A solid copper cube and a solid copper sphere, both of same mass & emissivity are heated to same initial temperature and kept under identical conditions. What is the ratio of their initial rate of fall of temperature?

Question

A solid copper cube and a solid copper sphere, both of same mass & emissivity are heated to same initial temperature and kept under identical conditions.  What is the ratio of their initial rate of fall of temperature?

Infinity Learn · Accepted Answer

If 'a' is the length of cube, surface area $$Scube=6a2$$ If 'r' is the radius of sphere, surface area  $$Ssphere=4$$$$π$$$$r2Both$$ the cube and sphere have the same volume as given Volume  $$V=a3$$  ∵$$V=43$$$$π$$$$r3$$∴$$a3=43$$$$π$$$$r3$$⇒$$ar=4$$$$π$$$$313$$ Area cube  Area sphere $$=6a24$$$$π$$$$r2=64$$$$π$$$$ar2=64$$π×$$4$$$$π$$$$323=6$$$$π$$$$13$$∵  mass are equal Rate of fall in temperature $$=$$ Surface area∵Rate of fall in $$temperature=$$ $$6$$$$π$$$$13$$

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