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# 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?

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a
6π13
b
6π23
c
6π3
d
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detailed solution

Correct option is A

If 'a' is the length of cube, surface area Scube=6a2 If 'r' is the radius of sphere, surface area  Ssphere=4πr2Both the cube and sphere have the same volume as given Volume  V=a3  ∵V=43πr3∴a3=43πr3⇒ar=4π313 Area cube  Area sphere =6a24πr2=64πar2=64π×4π323=6π13∵  mass are equal Rate of fall in temperature = Surface area∵Rate of fall in temperature= 6π13

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A solid copper sphere (density $\mathrm{\rho }$ and specific heat capacity c) of radius r at an initial temperature 200 K is suspended inside a chamber whose walls are at almost 0 K. The time required (in $\mathrm{\mu }$s) for the temperature of the sphere to drop to 100 K is

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