Uniform thermal expansion of metals

[DaveC426913]

TL;DR

Under uniform heating, what happens to distance X?

(What? No Grade School prefix? :) )

Apologies for the lowest form of physics question: a quiz on social media.

Does distance X
a. increase
b. decease
c. stay the same?


My rationale:

I did the simple version of this in grade 7 science class:

When both are in relative thermal equilibrium (say, room temperature) the ball does not fit through the ring.
Heat the ring and the ball slips through.

The experiment proves that, in this simple case at least, the ring expands uniformly, i.e. the inner edge of the ring expands outward, not inward.
(Or, perhaps more accurately, the metal near the inner edge of the ring might expand into the rings, but it is more than compensated for by the overall object's increase in dimensions, resulting in the actual final diameter of the ring increasing).

So, I am darned confident that the answer is: a. x increases.

But I could be wrong.



Some smartypantses have challenged this with a few spurious examples:

• Heated by how much? Heat it till it's liquid and the holes will vanish.
• "Some" metal alloys (eg. Invar) under very specific manufacturing conditions, can exhibit negative thermal expansion

But the "most correct" answer is: a.

Yes?

 

[A.T.]

Uniform expansion means that all distances increase. So if you assume that, the answer is a.

 

[DaveC426913]

Uniform expansion means that all distances increase. So if you assume that, the answer is a.

The only place it is assumed is in my answer. It is not in the problem.

So, the question remains unanswered.

Am I correct in my rationale (i.e. is my assumption warranted, as I apply it to the stated problem)?

 

[berkeman]

So, the question remains unanswered.

Am I correct in my rationale (i.e. is my assumption warranted, as I apply it to the stated problem)?

Which rationale explicitly? Sorry that I was confused a bit by your thread start.

My answer:

Spoiler

Uniform thermal expansion is the same as doing CTRL-scroll_in with your keyboard and mouse on a diagram or picture of the metal piece. All dimensions increase.

 

[DaveC426913]

Which rationale explicitly? Sorry that I was confused a bit by your thread start.

Right. Sorry. That's why it's so bad to quote from other sources without proper context.

Context: Some people (I won't call them fools) are arguing that X should decrease, because they think the metal surrounding the cavities will expand into the ... void.

[ EDIT ] Wait. That makes zero sense, even to any non-scientist! It's contradictory! Even if the metal expanded inward, that would still result in X increasing! I must have misinterpreted what they're saying!

I have posted prematurely.

Humble apologies. Please lock and delete. This whole thread makes no sense.

Uniform thermal expansion is the same as doing CTRL-scroll_in with your keyboard and mouse on a diagram or picture of the metal piece. All dimensions increase.

You know that and I know that, but that's a metaphor, not an explanation.

 

[berkeman]

Please lock and delete. This whole thread makes no sense.

No, no, no. The thread question is valid and comes up all the time.

 

[A.T.]

It is not in the problem.

That's a problem of the problem. It's vague, so people can argue about it forever.

 

[Herman Trivilino]

Every one-dimensional measurement increases by the same ratio. Put two marks anywhere on the disk and the distance between them will increase as described by $\Delta L=L_o\alpha \Delta T$. The holes in the disk are a distraction.

 

[Lnewqban]

You know that and I know that, but that's a metaphor, not an explanation.

Make the radii of the holes tend to zero: we have a body tending to look close to a coin.
If all the molecules of coin increase at once (uniform heating), its shape expands uniformly.

Make the radii of the holes tend to the radius of the disc: we have a body tending to look close to the ring shown in post 1.
If all the molecules of ring increase at once (uniform heating), its shape expands uniformly (increasing its internal diameter.

 

[DaveC426913]

The point i am now trying to establish is why did ANYONE think x would decrease?

At first I thought they had a point, but i cant even make it make sense.

Since the only answer is a, why do I need to verify?

 

[DaveC426913]

The holes in the disk are a distraction.

Something I noticed many people assumed: nowhere does it say they're "holes" they're "cavities", which does not suggest they cut all the way through. That is verified by the diagram, which does not indicate the inner circles have any substantial depth. They are depressions , not holes.