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| 1. |
Derive an expression for the excess pressure inside a soap bubble |
| Answer» Pnet = Pi - Pa Now, as the radius of the drop has increased, work has been done by the net internal pressure.So, this work done will be W = force x displacementorW = (pressure x area) x displacement and in this caseW = (pressure x area) x increase in drop radius so, the work done will beW = (P net x 4?r 2 ) x dr (1)but, the increase potential energy will be twicedU = 16?r.dr x S (2) this is because in case of a bubble there are two free surfaces, the outside surface and the inside surface. The potential energy will thus change accordingly. so, as (1) equals (2), we have(Pnet x 4?r2) x dr = 16?r.dr x Sor the net pressure inside a bubble will bePnet = 4S / r [twice than the that inside the drop] | |