The numbers for the linear expansion (ΔL) and the initial (T1) and final (T2) temperatures were taken from the table above and can be seen in the table bellow. The initial length (L1) of all of the rods was measured to 60 cm.
By utilizing the formula ΔL = α L1 (T2 – T1) to solve for the coefficient of linear expansion () the tested values for all the metals were found. These were then compared with their actual published values shown in the table bellow.
The tested values for the four metals were very similar to the accepted values. For copper the % deviation was 3.23 %, for brass the % deviation was 15.7 %, for stainless steel the % deviation was 7.875 %, and for aluminum the % deviation was 3.29 %.
There are differences in the coefficients of linear expansion because each element reacts differently to heat. Due to there different molecular structures each metal requires different amounts of heat to expand. The coefficients of linear expansion show these differences in the metals. Because of the complex crystalline structures and intermolecular forces holding each element in place restricts the expansions of these metals and since most elements have different structures and combination of bonding forces each one is different. This also explains the differences in metal polymers alloys and ceramics. Due to there molecular makeup they will all have different coefficients of linear expansion.
Conclusion:
Through this experiment, it is proven that different metals react differently to higher temperatures and that their properties cause them to behave differently. At the atomic level, the bonds created by the atoms of each material are in varying arrangements, which cause property differences. Such variations in atomic structure are the result of the individual characteristics present in the various metals tested. The reason some metals expanded more than others is due to their molecular structure and the way it conforms to produce that material’s coefficient of linear expansion. Generally, the experiment provided an insight of the kinds of details that must be considered when using metals in designs of any sort weather it be engines, bridges, or robotics the same principles apply and the same measures must be taken to ensure the system co-operates and holds steady for its purpose. Alloys are used for this reason to allow control of the amount of expansion a metal will have. Engines cannot have a metal, which expands greatly under heat because it will malfunction, therefore engineers must use alloys with high resistance and other corresponding characteristics. A metal is one of the most important materials when constructing landmarks or machinery, which means a complete understanding of its behavior, is necessary to ensure a successful project. There were some experimental errors in these results due to the temperature gauge used and the sensitivity of the equipment. Any jolt in the testing surface could throw off all of the results. The cooling periods also played a role because the temperature of the steam tube was not measured. Overall the experimental error was minimized in the testing yielding very accurate results.
Appendix: sample calculations
Copper
α= ΔL/ (L1 (T2 – T1))
=0.077cm/60cm(100oC -22oC)
=1.645x10-5
% Deviation = actual – tested / actual x 100%
= (17 x 10 –6 - 1.645x10-5)/ 17 x 10 –6 x 100%
= 3.23%
.
References
(1)Ryerson University Department of Mechanical and Industrial Engineering MTL 200 Materials Sciences 1
Prof. A, Varvani winter 2004 lecture notes, for Engineering Students in the First Year.
Toronto, Ontario, Canada. (2002)
(2)Ryerson University. Materials Sciences Laboratory Manual for Engineering Students in the First Year.
Toronto, Ontario, Canada. (2002)
(3)Serway and Beichner, Physics: For Scientists and Engineers. 5th Edition (Orlando, Florida), (2003)
(4) http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Thermal/ThermExpan.html
Coefficient of Linear Expansion of a Metal
Prepared by: Paul Mazzone
Marko Bilal
Dennice Yip
Section: 15
Experiment Performed:
Monday Feb 16
