The amount of work done in blowing a soap bubble such that its diameter increases from $d_1$ to $d_2$ is ( $T=$ surface tension of soap solution)

The work done equals the change in surface energy, given by $W = T \Delta A$, where $T$ is the surface tension and $\Delta A$ the area difference.

A soap bubble has two surfaces, so its total area is $8 \pi R^2$.

Given initial diameter $d_1$ and final $d_2$, radii are $R_1 = d_1 / 2$ and $R_2 = d_2 / 2$.

Initial area is $A_1 = 8 \pi (d_1 / 2)^2 = 2 \pi d_1^2$, final area $A_2 = 8 \pi (d_2 / 2)^2 = 2 \pi d_2^2$, so $\Delta A = 2 \pi (d_2^2 - d_1^2)$.

Therefore, work done is $W = T \cdot 2 \pi (d_2^2 - d_1^2) = 2 \pi T (d_2^2 - d_1^2)$.

This corresponds to option D.