Thermal Expansion and Hole Contraction

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Discussion Overview

The discussion centers around the effects of thermal expansion on a material with a hole in it. Participants explore whether the hole contracts or expands when the material is heated, examining the underlying physics and reasoning involved in thermal expansion and density changes.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant suggests that when a material with a hole is heated, the hole would contract due to the material expanding in all directions.
  • Another participant counters that the hole actually gets larger in proportion to the material's expansion.
  • A participant explains that since the material is solid and its density remains relatively constant, the hole must expand to maintain the overall volume during thermal expansion.
  • Another participant challenges the reasoning, stating that density can change in solids and emphasizes that heating a solid causes it to expand in all directions, leading to an increase in volume and a decrease in density.
  • A later reply elaborates that the mathematical relationship governing thermal expansion indicates that the hole must increase in size to satisfy volumetric relationships, otherwise it would imply an impossible volume change.
  • One participant reminds others to search the forum for previously discussed questions on thermal expansion, indicating that this topic has been addressed multiple times.

Areas of Agreement / Disagreement

Participants express differing views on whether the hole contracts or expands when the material is heated. There is no consensus reached, as some argue for contraction while others assert expansion.

Contextual Notes

Participants mention the relationship between volume, density, and thermal expansion coefficients, but the discussion does not resolve the assumptions or mathematical details involved in these relationships.

cowpuppy
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Say you had a material with a hole in it. When you heat this material, it expands. Would the hole then contract, since the material is expanding in all directions? My intuition says yes, but I'm told this is not the case, and I'm not sure about the physics behind it to reason to figure out why.
 
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Would the hole then contract

No the hole gets larger in the same proportion as the material.
 
Why?
 
Well it is a solid, so its density isn't changing (volume stays the same). The plate is expanding outward and getting slightly thicker due to thermal expansion, so the hole gets bigger, otherwise the volume would be changing.
 
I don't think that's the reason. Just because it is a solid doesn't mean the density doesn't change. And in the case of a block of material with no holes, if you were to heat it, it would expand in all unrestricted directions, and the volume (therefore, density, since mass is the same) would increase.
 
cowpuppy said:
I don't think that's the reason. Just because it is a solid doesn't mean the density doesn't change. And in the case of a block of material with no holes, if you were to heat it, it would expand in all unrestricted directions, and the volume (therefore, density, since mass is the same) would increase.

Now that I think about it, you are right, the solids can change density, but not very much.

If you look at the math, it tells you that the hole gets bigger (as do all the other dimensions). Physically, it represents the fact that not only does the expansion coefficient govern the lengths, but also the areas and volumes. In order to satisfy the volumetric (or areal) relationship with the expansion coefficient, the hole must get larger. If not, then you end up with more of a volume change than the material can physically undergo.

So like I said, the density of the solids can change, just not much, and just how much is governed by the expansion coefficient.
 
Hello cowpuppy.

It is good practice to do a forum search before asking a question. This question has been asked (and answered) lots of times at PF.

A simple search on 'themal expansion' would reveal the identical question, 5 days ago.

https://www.physicsforums.com/showthread.php?t=429479&highlight=thermal+expansion

And by the way, if the volume increases, but the mass does not then the density decreases. The proportionality is inverse!
 

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