The fact that air has to be blown into a drop of soap solution to make a bubble should suggest that the pressure within the bubble is greater than that outside. This is in fact the case: this excess pressure creates a force that is just balanced by the inward pull of the soap film of the bubble due to its surface tension.
Consider a soap
bubble of radius r as shown in Figure 1. Let the external pressure be Po and the
internal pressure P1.
The excess pressure P within the bubble is therefore
given by :
Excess pressure = P1 -
P1
Consider the left-hand half of the bubble. The force acting
from right to left due to the internal excess pressure can be shown to be PA, where A is the
area of a section through the centre of the bubble. If the bubble is in equilibrium this force is
balanced by a force due to surface tension acting from left to right. This force is 2x2πrT (the factor of 2 is necessary because the soap film has two sides)
where T is the coefficient of surface tension of the soap film. Therefore
2x2πrT = PA = Pπr2 giving: