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?
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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.
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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.
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$\begingroup$ My question is why are the edges only moving outwards and not inwards. If the point is to simply expand why doesn't it expand in all directions? $\endgroup$ Commented 6 hours ago
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1$\begingroup$ @user162803 each small segment does expand in all directions. But each small segment is also pushed away from other parts. The part of the segment that expands toward the center is less than the amount that the entire segment is pushed away from the center. $\endgroup$ Commented 3 hours ago
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The idea that the metal "expands in all directions" is compatible with the hole getting bigger. "Expands in all directions" roughly means that every atom in the object gets, on average, a little bit further away from every other atom.
Let's suppose that there are a fixed number of atoms around the inside circumference of the hole. (That's actually pretty close to the truth.) It's a ring of atoms. Not so much different from a ring of people standing in a circle If you had a ring of people standing in a circle, and you wanted everyone to get a little further from everyone else, would you ask them all to take a step forward (make the ring smaller?) or would you ask them all to take a step back?
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$\begingroup$ To make people stand a bit further from each other we could simply ask them to move in all directions hence making it a fuller circle and as a consequence them getting away from each other $\endgroup$ Commented 6 hours ago
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$\begingroup$ @user162803, That would be a good way to use people as a model of a gas. I was thinking that the "metal disk" you asked about was more of a solid object. My model of it was pretty sketchy. In a more complete version of it, there would be many concentric rings of people, and they all would be harnessed, and tied to their nearby neighbors with short ropes (metallic bonds) I'm thinking that they only way they could move so as to stretch all of the ropes would be for everybody to move away from the center. $\endgroup$ Commented 5 hours ago
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$\begingroup$ If there is a hole in between them why cant they move towards the center . For example if one person moves towards the center of the hole and one outwards wont all the ropes be stretched that way as well? $\endgroup$ Commented 5 hours ago
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1$\begingroup$ That's why the concentric rings. One person cannot move inward without pulling everyone behind them inward as well. $\endgroup$ Commented 4 hours ago