A wire is made by attaching two segments together end to end. One segment is made of aluminum and the other is steel. The effective coefficient of linear expansion of the two segment wire is 19×10−6/ ∘C. The fraction length of aluminum is [linear coefficients of thermal expansion of aluminum and steel are 23×10−6/ ∘C and 12×10−6/ ∘C,respectively]

The change in length of wire : =lAlαAlΔθ+lstαstΔθ associated with temperature change of Δθ, where αAl and αSt are the coefficient of linear expansion of aluminum and steel, respectively αAl=23×10−6/∘Cαst=12×10−6/∘CThe effective coefficient of linear expansion of the two segments of wire =19×10−6/∘Cl1αAlΔθ+l2αstΔθ=l1+l2αΔθl1l1+l2=α−l2l1+l2αstαAll1l1+l2=x, l1+l2=l, l2l1+l2=1−xx=α−(1−x)αstαAlx=α−αstαAl−αst=19×10−6−12×10−623×10−6−12×10−6=711