Sol. The pressure in a soap bubble of radius R is greater than the atmospheric pressure p 0 by p = 4 γ /R. The factor of 4 arises because both directions of curvature and the fact that the film is two-sided have to be taken into account. Clearly, the pressure is higher in the bubble of smaller radius and, therefore, the air flows into the larger bubble, as if inflating it to finally form a single bubble of radius R 3 .

The volume of air in the bubbles is proportional to R 3 , and therefore the ideal gas equation and the conservation of mass require that

+ = .

For bubbles of ordinary size, the pressure of curvature is many orders of magnitude smaller than the external atmospheric pressure. If the pressure of curvature is neglected the radius of the resulting bubble is –

R 3 .

If the radii are measured 'accurately', in order to determine the surface tension, the formula

γ =

is appropriate. In practice, however, this method cannot be applied, as the numerator is, as shown, almost equal to zero and thus would carry a large fractional uncertainty as a result of measurement error. Any measured data are likely to provide only a rough estimate of the surface tension.