A steel sphere of radius 0.1 m at 400°K is immersed in an oil at 300°K. If the centre of the sphere reaches 350°K in 20 minutes, how long will it take for a 0.05 m radius steel sphere to reach the same temperature (at the centre) under identical conditions? Assume that the conductive heat transfer co-efficient is infinitely large ?

Question

Accepted Answer

5 minutes. The time taken is proportional to the square of the radius (t ∝ r²). Since the new radius is half (0.1 m to 0.05 m), the time will be quartered (20 min / 4 = 5 minutes).