Two spherical soap bubbles of radii $r_1$ and $r_2$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

$A$ drop of water of volume $0.05\, cm^3$ is pressed between two glass plates,as a consequence of which it spreads and occupies an area of $40\, cm^2$. If the surface tension of water is $70\, dyne/cm$,then the normal force required to separate out the two glass plates will be in Newton.

The change in energy when a big drop is split into $n$ small droplets is:

Under isothermal conditions, two soap bubbles of radii $r_1$ and $r_2$ combine to form a single soap bubble of radius $R$. If $P$ is the outside pressure, find the surface tension $T$ of the soap solution.

$A$ hot air balloon is a sphere of radius $8 \ m$. The air inside is at a temperature of $60^{\circ} \ C$. How large a mass can the balloon lift when the outside temperature is $20^{\circ} \ C$? Assume air is an ideal gas,$R = 8.314 \ J \ mol^{-1} \ K^{-1}$,$1 \ atm = 1.013 \times 10^5 \ Pa$,and the membrane tension is $S = 5 \ N/m$.

$A$ liquid drop of volume $V$ is placed on the surface of a glass plate. Then,another glass plate is placed on it such that the liquid forms a thin layer of area $A$ between the surfaces of the two plates. To separate the plates,a force $F$ has to be applied normal to the surfaces. The surface tension of the liquid is