Question

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

• A. both of them will cool down at the same rate
• B. the cube will cool down slower than the sphere
• C. the sphere will cool down slower than the cube
• D. the information is insufficient

Answer 1

Answer: (C)

As $Q=ms\Delta T$
$\frac{dQ}{dt}=ms\frac{dT}{dt}$
$\Rightarrow \frac{dT}{dt}=\frac{1}{ms}\frac{dQ}{dt}$
Here, $\frac{dT}{dt}$ is the rate of cooling
$\frac{dQ}{dt}\propto A$ [Rate of heat transfer is directly proportional to the surface area]
$\therefore \frac{dT}{dt}\propto \frac{1}{m}\Rightarrow$ Heavier will cool slower.
For the same surface area, the volume of the sphere will be more than that of the cube, hence it will have more mass