012-07114D
Copyright, Warranty and Equipment Return
Please—Feel free to duplicate this manual
subject to the copyright restrictions below.
Copyright Notice
The PASCO scientific 012-07114 Thermal Expansion
manual is copyrighted and all rights reserved. However, permission is granted to non-profit educational
institutions for reproduction of any part of the 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 the 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. The 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.
➤ ➤
➤ 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
012-07114D Thermal Expansion Apparatus
Introduction
Introduction
The PASCO Model TD-8578 Thermal Expansion
Apparatus provides easy and accurate measurements
of the coefficient of linear expansion for brass, copper,
and aluminum.
To make the measurement, the brass, 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 0.2 °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-8578 Thermal Expansion Apparatus includes:
• A 40 cm long expansion base with a built-in dial
gauge and thermistor.
➤➤
➤ NOTE: The dial gauge can be removed or
➤➤
repositioned by loosening the set screw on the
dial gauge mounting block.
• Three metal tubes — brass, copper (99.5% Cu,
0.5% Te), and aluminum (98.9% Al, 0.7% Mg,
0.4% Si): 6.4 mm outside diameter.
• A foam insulator to avoid heat loss at the thermistor connection point.
• Thermoplastic elastometer tubing with 6.4 mm
I.D.
Additional Equipment Required
In addition to the TD-8578 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-8556A 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 container to catch the water as it drains out of the
tube.
➃ If additional data points are desired you will also
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 attached conversion table tag 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.
1
Thermal Expansion Apparatus 012-07114D
Accepted Values for Coefficient of
Thermal Expansion
Material
Copper
Brass
Aluminum
( x10-6/ C)
a
8
17
19
23
Changing Tubes
➤➤
➤Caution: When changing tubes, be careful not to
➤➤
pull the wires off of the thermistor.
➀ Compress the capture spring by pressing the two
ends together.
Replacement Parts
The following parts can be ordered from
PASCO scientific.
Item
Mod. Thermistor (100k )
V
PASCO #
150-031
AL Tube
Cu Tube
Brass Tube
Foam Insulator
Dial Gauge
648-07139
648-07141
648-07140
716-041
620-050
➁ Insert the curved lug of the thermistor between the
capture spring and the thermal tube.
➂ Release spring.
thermistor
capture spring
thermal rod
2
012-07114D Thermal Expansion Apparatus
Experiment: Measuring the Coefficient of Linear
Expansion for Copper, Brass, and Aluminum
Introduction
Most materials expand 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.
Materials that are not isotropic, such as an asymmetric crystal for example, α can have a
different value depending on the axis along which the expansion is measured.
α can also vary somewhat with temperature. Therefore, 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 brass. These metals are
isotropic, so it is necessary to measure α along only one dimension. Also, within the limits
of this experiment, α does not vary with temperature.
Procedure
➀ Measure L, the length of the copper tube at room temperature. Measure from the outer edge
of the stainless steel ring on one end, to the outer edge of the stainless steel ring at the other
end (see Figure 1). Record your
results in Table 1.
➁ Mount the copper tube in the expan-
sion base as shown in Figure 2. The
stainless steel ring 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.
➂ Use the capture spring on
the expansion tube to
attach the thermistor lug
somewhere in the middle
of the copper tube. The
lug will be aligned with
the axis of the tube, as
shown in Figure 2, so
there is maximum
contact between the lug
and the tube.
Figure 1 Measuring Tube Length
stainless steel ring
capture spring
slotted mounting block
Figure 2 Equipment Setup (Top View)
L
stainless steel ring
thermistor
contact indicator
3
Thermal Expansion Apparatus 012-07114D
➃ Place the foam insulator over the thermistor lug.
➄ Plug the leads of your ohmmeter into the banana plug connectors labeled THERMISTOR in
the center of the expansion base. The banana plug connectors are located at one end of
this unit in a stop bracket.
➅ Measure and record R
value in the table.
➆ Use tubing to attach your steam generator to the end of the copper tube. Attach it to the end
closest to the dial gauge.
➇ 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 ohmme-
ter. When the thermistor resistance stabilizes, record the resistance (R
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.)
➤ Repeat the experiment for the brass and aluminum tubes.
, the resistance of the thermistor at room temperature. Record this
rm
) in Table 1. Also
hot
Data and Calculations
TABLE 1 Data and Calculations
CALCULATIONS
8
rm
( C)
T
hot
L(mm)
R
rm
( )
V
DATA
D
L(mm)
R
hot
( )
V
T
copper
brass
aluminum
➀ Use the Thermistor Conversion Table on page 5 of this manual or on the tag attached to the
apparatus. Convert your thermistor resistance measurements, Rrm and R
measurements, Trm and T
➤ Note: To achieve 0.2°C accuracy for temperature, you must interpolate between the
temperature values listed in the Thermistor Conversion Table.
. Record your results in the table.
hot
, into temperature
hot
8
( C)
8
( C)
T
D
4
012-07114D Thermal Expansion Apparatus
➁ Calculate ∆T = T
– Trm. Record the result in the table.
hot
➂ Using the equation ∆L = αL ∆T, calculate α for copper, steel, and aluminum.
αCu = __________________
α
= __________________
Brass
αAl = __________________
Questions
➀ Look up the accepted values for the linear expansion coefficient for copper, brass, 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?
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 012-07114D
Notes
6
012-07114D Thermal Expansion Apparatus
Technical Support
Feedback
If you have any comments about the product or
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
feedback. Your input helps us evaluate and improve
our product.
To Reach PASCO
For technical support, call us at 1-800-772-8700
(toll-free within the U.S.) or (916) 786-3800.
fax: (916) 786-3292
e-mail: techsupp@pasco.com
web: www.pasco.com
Contacting Technical Support
Before you call the PASCO Technical Support staff, it
would be helpful to prepare the following information:
➤ 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 to facilitate description of individual parts.
➤ 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.
7
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