Two different wires having lengths L 1 and L 2 and respective temperature coefficient of linear expansion α 1 and α 2 , are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

Step-by-step solution

The wire are joined end-to-end, so they are in series combination, then total length of wire is given by L = L 1 + L 2     . . . ( 1 ) When the temperature is increase by ∆ θ , then its final length is given by using concept of linear expansion, L ' = L ( 1 + α ∆ θ )     . . . ( 2 ) Using equation ( 1 ) and ( 2 ) for the series combination of wires, final length is given by L ' = L 1 ' + L 2 '     . . . ( 3 ) ⇒ L 1 + L 2 ( 1 + α eff