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.
$\therefore W_{2} < 4W_{1}$