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Consider a cube with side length $a$. Then its perimeter is proportional to $a$, its surface area $A$ is proportional to $a^2$, and its volume $V$ is proportional to $a^3$. It's clear that any reasonable 3D shape satisfies the same kind of scaling, which implies $A \propto V^{2/3}$. However, it's possible for fractals to have perimeter/area/volume that ...


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I think the question is really pertinent. If you heat the liquid without any impurity and in a flask with very smooth walls, kept at higher pressure until the temperature is just below the boiling point at that pressure and you slowly start to reduce the pressure, you will find that the water is not started to boil, this state is known as super heated state. ...



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