A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is (αCu = 1.7×10-5K-1 and αAI= 2.2 ×10-5 K-1)

ICut = lcu(1+αCu∆T)--------(i)lAI' = IAl(1+αAl∆T) -----(ii)Equation (ii)-Eq. (i)lAl' = ICu' = lAl+lAIαAl∆T-(lCu+lCuαCu∆T)lAl' - lCu' = lAl - lCu+(lAlαAl-lCuαCu)∆TThe increase in length is not depend on temperature.αCulCu = αAllAl1.7 × 10-5×88 = 2.2×10-5×lAllAl = 68cm