Two rods having length l1 and l2, and made of materials with the linear expansion coefficient α1 and α2, respectively, were soldered together. What is the equivalent coefficients of linear expansion for the newly obtained rod ?

Let the length of the combined rod system after expansion would be L. Now, from the question we have L = L1 + L2Where L1 be the length the length of one rod after expansion and L2 be the length the length of another rod after expansionL1=l11+α1ΔT,L2=l21+α2ΔTL=l11+α1ΔT+l21+α2ΔTL=l1+l2+l1α1+l2α2ΔTL=l1+l21+l1α1+l2α2ΔTl1+l2α=l1α1+l2α2l1+l2