Why doesn't a metal disk expand in all directions when heated?

Question

The hole in a metal disk gets bigger when heated. This has been explained by the reason that if we take the already cut out piece of the metal and heat it separately it also gets bigger, but the metal of the cut out is a metal hence it expands , hole is the absence of metal so why doesn't the metal disc expand in all directions thus making the hole smaller?

Answer 1

Imagine you build a model of the disc out of LEGO bricks. And then you re-build the same model, brick-for -brick, out of the equivalent DUPLO bricks (they look the same but are 2x as big). Do you expect the hole in the DUPLO disc to be smaller or bigger than that in the LEGO disc?

With thermal expansion you have exactly the same principle at play. When you heat a material up, all the chemical bonds between the atoms get a bit longer. That is the reason for the overall expansion. The atoms stay exactly in their places relative to one another but all distances are (uniformly) larger. This is just like using somewhat bigger bricks to build otherwise the same model.

Answer 2

Cut the disk up into a series of thin rings. When a ring expands, its circumference grows. This means its radius grows. This still applies if you take out the innermost rings to leave a hole.

The thickness of each ring also grows. But suppose the thickness is $1/100^{th}$ of the circumference. The thickness increase will be $1/100^{th}$ of the circumference increase. Both inner and outer edges move outward.

Answer 3

It does expand in all directions. The way to prove that is not to see the hole in the middle get smaller, but to measure the thickness of the band (as opposed to the diameter of the whole ring) and see that it gets bigger. It just doesn't get as much bigger as the entire ring, so the hole still grows.