Serway & Jewett — Temperature: Problem 38

A bimetallic strip of length \(L\) is made of two ribbons of different metals bonded together. (a) First assume the strip is originally straight. As the strip is warmed, the metal with the greater average coefficient of expansion expands more than the other, forcing the strip into an arc with the outer radius having a greater circumference (Fig. P18.38). Derive an expression for the angle of bending \(\theta\) as a function of the initial length of the strips, their average coefficients of linear expansion, the change in temperature, and the separation of the centers of the strips (\(\Delta r = r_2 - r_1\)). (b) Show that the angle of bending decreases to zero when \(\Delta T\) decreases to zero and also when the two average coefficients of expansion become equal. (c) What If? What happens if the strip is cooled?