# How to reduce size of bracelets using physics?

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?

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

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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