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COEFFICIENT OF LINEAR EXPANSION OF A METAL

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.
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.

(pyrex)GlassBrassCopperSteelAluminum
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)
The results were calculated by the following equation 1:
= the coefficient of linear expansion of the material
The following equation 2 was changed by equation 1, which was used to calculate the
=L.
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:
L = (0.15)/1000(m), L1 = 0.6m, T2 = 95XC,T1 =27XC
=(0.15/1000).= 3.68 (XC)-1 x 10-6
L = (0.88)/1000(m), L1 = 0.6m, T2 = 98XC,T1 =27XC
=(0.88/1000).= 20.7 (XC)-1 x 10-6
L = (0.79)/1000(m), L1 = 0.6m, T2 = 98XC,T1 =27XC
=(0.79/1000).= 18.6 (XC)-1 x 10-6
L = (0.74)/1000(m), L1 = 0.6m, T2 = 98XC,T1 =27XC
=(0.74/1000).= 17.4 (XC)-1 x 10-6
L = (1.09)/1000(m), L1 = 0.6m, T2 = 98XC,T1 =27XC
=(1.09/1000).= 25.6 (XC)-1 x 10-6
The percent deviation of the was shown in the following:
% of Glass= (3.6 x 10-6) – (3.3 x 10-6)x 100
% of Brass= (20.7 x 10-6) – (20 x 10-6)x 100
% of Copper= (18.6 x 10-6) – (17 x 10-6)x 100
% of Stainless = (17.4 x 10-6) – (1.6 x 10-6)x 100
% of Aluminum= (25.6 x 10-6) – (23.6 x 10-6)x 100
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
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.

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.


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