An aluminium rod is 2.00 m long at 15 °C. It is first heated uniformly to 45 °C and then further heated to 95 °C. Assume the coefficient of linear expansion of aluminium remains constant at 2.3×10−5K−1.
(i) Find the length of the rod after it reaches 45 °C.
(ii) Find the length of the rod after it reaches 95 °C.
(iii) Show numerically that the total increase in length obtained by adding the results of the two stages is equal to the increase that would be obtained if the rod were heated directly from 15 °C to 95 °C in one step.