# A question about heating aluminium with a hole in it

1. Mar 5, 2009

### fluidistic

Hi PF,
I watched a video on youtube about a physics professor who asked some questions at the end of the video but didn't answer them. One really interested me.
If you have a plane aluminum plate with a very little hole say in its center and you heat the whole plate. What happens to the size of the hole?
1-It could expend as the plate would do. 2-It could get smaller because the walls of the hole would expend where the hole is. 3-Or it could be of the same size.
I thought it would stay more or less of the same size because of 1 and 2 combined.
But I asked a friend of mine (I find him really brilliant) and he told me it would expend because there's no point on the aluminum plate that would get compressed. I was amazed about how fast he answered to the question and I think he is right.
So I'm asking you in order to be sure of it! Thanks.

2. Mar 5, 2009

### Q_Goest

Hi fluidistic. This question actually comes up quite a bit in the real world. There are lots of instances where there's a hole in a part that gets hot and you need to know what happens to the size of that hole. The hole always gets bigger assuming the material expands. Think of it this way - all the molecules or atoms simply get farther apart.

To calculate the increase, just use the coefficent of expansion and multiply times any given dimension. So let's say the expansion coefficient results in a linear part increasing in length by 0.001" per inch. For a hole in a part, the diameter would similarly increase 0.001" per inch.

3. Mar 5, 2009

### alxm

The hole gets bigger. Just think about what'd happen if you just _drew_ a circle on the plate. It'd get bigger right? Or if you cut out a circular bit and heated it the same amount? It'd get bigger too, but it should still fit in the hole (since they're the same temperature?, right?

4. Mar 5, 2009

### fluidistic

Ok thanks to both! My friend was right. I understand better now.

5. Mar 5, 2009

### Mapes

Of course, if we fix the edges of the plate, the hole will get smaller...

A further question that might be interesting to explore: what edge constraint would result in the hole not changing size or shape?