If a soap bubble expands, the pressure inside the bubble:
- decreases
- decreases
- remains the same
- In equal to the atmospheric pressure
The Correct Option is A
Solution and Explanation
The phenomenon relating to the pressure inside a soap bubble can be understood through the principles of fluid mechanics. A soap bubble is characterized by two layers of soap film with air trapped between them. The pressure inside the bubble is determined by both the surface tension of the soap film and the radius of the bubble according to the Young-Laplace equation:
P = P0 + \(\frac{4γ}{R}\)
where:
- P is the internal pressure of the bubble.
- P0 is the atmospheric pressure outside the bubble.
- γ is the surface tension of the soap solution.
- R is the radius of the bubble.
When a soap bubble expands, the radius (R) of the bubble increases. According to the equation, increasing the value of R while keeping surface tension constant results in the term \(\frac{4γ}{R}\) decreasing. Consequently, the internal pressure P also decreases if P0 is constant (atmospheric pressure). Thus, the correct answer is that the pressure inside the bubble decreases as it expands.
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Concepts Used:
Mechanical Properties of Fluid
The science of the mechanical properties of fluids is called Hydrostatics. A fluid is a substance that relents to the slightest pressure. Fluids are categorized into two classes famed by the names of liquids, and elastic fluids or gases, which later comprehend the air of the atmosphere and all the different kinds of air with which chemistry makes us acquainted.
Streamline Flow:
A streamline is a curve the tangent to which at any point provides the direction of the fluid velocity at that point. It is comparable to a line of force in an electric or magnetic field. In steady flow, the pattern of the streamline is motionless or static with time, and therefore, a streamline provides the actual path of a fluid particle.
Tube of Flow:
A tubular region of fluid enclosed by a boundary comprises streamlines is called a tube of flow. Fluid can never cross the boundaries of a tube of flow and therefore, a tube of flow acts as a pipe of the same shape.
Surface Tension and Viscosity:
The surface tension of a liquid is all the time a function of the solid or fluid with which the liquid is in contact. If a value for surface tension is provided in a table for oil, water, mercury, or whatever, and the contacting fluid is unspecified, it is safe to consider that the contacting fluid is air.