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(D) The work done in blowing a soap bubble is given by $W = T \cdot \Delta A$, where $T$ is the surface tension and $\Delta A$ is the change in surfac

Vedclass · Accepted Answer

$(4)^{1/3} W$

Vedclass · Answer

(D) The work done in blowing a soap bubble is given by $W = T \cdot \Delta A$, where $T$ is the surface tension and $\Delta A$ is the change in surface area. For a soap bubble, the surface area is $A = 2 	imes (4 \pi r^2) = 8 \pi r^2$. Thus, $W \propto r^2$.Since the volume of the bubble is $V = \frac{4}{3} \pi r^3$, we have $r \propto V^{1/3}$.Substituting this into the work relation: $W \propto (V^{1/3})^2 = V^{2/3}$.Let $W_1 = W$ for volume $V_1 = V$, and $W_2$ be the work for volume $V_2 = 2V$.Then, $\frac{W_2}{W_1} = \left( \frac{V_2}{V_1} ight)^{2/3} = \left( \frac{2V}{V} ight)^{2/3} = (2)^{2/3}$.Therefore, $W_2 = (2)^{2/3} W = (2^2)^{1/3} W = (4)^{1/3} W$.

The work done in blowing a soap bubble of volume $V$ is $W$. The work done in blowing the bubble of volume $2V$ from the same soap solution is

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