# Coin heated

1. Jul 22, 2007

### Jean-Louis

I have a copper coin with a hole in the centre. The hole is a circle. If the coin is heated, the metal will expand towards all directions in and out, so the radius of the circle will be decreased. Correct?

2. Jul 22, 2007

### xez

Well if you had an infinitely thin ring of copper and heated
it, it could only increase in circumference, so the hole
would actually get bigger as the radius of the ring increased.

I believe that your statement that it expands in every
direction is more or less true. What has to be considered,
though, is the real world behavior of such an object where
every atom is expanding just a little bit. The expansion
will create a somewhat complicated stress/strain response
in the metal, and the particular amount of displacement
in a given area would be the result of lessening the overall
stress energy of the metal.

Though expanding from metal into free air is a pretty low
energy thing to do since there wouldn't be back-pressure
from the air in the hole, you must also consider that
there would be a compression of the metal encircling the
air-hole since more metal would have to be squeezed into
a smaller space circumferentially too.

I think that mainly it'd follow the path of expanding
outward radially since that'd seem to lessen strees on the
whole of the piece.

Certainly if it became really hot to liquefy, though, you'd
expect that it'd start to slump/flow/creep to fill in a small
hole.

It'd make an interesting FEM analysis.

Empirically I've never seen a hot 'nut' or 'washer' become
more difficult to put around a cold bolt, or a hot jar lid
become harder to screw around a cold jar. That would
tend to support the theory that mostly it'd just expand
outward as the lowest energy lowest stress option.

3. Jul 22, 2007

### cesiumfrog

Divide the ring into 16 segments. Now make one of those segments twice as large. What inner diameter will 16 of those give rise to?

4. Jul 22, 2007

### Staff: Mentor

Incorrect. Do the exercise that cesiumfrog suggests. All linear dimensions will expand, including that of the hole.

5. Jul 22, 2007

### belliott4488

Or, just draw two concentric circles on your computer screen and then zoom in on the image. The geometry is the same.

6. Jul 22, 2007

### DaveC426913

I did this experiment in Grade 7.

You have a metal ball and a metal ring. The ball is slightly too large to fit through the ring.

Heat the ring for a few minutes over a Bunsen burner and now the ball can slip through the ring.

QED.

7. Jul 22, 2007

### Gokul43201

Staff Emeritus
If the radius decreased, what could you say about the interatomic spacing in the tangential direction, along this inner wall? Would it have increased or decreased? What would you expect heating to produce (an increase or a decrease in the interatomic spacing)?