A long iron rod initially at a temperature of 20°C has one end dipped in boiling water (100°C) at time, t = 0. The curved surface of the rod is insulated so that heat conduction is one dimensional in the axial direction. The temperature at a distance 100 mm from the dipped end becomes 40°C at time, t = 200 s. The same temperature is achieved at a distance of 200 mm from the dipped end at time
A)t = 283 s
B)t = 356 s
C)t = 400 s
D)t = 800 s

Question

Quizplus · Accepted Answer

The time taken for the temperature to reach a certain point in a rod is proportional to the square of the distance from the heat source. Doubling the distance (from 100 mm to 200 mm) means the time will be four times longer (since 200^2/100^2 = 4). Therefore, 200 s * 4 = 800 s.

A Long Iron Rod Initially at a Temperature of 20°C