A brass rod of length 50 cm and diameter 3.0 cm 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? (Coefficient of linear expansion of brass = 2.0 x10-5/°C, steel = 1.2 x 10-5/°C)

Change in temperature of each rod,∆T = 250 - 40 = 210°CClearly, change-in length of the brass bar∆Lb = α0L∆T = (2.0 x 10-5) x 50 x 210 = 0.21 cmand change in length of steel rod∆Ls = αsL∆T = (1.2×10-5)×50×210 = 0.126 cmSince the ends of the rod are free to expand, change in the length of the combined rod∆L = ∆Lb+∆Ls = 0.21 + 0.13 = 0.34 cm