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 ___________________?

Question

Accepted Answer

t = 800 s. The time taken for a given temperature change is proportional to the square of the distance from the source. Since the distance doubled (100mm to 200mm), the time should increase by a factor of $2^2=4$. Thus, $200 	ext{ s} 	imes 4 = 800 	ext{ s}$.