Obtain the expression for excess pressure inside a soap bubble.

Explanation

Excess pressure inside a soap bubble
Consider a soap bubble of radius R and the surface tension of the soap bubble be T as shown. A soap bubble has two liquid surfaces ion contact with air, one inside the bubble and other outside the bubble. Therefore, the force on the soap bubble due to surface tension is `2xx2piRT`. The various forces acting on the soap bubble are

(i) Force due to surface tension `F_(tau)=4piRT` towards right
(ii) Force due to outside pressure,
`F_(P_(1))=P_(1)pi R^(2)` towards right
(iii) Force due to inside pressure,
`F_(P_(2))=P_(2)piR^(2)` towards left
As the bubble is in equilibrium,
`F_(P_(2))=F_(T)+F_(P_(1))`
`P_(2)pi R^(2)=4piRT+P_(1)piR^(2)rArr (P_(2)-P_(1))piR^(2)=4piRT`
Excess pressure is `DeltaP=P_(2)-P_(1)=(4T)/(R)`.