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10-2.Transmission of Heat
medium
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
A
Both the cube and the sphere cool down at the same rate
B
The cube cools down faster than the sphere
C
The sphere cools down faster than the cube
D
Whichever is having more mass will cool down faster
Solution
(b)Rate of cooling of a body $R = \frac{{\Delta \theta }}{t} = \frac{{A\varepsilon \sigma ({T^4} – T_0^4)}}{{mc}}$
==> $R \propto \frac{A}{m} \propto \frac{{{\rm{Area}}}}{{{\rm{Volume}}}}$
==> 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.
Standard 11
Physics
