Question

A soap bubble of radius $R$ is blown. After heating the solution a second bubble of radius $2R$ is blown. The work required to blow the second bubble in comparison to that required for the first bubble is

• A. Double
• B. Slightly less than double
• C. Slightly less than four times
• D. Slightly more than four times

Answer 1

Answer: (C)

Work done to form a bubble of radius $R$
$W_1=8\pi R^2{T}_1$
Work done to form a bubble of radius $2R$
$W_2=8\pi {\left(2R\right)}^2{T}_2=32\pi R^2{T}_2$
$\therefore \frac{W_1}{W_2}=\frac{T_1}{4T_2}$
If surface tension o f soap solution is same, then
$W_2=4W_1$
But in the problem the temperaturew of solution is increased. So its surface tension decreases.
$\therefore W_2<4W_1$