A rod of length l, has linear coefficient of thermal expansion $\mathrm{\alpha }$ which is given as $\mathrm{\alpha }={\mathrm{\alpha }}_0+{\mathrm{\alpha }}_1\mathrm{x}+{\mathrm{\alpha }}_2\mathrm{T}.$ The rod is heated from temperature ${\mathrm{T}}_0 \mathrm{\&} {\mathrm{T}}_1$. Then choose the INCORRECT statement(s):

Total elongation in the rod varies linearly with length ‘l’ of the rod.

Dimensional formulae of ${\mathrm{\alpha }}_0, {\mathrm{\alpha }}_1 \mathrm{\&} {\mathrm{\alpha }}_2$ are different.

Net elongation in the rod is given by $\text{Δ}\mathcal{\text{l}}{\text{=α}}_0\mathcal{l}({\mathrm{T}}_1-{\mathrm{T}}_0)+{\mathrm{\alpha }}_1\frac{\mathcal{l}}{2}({\mathrm{T}}_1-{\mathrm{T}}_0)+{\mathrm{\alpha }}_2\mathcal{l}({\mathrm{T}}_1^{\mathrm{\hspace{0.17em}}2}-{\mathrm{T}}_0^{\mathrm{\hspace{0.17em}}2})$

Change in length of small element of length ‘dx’ is different for different portion of rod.