The surface tension of the soap water
solution is `1/ (10 pi)` N/m . The free energy of the
surface layer of a soap bubble of diameter 5 mm will be

Options

A. `2.5 xx 10^(-6) J`
B. `1 xx 10^(-7) J`
C. `8 xx 10^6 J`
D. `5 xx 10 ^(-6) J`

Answer

D

Explanation

As, we know that the surface energy of a soap bubble,
` W= AT `
so, `W ^' = 2A^' T` `[A^' = 2A]`
Since, a soap bubble has double surface area.
given surface tension of soap water solution `T 1/ (10pi)` N/m and diameter of soap bubble = 5 mm
Now, `W ^' = 2(pi D^2) T = 2 xx pi xx 25 xx 10^(-6) xx 1/(10pi)`
`rArr W ^' = 5xx10^(-6) J`