A soap bubble is blown slowly at the end of a tube by a pump...

A soap bubble is blown slowly at the end of a tube by
a pump supplying air at a constant rate. Which one of the following graphs represents the correct variation of the excess of pressure inside the bubble with time?
(A)
(B)
(C)
(D)

Key Concepts

Graphical Representation of Non-linear Relationships

The interplay between constant volume growth and the inverse relationship between pressure and radius results in a non-linear, decreasing graph for excess pressure over time. Interpreting such graphs requires understanding how the dimensions of the bubble (and therefore its pressure characteristics) change with time under given conditions.

Relationship between Volume Growth and Radius

When a bubble grows at a constant rate by increasing its volume, the radius increases according to the cube-root of the volume. This nonlinear relationship means that even though the volume increases linearly with time, the radius increases more slowly, influencing the rate at which the excess pressure (inversely related to the radius) decreases.

Laplace Pressure

Laplace pressure describes the excess pressure inside a curved surface (such as a bubble) due to surface tension. According to Laplace’s law, the pressure difference is directly proportional to the surface tension and inversely proportional to the radius of the bubble, meaning that as the bubble grows larger, the excess pressure decreases.

Surface Tension

Surface tension is a liquid property that tends to minimize the surface area of a liquid. It creates a cohesive force along the surface, leading to a pressure difference across a curved interface. This concept is crucial for understanding the formation and stability of bubbles and droplets.

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