A metal annulus of radius R has a hole inside of radius r.
As the annulus thermally expands, R increases, but what happens to r?
The inner radius expands, just as does the outer radius, proportionally to the material's coefficient of thermal expansion. The more intuitive idea, that the expanding material would "fill-in" the hole, is wrong.
The classic demonstration of how best to think about this is to imagine a grid of tiles expanding:
A ---> B
ooo OOO
ooo OOO
ooo OOO
The annulus is like this, but with the center tile missing.
The coefficient is usually positive, with exceptions being rubber and near freezing water, which contract when heated. The coefficient is a proportionality constant of added: length, area, or volume (for isotropic materials) /T, with the linear constant being approximately 1/2 the areal and 1/3 the volumetric constants.
The only way to make the annulus hole shrink is to constrain the outer radius from expansion, which, inside machines, often happens.
This leads one to think about the uniformly expanding universe, where space itself is currently (and likely forever) expanding. Recent theories of a possible "accelerating expansion" offer future scenarios with Earth and even atoms expanding catastrophically, as discussed recently
here.
Edited on February 26, 2019, 12:39 pm
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