Question

A sphere, a cube and a thin circular plate are made of same material and all have same mass. These are heated to ${200}^{\circ }\text{C}$ and then placed in a room. Then the

• A. Temperature of sphere drops to room temperature at last
• B. Temperature of cube drops to room temperature at last
• C. Temperature of thin circular plate drop to room temperature at last
• D. Temperatures of all the three drop to room temperature at the same time

Answer 1

The correct option is A Temperature of sphere drops to room temperature at last

$\frac{dT}{dt}=\frac{ϵA\sigma }{mc}(T^4-T_0^4)=\frac{ϵA\sigma }{V\rho c}(T^4-T_0^4)$
We know that,
$\therefore$ Rate of cooling $R\propto A$
(As masses are equal, volume of each body must be equal because material is same)
i.e. rate of cooling depends on the surface area and we know that for a given volume the surface area will be minimum for sphere. It means the rate of cooling will be minimum in case of sphere.
So the temperature of sphere drops to room tempereature at last.