Question

A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature and enclosed in the same surroungings. 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

The correct option is B

The cube cools down faster than the sphere

Rate of cooling of a body
$R=\frac{△\theta }{t}=\frac{Aϵ\sigma \left(\right)T^4-T_0^4}{mc}$
$\Rightarrow R\propto \frac{A}{m}\propto \frac{Area}{Volume}$
$\Rightarrow$ 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.