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Experiment: Thermal Expansion Apparatus

Purpose To use steam heating pot to generate steam. Make the steam flow through the metal rod

to make it expand, and then use the dial indicator to measure the length of the metal rod

after expansion in order to calculate the coefficient of linear expansion.

Theory Most solids do expand when heated, and its length changes by an amount proportional to the original length and the change in temperature.

L－L0＝L0αT (1)

L＝L0（1┼αT） (2)

In the equation,

L0: the length at 0℃

L: the length at T℃

α: the constant of proportionality, called the coefficient of linear expansion

In the equation,

L1: the length at T1℃

L2: the length at T2℃

So we obtain the equations below,

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L1＝L0（1┼αT1） (3)

L2＝L0（1┼αT2） (4)

2

1

LL

＝2

1

T1T1

＝1221

12

TL-TLL-L (5)

The difference of L1 and L2 is minimal, so L2~ L1, we obtain,

＝TL

L

1 (6)

In the equation,

△L: L2－L1

△T: T2－T1

Linear expansion coefficient is defined as the increment of length of a solid in a unit of length for a rise in temperature of 1° at constant pressure. Instead of the increase of the length, but also consider the expansion in volume. By equation (2), we obtain, V＝V0（1┼βT） (7)

In the equation,

V0: the volume at 0℃

V: the volume at T℃

β: the volume expansion coefficient

Assume that the side length of a cube is L, the volume at T sho℃ uld be,

V＝ 3L ＝3

oL 3T1 ＝3

oL 3322 TT3T31

Since α is a small number, 2 and 3 can be gotten rid of in the equation, that is

V＝3

oL （1＋3 T） (8)

Compare equation (7) to equation (8), we know that the volume coefficient is three

times the coefficient of linear expansion, soβ＝3α. Although the conclusion above

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But the volume of an object can be divided into many cubes, so for any solid, this

conclusion is correct.

Instrument

Fig. 1

NO Accessory Quantity 1 Steam Generator 1 2 Steam Heating Pot 1 3 Steam Heating Pot Lit 1 4 Fixer 1 5 Aluminum Rod 1 6 Metal Rod 1 7 Brass Rod 1 8 Base 1

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9 Zeroing Knob 1 10 Metal Rod Supporting Base 2 11 Dial Indicator 1 12 Digital Electronic Thermometer 1 13 Thermometer Socket 1 14 Water Container 1 15 Steam Conduit 2

Steam Generator

HOW TO USE 1. Switch: this switch will illuminate when the heater starts heating.

2. Temperature control knob: temperature control protection switch. The generator starts to heat up when the knob is turned till the switch lights up but No Water Indicator doesn’t.

3. No water indicator: the indicator lights up when in a non-heated or no water state.

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4. Fuse reversion button: it trips when there is no water or overheating, push this

button to turn it on again when the generator cools off. 5. Regularly clean the device using heated citric acid with water to maintain the

efficiency. 6. Avoid getting water on sockets and switches.

Procedure 1. Wear gloves when using the device since the temperature is very high. 2. Measure the original length of the metal rod and record. 3. Fill the pot 80 % full with water. The experiment set is shown as Fig. 2.

4. Make the metal

end of the zeroing knob against the groove of the metal bar and the other end to fit the dial indicator as shown in Fig. 3.

Fig. 2

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Fig.3

4. Record the room temperature and the initial reading of the dial indictor. (start from

4 mm).

5. Turn the switch on to generate the steam.

6. When the steam is generated after 15 minutes, observe the thermometer and dial

indicator.

7. When the temperature is stable, record the readings down ( at about 98℃ to 100℃)

8. Turn the zeroing knot to zero, and then change the metal rod when the metal rod

and conduit cool off. Calculate the elongation of metal rod and the coefficient of

linear expansion.

9. Replace the metal rod, and repeat steps 3 to 8.

Experimental Record Coefficient of linear expansion of metal: α（×10-6）1/ C

Substance gold silver Brass steel aluminum lead Coefficient of

linear expansion 14.70 18.90 19.06 11.40 22.20 27.09

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Brass: original length 1L = Temperature Length (dial indicator)

T1 T2 T initial reading (mm)

Elongation (mm)

L mm

Average value =

Aluminum：original length 1L =

Temperature Length (dial indicator) T1 T2 T initial reading

(mm) Elongation

(mm) L mm

Average value =

Unknown metal: original length 1L =

Average value =

Temperature Length (dial indicator) T1 T2 T initial reading

(mm) Elongation

(mm) L mm

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Questions and Discussions 1. What causes the errors?

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Atis Scientific Instruments Co.,Ltd

Tel：8866-2925201

Address：1F., No.18, Nanming St., South Dist.,

Tainan City 702, Taiwan (R.O.C.)

Website：http://www.atis.com.tw

E-mail：atis@atissi.com.tw