Question

Pressure inside a soap bubble is greater than the pressure outside by an amount;(given : R = Radius of bubble, S = Surface tension of bubble)

• A. $\frac{4S}{R}$
• B. $\frac{4R}{S}$
• C. $\frac{S}{R}$
• D. $\frac{2S}{R}$

Answer 1

The Correct Option is A

The pressure differential across a soap bubble's film is determined by its surface tension and dimensions. A soap bubble consists of a thin liquid layer with inner and outer surfaces exposed to air.

The surface tension acting on these two surfaces creates an elevated internal pressure. The formula quantifying this excess pressure for a soap bubble is:

\(\Delta P = \frac{4S}{R}\)

• \(S\) denotes the surface tension of the liquid forming the bubble.
• \(R\) represents the bubble's radius.

The formula incorporates a factor of four because a soap bubble possesses two surfaces. A single curved surface under tension typically generates an excess pressure of \(\Delta P = \frac{2S}{R}\); however, the bubble's dual surfaces necessitate accounting for surface tension effects on both, hence the doubling of the standard formula.

Examining the provided options:

• \(\frac{4S}{R}\): This correctly represents the pressure difference between the interior and exterior of a soap bubble.
• \(\frac{4R}{S}\): This option is incorrect due to an inversion of the physical dependencies and dimensions.
• \(\frac{S}{R}\): This formula is insufficient as it does not account for the contribution of both surfaces.
• \(\frac{2S}{R}\): This formula applies to a single spherical surface, not to a bubble with two such surfaces.

Consequently, the accurate expression for the excess pressure is: \(\frac{4S}{R}\).