Coefficient Of Linear Expansio Essay, Research Paper

Introduction

Most solid materials expand upon heating and contract when cooled because it undergoes a change in the energy state of its molecules or atoms. According to the atomic perspective, the average vibrational amplitude of an atom increases as the temperature rises. Each material has a property called coefficient of linear expansion that is indicative of the extent to which a material expands upon heating or contracts when cooling. The coefficient of expansion is re very important to all structures and foundation of buildings to avoid the possibility of collapsing.

Objective

The objective of this experiment is to calculate the coefficient of linear expansion of a metal. The change in length of several materials such as glass, brass, copper, stainless steel and aluminum will be determined and the corresponding coefficient of linear expansion would be calculated.

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Metal

(pyrex)Glass Brass Copper Steel Aluminum

Data T1=27 XC

T2=95 XC

L1=0.6m T1=27 XC

T2=98 XC

L1=0.6m T1=27 XC

T2=98 XC

L1=0.6m T1=27 XC

T2=98 XC

L1=0.6m T1=27 XC

T2=98 XC

L1=0.6m

t(s) +L(0.01mm) T ( XC) +L(0.01mm) T ( XC) +L(0.01mm) T ( XC) +L(0.01mm) T( XC) +L(0.01mm) T ( XC)

10 5 27 10 27 5 27 30 40 19 27

20 9 30 20 30 15 27 40 49 33 27

30 11 45 30 35 28 27 52 68 53 30

40 14 59 45 58 41 38 64 80 71 55

50 15 63 55 77 53 62 71 85 90 72

60 15 69 68 83 66 78 73 88 104 81

70 15 78 83 88 76 84 74 90 106 86

80 15 81 86 90 79 88 74 91 107 88

90 16 83 87 91 79 90 74 92 107 90

100 16 84 87 93 79 91 74 93 108 91

110 16 86 87 93 79 92 74 94 108 93

120 16 88 87 93 79 93 74

95 108 93

130 16 89 87 93 79 94 74 95 109 94

140 16 90 87 93 79 94 74 95 109 94

150 16 90 87 93 79 95 74 95 109 95

160 16 91 87 93 79 95 74 95 109 95

170 16 91 87 93 79 95 74 95 109 95

180 16 91 87 94 79 96 74 96 109 96

190 16 92 87 94 79 96 74 96 109 96

200 16 92 87 94 79 96 74 96 109 96

210 16 92 87 94 79 96 74 96 109 96

220 16 93 87 94 79 96 74 97 109 97

230 16 93 87 94 79 97 74 97 109 97

240 15 93 87 94 79 97 74 97 109 97

250 15 93 88 95 79 97 74 97 109 97

260 15 94 88 95 79 97 74 97 109 97

270 15 94 88 95 79 97 74 98 109 97

280 15 94 88 95 79 98 74 98 109 98

290 15 94 88 95 79 98 74 98 109 98

300 15 95 88 98 79 98 74 98 109 98

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Results

The results were calculated by the following equation 1:

+L = + L1 ( T2 V T1)

where +L = the change in length

L1 = the original length

T2 = the final temperature

T1 = the initial temperature

+ = the coefficient of linear expansion of the material

The following equation 2 was changed by equation 1, which was used to calculate the +

+ = +L .

L1 ( T2 V T1)

The coefficient of linear expansion ( +) of five metals were calculated by equation 2. The accepted value of five metals in the text book (pg. 646) was shown in the following:

Metal + [ ( XC)-1 x 10-6

(Pyrex) glass 3.3

Brass 20.0

Copper 17.0

Stainless steel 16.0

Aluminum 23.6

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Calculations

+ for (Pyren) glass:

+L = (0.15)/1000(m), L1 = 0.6m, T2 = 95 XC, T1 =27 XC

+ = (0.15/1000) . = 3.68 ( XC)-1 x 10-6

0.6(95 V 27)

+ for Brass:

+L = (0.88)/1000(m), L1 = 0.6m, T2 = 98 XC, T1 =27 XC

+ = (0.88/1000) . = 20.7 ( XC)-1 x 10-6

0.6(98 V 27)

+ for Copper:

+L = (0.79)/1000(m), L1 = 0.6m, T2 = 98 XC, T1 =27 XC

+ = (0.79/1000) . = 18.6 ( XC)-1 x 10-6

0.6(98 V 27)

+ for Stainless steel:

+L = (0.74)/1000(m), L1 = 0.6m, T2 = 98 XC, T1 =27 XC

+ = (0.74/1000) . = 17.4 ( XC)-1 x 10-6

0.6(98 V 27)

+ for Aluminum:

+L = (1.09)/1000(m), L1 = 0.6m, T2 = 98 XC, T1 =27 XC

+ = (1.09/1000) . = 25.6 ( XC)-1 x 10-6

0.6(98 V 27)

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The percent deviation of the + was shown in the following:

% of Glass = (3.6 x 10-6) – (3.3 x 10-6) x 100

3.3 x 10-6

= 9.1%

% of Brass = (20.7 x 10-6) – (20 x 10-6) x 100

20 x 10-6

= 3.5 %

% of Copper = (18.6 x 10-6) – (17 x 10-6) x 100

17 x 10-6

= 9.4 %

% of Stainless = (17.4 x 10-6) – (1.6 x 10-6) x 100

steel 1.6 x 10-6

= 8.75 %

% of Aluminum = (25.6 x 10-6) – (23.6 x 10-6) x 100

23.6 x 10-6

= 8.5 %

Discussion

The result of the experiment turned out to be fairly close to the accepted value. The percentage deviation of the coefficient of linear expansion was in a range of 3.5% to 9.4% which was less than what it was expected due to many sourse of errors occurred during the experiment listed below.

It was very difficult to work with metals that had great coefficient of expansion

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like brass and aluminum. Such metal expansed very rapidly within a short period of time, and the change in length of the metal can only be appoximated. And also due to the human reaction time and human judgement, the result of the experiment data was

affected. In order to reduce these source of errors, computerize thermometer and extensometer will have much efficiency and also it could produce more accurate data.

During the heating process, the steam was supposed to follow the cradle (hollow metal tube) and exit from a small opening on the other end of the cradle. Since the simple hollow metal tube was not well insulated, some steam and hot water were leaking out from both sides of the rubber jacket and also though the opening for the thermometer. The results of the data were slightly affected due to heat lost.

After the first specimen rod was done, the percent deviation of glass, copper, stainless steel and aluminum have increased noticeably. One of the reasons is that the metal tube was not able to return back to its original temperature or its normal state within a short period of time, even though it was cooled down by running under the water. Another factor was that the thermometer also could not return to the room temperature.

Conclusion

The experiment was luckily conclused fairly similar to the accepted value. However, because only appoximation of datas and other source of errors, the accuracy of the data could be questionable.