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 i

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

TestHub · Accepted Answer

The work done in blowing a soap bubble of radius $R$ is given by $W = 2 \times 4 π R^{2} \times T = 8 π R^{2} T$ , where $T$ is the surface tension of the soap solution.

For the first bubble of radius $R$ , the work done is $W_{1} = 8 π R^{2} T_{1}$ .

For the second bubble of radius $2 R$ , the work done is $W_{2} = 8 π (2 R)^{2} T_{2} = 32 π R^{2} T_{2}$ .

The ratio of the work done is $\frac{W _{2}}{W _{1}} = \frac{32 π R ^{2} T _{2}}{8 π R ^{2} T _{1}} = 4 \frac{T _{2}}{T _{1}}$ .

When the solution is heated, its temperature increases. The surface tension of a liquid decreases with an increase in temperature, so $T_{2} < T_{1}$ .

Therefore, $\frac{W _{2}}{W _{1}} < 4$ , which means the work required to blow the second bubble is slightly less than $4$ times the work required for the first bubble.

Answer: slightly less than $4$ times

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