A sheet of metal with a hole in the middle is heated up. Will the hole become smaller or bigger?

Question

Assume the sheet is an infinite plane. Will the hole expand inwards or outwards?

Answer 1

It may seem counterintuitive, but the hole should grow bigger. The distance between atoms grows at the hole perimeter, and the atoms outside the perimeter also have room to expand outward. The distance between atoms grows everywhere. Since the distance between atoms at the hole perimeter grows, and the number of atoms does not change, the circumference should grow. Hence the width of the hole (proportional to the circumference) also grows.

If the hole size is much larger than the interatomic distance, this is the only stable solution, since pushing atoms inward would crowd them together (not favored at higher temperature).

The "wiggly ring of atoms" solution is also unstable, and eventually becomes a larger ring of atoms, corresponding to a larger hole size.

Answer 2

Larger if the metal is in the form of a disk, and also larger if the hole is in the form of a cylinder. You do not specify the shape other to say it is infinitely large sheet, not whether flat or curved in some manner. In the case of the disk, consider the hole to be exactly as big as the diameter of 1 atom and the thickness of the sheet to be also 1 atom. Then, consider as the metal heats, the average distance between all atoms gets larger, which makes the atoms adjacent to the hole move outwards from the center, making the hole slightly larger than 1 atom diameter as the closest ring of atoms surrounding the hole move slightly further apart and still remain in the plane. In the case of a cylinder, it could be infinitely long with a finite diameter, and in this case, as the atoms average distance apart increases, so does the diameter of the cylinder. I have no definitive source for this... this is just what I THINK would happen... For a practical demonstration, think of a barrel hoop or a wagon wheel. A metal band is heated, put over the barrel staves or the wagon wheel circumference and as it cools, it compresses the barrel or wagon wheel. This is more like my analogy of a cylinder, but if you shrink the width of the hoop to a single atom instead of a couple of inches and extend that single atom thickness to infinity, then it fits your question. The diameter of the hole in the sheet of metal gets larger when the sheet is heated.

Answer 3

The hole becomes bigger.
Two examples.

Suppose you form a circle by laying down a piece of string of a certain length. Now remove the string and do the same with a slightly longer string. You will form a larger circle.

Second example: Wagonmakers and barrelmakers used this trick to keep a round form together with an iron band.
They would make an iron band that would be slightly too small for the wheel (or the barrel).
Then they would heat the band so it expanded. Then they could just slip it over the wheel or the barrel and when it cooled, the strip of iron would shrink and pull everthing together.

There is no fundamental difference between a strip of iron or a sheet of metal. Yes, the sheet will be thicker, seen from the hole in the middle. But the principle is the same and there is no thickness for which this effect is suddenly reversed.

Answer 4

Well,
when a metal is heated up it expands on all free directions of motion.
In your question, you have not said that there is a restricted direction. So, the metal sheet will expand in all directions.
By this, the metal will expand inward as will as outward, they will expand on the cost of the metal sheet thickness. So nor of them will affect the other and the hole becomes smaller.

Answer 5

It would be smaller as when metal or any material heats up, the atoms of the material get more excited, spreading out and making the metal expand. This metal would then look for any open space it could spread into, in this case the hole in the metal. So it would expand. Hope this helps!

Answer 6

I assume you mean if heated! If so, great question.

When you heat a metal ring, it expands. The outside and inside diameter expand. It's how they fit train wheels.

But what if its an infinite sheet? My instinct says as internal kinetic energy increases, so does average atomic crystalline spacing. Atoms push each other apart, so push towards the circle centre, making the hole smaller, right?

Another way of thinking about the problem is that all linear dimensions must increase. This includes the dimension measured around the circumference of the circle, so the hole must also increase in size! This choice now makes more sense to me, as if atomic spacing increases, so must the hole size.

There's my whole thought process on that one. I think the hole INCREASES if you heat it.

Cheers,
Ben

Answer 7

It actually becomes bigger.
That's the property we use in the industry so as to "glue" a bolt to a screw:
The bolt is heated up (and its hole expands)
the screw is put to a low temperature (its diameter becomes smaller)
the pieces are then assembled and let at room temperature:
the screw expands and the bolt's hole rectracts.

Answer 8

The diameter of the hole will grow larger. The diameter will increase by the coefficient of thermal expansion times the change in temperature.

Answer 9

Inwards...get smaller. The material will expand and fill the hole somewhat.

Answer 10

Outwards. Everything expands when heated, with the exception of water.