Excess Pressure In A Liquid Drop

Surface tension makes a liquid surface behave like a stretched elastic membrane, and for a spherical liquid drop with a single curved surface the excess internal pressure is $\Delta P=\frac{2S}{r}$, where $S$ is the surface tension and $r$ the radius. The factor of two arises because the curved surface tends to contract, squeezing the enclosed liquid until the pressure difference balances the surface forces. Substituting $S=0.072\text{N/m}$ and $r=1\times 10^{-3}\text{m}$ gives $\Delta P=\frac{2\times 0.072}{10^{-3}}=144\text{Pa}$. The value 72 Pa drops the factor of two and treats the drop like a flat film. The value 288 Pa uses the soap-bubble formula $4S/r$, which applies only when there are two liquid–air surfaces. The value 36 Pa halves the result without justification. This matches the NCERT derivation distinguishing a single-surface drop from a two-surface bubble. As a check, the excess pressure rises as the drop gets smaller, so a millimetre drop showing only a modest 144 Pa above atmospheric is physically reasonable.