At 20^∘ C, the surface tension of water is 72.8 dynes/cm....

At $20^{\circ} \mathrm{C},$ the surface tension of water is 72.8 dynes/cm. Find the excess pressure inside of (a) an ordinary-size water drop of radius 1.50 $\mathrm{mm}$ and (b) a fog droplet of radius 0.0100 $\mathrm{mm} .$

Key Concepts

Curvature of a Surface

The curvature of a surface, particularly in the case of spherical droplets, is quantified by the inverse of the radius. A smaller radius corresponds to a higher curvature, which in turn results in a larger pressure difference across the interface due to the effects described by the Laplace pressure equation. Understanding curvature is vital for analyzing the behavior and stability of small-scale liquid structures.

Excess Pressure in Droplets

Excess pressure refers to the additional internal pressure present in a droplet compared to the external pressure, primarily due to the effects of surface tension acting along a curved surface. The magnitude of the excess pressure increases as the droplet’s radius decreases, making it a key factor in phenomena involving small droplets such as fog formation and emulsions.

Surface Tension

Surface tension is a physical property of liquids that describes the elastic tendency of a fluid surface to minimize its area. It results from the cohesive forces between liquid molecules and is measured as force per unit length. This property plays a critical role in phenomena involving liquid interfaces, such as drops and bubbles.

Laplace Pressure

Laplace pressure is the pressure difference across the interface of a curved surface, such as that of a droplet or bubble. It is described by the Laplace equation, which for a spherical interface states that the difference in pressure is proportional to the surface tension and inversely proportional to the radius of the sphere. This concept is essential for understanding why small droplets or bubbles have higher internal pressure.

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