The work done in blowing a soap bubble of radius $R$ is $W_1$ and that of radius $2R$ is $W_2$. The ratio of $W_1$ to $W_2$ is

The surface tension of the soap water solution is $\frac{1}{10 \pi} \text{ N m}^{-1}$. The free energy of the surface layer of a soap bubble of diameter $5 \text{ mm}$ will be:

If the work done in blowing a soap bubble of radius $R$ is $W$, then the work done in blowing a soap bubble of radius $2R$ is: (in $W$)

$A$ soap bubble of surface tension $0.04 \ N/m$ is blown to a diameter of $7 \ cm$. If $(15000 - x) \ \mu J$ of work is done in blowing it further to make its diameter $14 \ cm$, then the value of $x$ is . . . . . . . (Take $\pi = 22/7$)

$A$ 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

In an isothermal process,$2$ water drops of radius $1 \, mm$ are combined to form a bigger drop. Find the energy change (in $\mu J$) in this process if the surface tension $T = 0.1 \, N/m$.