Question

A spherical soap bubble has a radius ${}^{\prime }{r}^{\prime }$. The surface tension of the soap film is $T$.The energy needed to double the diameter of the bubble at the same temperature is:

• A. $24\pi r^2\sigma$
• B. $4\pi r^2\sigma$
• C. $2\pi r^{2}T\sigma$
• D. $12\pi r^{2}T\sigma$

Answer 1

Answer: (A)

$24\pi r^2\sigma$

The energy needed to double the diameter of the bubble is given as
$W=8\pi \sigma (r_2^2-r_1^2)$
We have $r_2=2r_1$
or
$W=8\pi \sigma \left(3r_1^2\right)=24\pi \sigma r^2$