Assume that the coefficient of linear expansion of the material of a rod remains constant, equal to `alpha^(@)C^(-1)` for a fairly large range of temperature. Length of the rod is `L_0` at temperature `theta_(0)`. (a) Find the length of the rod at a high temperature `theta`. (b) Approximate the answer obtained in (a) to show that the length of the rod for small changes in temperature is given by `L = L_0 [1 + alpha (delta- delta_(0))]`

Answer

`L=L_(0)e^(alpha(theta-theta_(0)))`