Question

Question: In the relation \(\Delta l = \alpha {l_{\rm{o}}}\Delta T\), should \({l_{\rm{o}}}\) be the initial length, the final length, or does it matter?

Short answer

\({l_{\rm{o}}}\) should be the initial length of the object.

Step-by-step solution

Meaning of thermal expansion

Thermal expansion may be defined as the change in the shape and size of an object accompanying a temperature change.

In the case of the solid object, all types of thermal expansion (linear, volume, and area) happen.

Formula for the final length of the object for linear expansion

The expression for the linear expansion of an object is as follows:

\(\Delta l = \alpha {l_{\rm{o}}}\Delta T\)

Here, \(\Delta l\) is the change in length; \(\Delta T\) is the change in the temperature; \(\alpha \) is the coefficient of linear expansion; \({l_{\rm{o}}}\) is the initial length of the object.

The change in length depends upon the initial length of the object. So, the final length of the object is equal to the initial length plus the change in length of the object.

\(l = {l_{\rm{o}}} + \alpha {l_{\rm{o}}}\Delta T\)

Here, \(l\) is the final length of the object.

If the temperature change is negative, the final length of the object decreases, but the initial length of the object will not change.

Thus, we can conclude that \({l_{\rm{o}}}\) should be the initial length of the object.