Question

we have a metal plate that has a circular hole with radius "R". if we raise the temperature of this plate, what happened with radius of hole?
increasing, decreasing or stay constant?

Answer 1

If the hole is filled with a piece of the same metal, what do you think happens to the filling?

Answer 2

expansion!

Answer 3

but air not act as a metal?

Answer 4

Think of a plate without a hole.
Now sawcut a hole, with an infinitely thin gap.
What happens to the cut-out when heated?
Therefore what happens to the hole when heated?

Answer 5

sry, please describe by details!

Answer 6

ok.

Let's say we have two identical metal plates, both free of stress (which could change the size of the plates) and at the same temperatures.

One of the plates has a hole cut in it and the other does not, but have the exact outline of the hole (of the other plate) inscribed on the plate at the same position.

If both plates are subject to the same temperature increase of 100 degrees, how do the diameters of
1. the hole of the first plate, and
2. the "outline" of the hole on the plate without a hole
differ?

Answer 7

we aint interested in air, the metal expands in every way, radius increases

Answer 8

I got it!
you said that radius increasing!
but we have differs between plates:
hole being or not!
this is the question!

Answer 9

The key fact is that the length of all edges should increase, as the atoms along the edge move further away from each other. That means the circumference of both the outer edge and the edge along the hole should increase.

Answer 10

Look. While the textbook answer to this question is what people are claiming - substitute the inner circular plate into the whole and the two should expand in unison. But isn't that an assumption really? Its idealised to expect that the expansion would not depend on the structure, the shape.
Maybe we wont really have a numerical, quantitative answer out of it,
but i visualize that in REAL situation, the inner ring should buckle up if confined to the same plane, or the entire annular ring gets strained into a slightly conical shape.
kmazraee has a point there. He didn't solve it at the first go because the assumption of ideal expansion is .. not intuitive - unless you want the problem to be solved real bad ! :D

Answer 11

basically radius of that hole will decrease...due to expansion of metal see how ...expansion will contract the inner radius second state is the state after being expanded

Answer 12

plate is just not expanding out....it is also expanding inwards

Answer 13

expanding along every direction

Answer 14

Usually it decreases with increase of temperature.

Answer 15

@kmazraee

Answer 16

suppose that is the inner ring with the dots being atoms and the lines being their bonds. As they heat up, the bonds get longer, so whether this is an inside ring or outside ring doesn't matter.

Answer 17

ok this is interesting! @Kainui might have hit it home. Imagine annular rings which form the plate. Heat one - its circumference increases linearly, as does it radius. And this is valid at all radii.
Bravo.

i think that this problem might have much more to it when applied to other shapes though. The circle is a special example perhaps.

Answer 18

more discussion about this at - http://www.eng-tips.com/viewthread.cfm?qid=246558

i don't think the problem is as simple as it is made out to be

Answer 19

@mayankdevnani whats your reasons?

Answer 20

@kmazraee didn't you get answer yet?

Answer 21

@d3banjan The "circle" is no different than any other shape on the molecular level. Consider how much a mole is and the average bond length between atoms. This these are things on the scale of 10^-23 and 10^-10 and are extraordinarily tiny. The picture I drew helps give the intuition, but there is really no circle of atoms in a washer. It's just a bunch of atoms clumped in together forming some kind of crystalline structure.

People have been running metal lids on glass jars under hot water for a long time to loosen them and it's exactly because this is true. Physics is based off of observations, and in the end if you don't believe me or take the intuition I offered you, then find something else that works for you, because in the end you can do the experiment and find that the hole does indeed get bigger whether it's tiny invisible demons pushing it apart when summoned by the heat or what I said lol.

Answer 22

Back to the original question.
The idea of cutting out a hole, and leaving it inside the hole will give us the answer right away. Reasoning:
We know exactly how a circular cut-out will expand, whether in the hole or not.
As for the hole from which the cut-out was made, it has to still fit the cut-out, if we were to put it back into one piece. So the hole will expand exactly like if it were a piece of the same metal.

Answer 23

tnx my dear friends! good solving! :D