Thermal Expansion and Hole Contraction

[cowpuppy]

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.

 

[Studiot]

Would the hole then contract

No the hole gets larger in the same proportion as the material.

 

[cowpuppy]

Why?

 

[boneh3ad]

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.

 

[cowpuppy]

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.

 

[boneh3ad]

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.

 

[Studiot]

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!