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My mom has a set of bangles (bracelets) made of gold like the ones shown in the picture. Problem is the size (diameter) of these bangles is a bit more than required. If she goes to a goldsmith he cuts a piece from the bangle and rejoins the ends.

My idea is: why not put it under ice for a a significantly long time so that the compression induced due to cold is permanent and won't be undone at the room temperatures (27-32 degrees centigrade). But I'm also bit skeptical because I don't know what I don't know. Will this work? I know gold is relatively inert but does it anyway get affected by ice? Will the reduction in size be uniform? or is there a possibility of uneven deformation? Is there any other way it can be done using physics?

enter image description here

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The elongation, or shortening of the materials with temperature depends on the coefficient of linear thermal expansion of the material with which it is made (here: gold)

$$\alpha = \frac{1}{L}\frac{dL}{dT}$$ Integrating, $$L = L_0\ e^{\alpha\Delta T}$$ $$L \approx L_0(1+\alpha\Delta T)$$

In your case, $L$ = circumference. Change in radius will be given by: $$dr = \dfrac{dL}{2\pi}$$

The decrease in circumference, and in turn, radius, is very small even for largely negative changes in temperature, due to the fact that $\alpha$ of most materials is very small ( of the order of $10^{-6}$)

Changes in the length are temporary, because as soon as you again increase the temperature, length will start increasing again.


Regarding uniformity, although a perfect material shape would expand or contract uniformly, but most real objects suffer from imperfection, which may lead to somewhat non-uniform expansion

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Your idea won't work because the bangles will always expand when they warm up again. On the other hand, if the bangles were heated while in a press so that they can't expand (the press would have to be just big enough to hold the bangle), the metal would have to deform by making the bangles a bit thicker. In this case, when the metal is cooled, it would still have to shrink, resulting in a bangle with a smaller diameter.

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