The aluminum rod (al) is inside the steel tube (s). There is an air gap between them as shown. There is a temperature change ?T which affects both the aluminum rod and the steel tube.

What is the minimum temperature change ?T needed so that there is no air gap. Solve the symbolic expression for ?T and calculate its numerical value.

(P = 0)

Hint: You can look at the thermal expansion of radiuses or perimeters.