Excess Pressure In Bubbles

Question

Consider a soap bubble and a liquid drop of the same radius made from liquids of equal surface tension; how does the excess pressure inside the soap bubble compare to that inside the drop?

RankGuru · Accepted Answer

As outlined in NCERT Class 11, Chapter 10 (Mechanical Properties of Fluids), surface tension creates a pressure difference across a curved liquid surface. A liquid drop has a single surface, so its excess pressure is $\Delta P_{drop} = \dfrac{2T}{r}$. A soap bubble, however, has two surfaces in contact with air (inner and outer film), so its excess pressure is $\Delta P_{bubble} = \dfrac{4T}{r}$. Taking the ratio for equal $T$ and equal $r$: $\dfrac{\Delta P_{bubble}}{\Delta P_{drop}} = \dfrac{4T/r}{2T/r} = 2$. Hence the soap bubble has twice the excess pressure of the drop. The option 'equal' ignores the bubble's two surfaces. The option 'half' inverts the relationship. The option 'four times' wrongly squares the surface count. A consistency check confirms that because a soap film exposes two surfaces while a solid drop exposes only one, doubling the excess pressure is physically expected, and both expressions correctly carry units of pressure when $T$ is in N/m and $r$ in metres.

Excess Pressure In Bubbles

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