Linear Expansion: Why Not Volume Expansion?

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Discussion Overview

The discussion revolves around the concept of linear expansion in materials, particularly focusing on why linear expansion is often emphasized over volume expansion in contexts such as railway rails. Participants explore the relationship between linear and volume expansion and the conditions under which each occurs.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions why only linear expansion is noted in the case of railway rails, suggesting that volume expansion should also occur with temperature increases.
  • Another participant challenges this notion, arguing that linear expansion inherently includes volume expansion since all three dimensions of an object expand, leading to an increase in volume.
  • A different perspective is presented, stating that while all dimensions expand, linear expansion is emphasized because the expansion in one direction (length) is significantly greater than in the other dimensions for certain objects like rods or plates.
  • It is noted that the percentage expansion is consistent across all linear dimensions for isotropic materials, with the actual change in length being proportional to the original length and temperature change.
  • Further clarification is provided regarding anisotropic materials, where expansion may vary depending on the orientation of the material's atomic structure, but for uniform materials like steel rails, expansion is uniform in all directions.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between linear and volume expansion, with some asserting that both occur simultaneously while others emphasize the predominance of linear expansion in specific contexts. The discussion remains unresolved regarding the emphasis on linear versus volume expansion.

Contextual Notes

Participants mention the influence of material composition and orientation on expansion characteristics, indicating that assumptions about uniformity may not apply universally.

Milind_shyani
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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?
 
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What makes you think that you can have linear expansion without volume expansion? (All three linear dimensions will expand, giving volume expansion.)
 
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
 
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:
[tex]\Delta L = \alpha L_0 \Delta T[/tex]

* for an isotropic material, of course
 
Last edited:
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.
 

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