Linear Expansion: Why Not Volume Expansion?

[Milind_shyani]

Hi,
I want to ask one question about linear expansion.
For eg if we take tke railway rails. then during summer due to the incresing heat the length of the rails increase. Now anything which has a mass has a volume so when the temperature of the metal rails increase during summer, why is it so that only linear expansion takes place in the rails why not VOLUME EXPANSION?

 

[Doc Al]

What makes you think that you can have linear expansion without volume expansion? (All three linear dimensions will expand, giving volume expansion.)

 

[vaishakh]

We say an object like rod expandlinearly coz it expansion in other dimensions is negligible compared to the linear one. Similar for a metal sheet or plate. But actually they all expand in all dimensions. I think an explanation to this is given in H C Verma

 

[Doc Al]

The percentage expansion is the same* for any linear dimension (in all directions); the actual change along any particular direction is of course proportional to the original length along that direction:
\Delta L = \alpha L_0 \Delta T

* for an isotropic material, of course

 

[rindech]

To be more precise: If the material is of a constant uniform composition, then it will expend equally in all directions. If the material is composed of different atoms oriented diversely with respect to an orthogonal set of axes, then the material is considered anisotropic, and the coefficients of expansion may vary depending upon the axis chosen. But in your steel rail example, it will expand uniformly in all directions; as one dimension is so much larger than the other, the net effects of the expansion along its length are more observable.