# The bigger you are, the hotter you fall

A small sphere falls from rest in a viscous fluid. Due to viscous friction, heat is produced as the sphere moves relative to the fluid. The rate of heat production at terminal velocity is directly proportional to the $$n^{\textrm{th}}$$ power of the sphere's radius.

Use physical reasoning, scaling, dimensional analysis, or whatever tactics (apart from Google) you can think of to find $$n$$.

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