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.
A)5 minutes
B)10 minutes
C)20 minutes
D)40 minutes

Question

Quizplus · Accepted Answer

The time taken for the center of a sphere to reach a certain temperature is proportional to the square of its radius when the conductive heat transfer coefficient is infinitely large. Since the radius of the second sphere is half of the first, the time taken will be (0.05/0.1)^2 = 1/4 of the original time, which is 20 minutes. Therefore, it will take 5 minutes.

A Steel Sphere of Radius 0