A wire is made by attaching two segments together end to end. One segment is made of aluminium and the other is of steel. The effective coefficient of linear expansion of the two-segment wire is 19 × 10 - 6 ° C - 1 . If the fractional length of aluminium is p q where p and q are the least positive integers, then what is the value of p + q ? (linear coefficients of thermal expansion of aluminium and steel are 23 × 10

Step-by-step solution

The change in length of wire = l ⁡ A l ⁡  α A l ⁡ Δ θ + l ⁡ st  α st Δ θ associated with a temperature change of Δ θ , where α A l ⁡ and α St are the coefficient of linear expansion of aluminium and steel, respectively α A l ⁡ = 2 3 × 1 0 - 6   ∘ C - 1 α St = 1 2 × 1 0 - 6   ∘ C - 1 The effective coefficient of linear expansion of the two segments of wire = 1 9 × 1 0 - 6 / &