Question

Radius of a soap bubble is $r$, surface tension of soap solution is $T$. Then without increasing the temperature, how much energy will be needed to double its radius.

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

Answer 1

Answer: (D)

$24\pi r^{2}T$

As we know ,

without increasing temperature increasing radius will be done by performing some work on the bubble,

$W=8\pi T(R_2^2-R_1^2)$
$=8\pi T\left[\right(2r{)}^2-\left(r{)}^2\right]=24\pi r^{2}T$