Question

A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature $120^{\circ }C$, 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

Answer 1

Answer: (B)

Rate of cooling of a body $R=\frac{\Delta \theta }{t}$
$=\frac{A\epsilon \sigma \left(T^4-T_0^4\right)}{mc}$
$\Rightarrow R\propto \frac{A}{m}\propto \frac{\text{ Area }}{\text{ Volume }}$
$\Rightarrow$ For the same surface area. $R\propto \frac{1}{\text{ Volume }}$
$\because$ Volume of cube $<$ Volume of sphere
$\Rightarrow R_{\text{Cube }}>R_{\text{Sphere }}$ i.e., cube, cools down with faster rate