Question

You want to insert an aluminum rod, which at 20°C has a radius of 1.00020 cm into a copper tube
which has a radius of 1.00010 cm at the same temperature. You decide to put both of them in the
refrigerator. At what temperature will the rod just fit if both are cooled to the same temperature?
The coefficient of thermal expansion for aluminum is 2.4 × 10-5 K-1, and that of copper is 1.7 ×
10-5 K-1.

Answer 1

For this to happen, the compression in aluminum must be 0.0001 cm more than that of copper
Let the temperature of refrigerator = t

compression in Al , x = 1.0002*2.4*10^-5*(20-t)
compression in Cu , x - 0.0001 = 1.0001*1.7*10^-5 *(20-t)
approximate 1.0001 and 1.0002 to 1 and substitute x in the second equation

2.4*10^-5 * (20-t) -10^-4 = 1.7*10^-5(20-t)
0.7*10^-5 *(20-t)= 10^-4
t = 40/7 = 5.714 degrees C