If two soap bubbles of equal radii $r$ coalesce,then the radius of curvature of the interface between the two bubbles will be:

Two soap bubbles coalesce to form a single bubble. If $V$ is the subsequent change in volume of contained air and $S$ is the change in total surface area, $T$ is the surface tension and $P$ is atmospheric pressure, then which of the following relations is correct?

Pressure inside a soap bubble is greater than the pressure outside by an amount: (given: $R =$ Radius of bubble,$S =$ Surface tension of bubble)

$A$ 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 $S = 5 \ N/m$.

The radii of two soap bubbles are $r_1$ and $r_2$. In isothermal conditions,they meet together in a vacuum. Then the radius of the resultant bubble is given by

Small drops of liquid of the same radius coalesce to form a big drop. The ratio of the total surface energies after and before the change is: