Question

A sphere, a cube and a thin circular plate, all made of same substance and all have same mass. These are heated to 200^0C 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 drops to room temperature at last
• D. Temperature of all the three drops to room temperature at the same time

Answer 1

Answer: (A)

Temperature of sphere drops to room temperature at last

Answer 2

$\frac{dT}{dt} = \frac{eA\sigma}{mc}(T^{4} - T_{0}^{4}) = \frac{eA\sigma}{V\rho c}(T^{4} - T_{0}^{4})$

∴ Rate of cooling $R \propto A$

[As masses are equal then volume of each body must be equal because materiel is same]

i.e. rate of cooling depends on the area of cross-section and we know that for a given volume the area of cross-section 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 temperature at last.