Question
A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature ${120^o}C$, then
✓
Answer
(b)Rate of cooling of a body $R = \frac{{\Delta \theta }}{t} = \frac{{A\varepsilon \sigma ({T^4} - T_0^4)}}{{mc}}$
==> $R \propto \frac{A}{m} \propto \frac{{{\rm{Area}}}}{{{\rm{Volume}}}}$
==> $R \propto \frac{A}{m} \propto \frac{{{\rm{Area}}}}{{{\rm{Volume}}}}$
==> For the same surface area. $R \propto \frac{1}{{{\rm{Volume}}}}$
( Volume of cube < Volume of sphere
==> ${R_{Cube}} > {R_{Sphere}}$ i.e. cube, cools down with faster rate.
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