Q. A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature $120℃$, 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
Explanation
(b) Rate of cooling of a body $R = \frac{\mathrm{\Delta}\theta}{t} = \frac{A\varepsilon\sigma(T^{4} - T_{0}^{4})}{mc}$
$\Rightarrow R \propto \frac{A}{m} \propto \frac{Area}{Volume}$
$\Rightarrow$ For the same surface area, $R \propto \frac{1}{Volume}$
$\because$ Volume of cube < Volume of sphere
$\Rightarrow R_{Cube} > R_{Sphere}\ i.e.$ cube, cools down with faster rate
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.