Externally applied mechanical forces acting on a body, such as normal and shear forces, will cause deformation dependent on the
characteristics of that body and the magnitudes of the applied forces. Similarly, changes in temperature can cause deformation (i.e., expansion or contraction) as particles and bonds inside the material undergo changes in energy. For simple geometries, the changes in volume are proportional in the linear dimensions. Each of the 25cm×5cm25cm×5cm beams below is subjected to a 20 degree change in temperature. Rank the items based on the total change in length along the long axis of the beams. Many polymers such as polyethylene are significantly affected by changes in temperature, especially when compared to the metal and mineral materials discussed here. To a lesser degree, soft metals likewise are significantly affected by temperature changes. For example when heated, lead expands almost a third more than aluminum and almost twice as much gold. However, hard metals and materials, such as platinum and quartz, do not deform significantly in response to temperature. Because platinum is a metal, it will deform almost nine times more than quartz.
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Given:
The limit problem is:
To find:
The value of the given limit problem.
Solution:
We have,
It can be written as:
Applying limit, we get
Therefore, the value of given limit problem is .