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Question #42111

Difficulty: 8/10 | 🟢 Free

The Question

A spherical soap bubble of initial radius $R_0$ contains a monoatomic ideal gas. The initial external atmospheric pressure is $P_0 = \frac{12 S}{R_0}$ , where $S$ is the surface tension of the soap solution. The system is initially in thermal and mechanical equilibrium. The external pressure is then slowly reduced to zero, allowing the bubble to expand reversibly and adiabatically to a new equilibrium radius $R$ . Calculate the work done against the external atmospheric pressure during this expansion.

Options

A.
$8 \pi S R_0^2$
B.
$16 \pi S R_0^2$
C.
$24 \pi S R_0^2$
D.
$12 \pi S R_0^2$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Excess Pressure|Work Done in Stretching|Thermodynamics

Why This Question Is Tricky

Common Mistakes

This question tests the interplay between the First Law of Thermodynamics and the Work-Energy theorem in the context of surface tension.

The primary trap is assuming that the work done by the expanding gas ( $W_{gas} = \int P_{int} dV$ ) is entirely transferred to the surrounding atmosphere.

Students often fail to recognize that the gas must also do work to stretch the soap film, which stores energy as surface potential energy.

Consequently, they might select $16 \pi S R_0^2$ (ignoring surface energy) or $24 \pi S R_0^2$ (incorrectly adding it).

Additionally, forgetting the factor of 2 for the two surfaces of a soap bubble leads to another common error.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Mechanical Properties of Fluids - Class 11 Part 2
Concept	Excess Pressure (Laplace Law)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free