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

To determine the pressure difference between the inside and outside of a soap bubble, we use the concept of surface tension and the geometrical properties of the bubble.

When a bubble forms, it consists of a thin film of liquid. The bubble has two surfaces in contact with air: one on the inside and one on the outside.

The excess pressure inside a bubble is due to the surface tension acting on these two surfaces. For a soap bubble, this pressure difference can be expressed using the formula for excess pressure due to surface tension:

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

• \(S\) is the surface tension of the bubble.
• \(R\) is the radius of the bubble.

The formula \(\Delta P = \frac{4S}{R}\) arises because a soap bubble has two surfaces (inside and outside). Normally, for a single surface, the formula is \(\Delta P = \frac{2S}{R}\), but since a soap bubble has two surfaces, the surface tension formula must account for both, doubling the typical expression.\

Now, let's analyze the options given:

• \(\frac{4S}{R}\): This is the correct formula for the excess pressure inside a soap bubble over the pressure outside.
• \(\frac{4R}{S}\): This option is incorrect because the dimensions and dependency are reversed.
• \(\frac{S}{R}\): This does not account for twice the surface tension from two surfaces and thus is incorrect.
• \(\frac{2S}{R}\): Correct for a single spherical surface, but not for a bubble with two surfaces.

Therefore, the correct answer is: \(\frac{4S}{R}\).

Answer 2

For a soap bubble, there are two liquid-air surfaces, so the excess pressure \( \Delta P \) inside the bubble is given by:
\[\Delta P = 2 \left( \frac{2S}{R} \right) = \frac{4S}{R}\]