Science question: heating a sheet of metal

I was thinking about Dr. Julius Sumner Miller (a science popularizer of the 50s & 60s) and remembered that, the last time I saw him on TV, he posed a question, but didn’t give the answer. I’m still wondering what the answer might be.

He showed a bit of sheet metal about 6 in. x 6 in. A small hole (about 1/4 in. in diameter) is drilled in it. His question was: If you heat the sheet of metal, the metal will expand. Will the hole become smaller, larger, or stay the same size?

I don’t have a whole lot of expertise to base this on, but I think it gets larger. Metal expands when heated because each of the atoms in the lattice that make up the solid gets more energy - this means that it can move ever so slightly further away from all of it’s nearest neighbours.

This has the effect of enlarging the whole piece of metal as though you’d simply magnified it - like if you have an image on your PC and you tell Photoshop to make it 10% bigger.

If all the atoms on the inside of the hole were like a ring of people holding hands, and all of their arms got slightly stretched, the hole would get bigger.

I seem to recall a demonstration of this when I was at school, with a ring and a sphere - the sphere would fit through the ring only when it had been shrunk by being dunked in liquid nitrogen or something or the ring had been heated. However, this was a ring, not a sheet, and it was about 15 years ago too.

Larger - imagine instead you had a solid sheet of metal, and drew a circle on it with a sharpie. If you were to expand the metal by heating, you would expect this circle to get larger, wouldn’t you? The hole would be no different, because the metal gets larger but retains all of its original proportions.

You may already have used this to your advantage by running hot water over the lid of a stuck jam jar.

Not that I think the laws of Physics have changed. Just that I might be remembering incorrectly.

Taken to extremes, the effect has been used for centuries as a technique for getting iron bands onto cartwheel rims - heat the iron band (and an iron band is just a piece of metal with a hole in it - it just happens to have a lot of ‘hole’ and not much ‘metal’) and it expands; drop it onto the wheel rim and cool it with water and it immediately contracts, gripping tight to the rim and binding the whole wheel together very tightly.

Many years ago the scientists at the U of Rochester built a “360 degree heat pipe” by placing two metal disks on either side of a really short piece of glass tubing. They heated the two disks in the center, but not the outer edge, and the result was that the center expanded extraordinarily.

The outside didn’t.

The only way this could happen was for the plate to turn into a paraboloid, with the center byulging out. If there had been a hole in it, it would’ve gotten bigger.