A brass rod of length 50 cm and diameter `3.0` mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at `250 ^(@) C`. if the original lengths are at `40.0 ^(@) C`? Is there a "thermal stress developed at the junction ? The ends of the rod are free to expand (Co-efficient of linear expansion of brass `= 2.0 xx 10^(-5) K^(-1) , " steel " = 1.2 xx 10^(-5) K^(-1))`.

Explanation

Since the ends of the combined rod are not clamped, each rod expands freely.
`Delta l_("brass ") = 0.21 cm, Delta l_("steel") = 0.126 cm = 0.13 cm`
Total change in length ` = 0.34` cm. No .thermal stress. is developed at the junction since the rods freely expand.