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

The correct option is B

The cube cools down faster than the sphere

$Rateofcoolingofabody$

$R=\frac{△\theta }{t}=\frac{Aϵ\sigma (T^4-T_0^4)}{mc}$

$\Rightarrow R\alpha \frac{A}{m}\alpha \frac{Area}{Volume}$

$\Rightarrow Forthesamesurfacearea.R\alpha \frac{1}{Volume}$

$\because Volumeofcube<Volumeofsphere$

$\Rightarrow R_{Cube}>R_{Sphere}i.e.cube,coolsdownwithfasterrate.$