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(C) The work done to blow a soap bubble of radius $r$ is given by $W = T 	imes \Delta A$,where $T$ is the surface tension and $\Delta A$ is the chang

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slightly less than $4$ times.

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(C) The work done to blow a soap bubble of radius $r$ is given by $W = T 	imes \Delta A$,where $T$ is the surface tension and $\Delta A$ is the change in surface area. Since a soap bubble has two surfaces,$\Delta A = 2 	imes (4 \pi r^2) = 8 \pi r^2$.For the first bubble of radius $R$: $W_1 = 8 \pi R^2 T_1$.For the second bubble of radius $2R$: $W_2 = 8 \pi (2R)^2 T_2 = 32 \pi R^2 T_2$.If the temperature remained constant $(T_1 = T_2)$,the work $W_2$ would be exactly $4 W_1$.However,heating the solution decreases the surface tension $(T_2 Therefore,$W_2 = 4 W_1 	imes (T_2 / T_1)$. Since $T_2 < T_1$,it follows that $W_2 < 4 W_1$.

$A$ soap bubble of radius $R$ is blown. After heating a solution,a second bubble of radius $2R$ is blown. The work required to blow the $2^{nd}$ bubble in comparison to that required for the $1^{st}$ bubble is

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