The temperature of a metal strip having coefficient of linear expansion $\alpha$ is increased from $T_1$ to $T_2$ resulting in an increase of its length by $\Delta L_1$. The temperature is further increased from $T_2$ to $T_3$ such that the increase in its length is $\Delta L_2$. Given $T_3 + T_1 = 2T_2$ and $T_2 - T_1 = \Delta T$, the value of $\Delta L_2$ is . . . . . . .

• A
  $\Delta L_1[1 + 2\alpha^2(\Delta T)^2]$
• B
  $\Delta L_1[1 + \alpha^2(\Delta T)^2]$
• C
  $\Delta L_1[1 + 2\alpha \Delta T]$
• D
  $\Delta L_1[1 + \alpha \Delta T]$