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Question #43180

Difficulty: 8/10 | 🟢 Free

The Question

A spherical soap bubble of initial radius $R_0$ and surface tension $\gamma$ is placed in a vacuum chamber. It contains an ideal gas. An isotropic point source of light is located at the exact center of the bubble. When turned on, the source emits a constant total electromagnetic power $W$ . The inner surface of the soap bubble completely absorbs the incident light. Due to the radiation pressure, the bubble slowly expands and reaches a new stable equilibrium radius $R = 2R_0$ . Assuming the gas undergoes an isothermal process, what is the required power $W$ of the light source? (Let $c$ be the speed of light in vacuum).

Options

A.
$24 \pi R_0 \gamma c$
B.
$12 \pi R_0 \gamma c$
C.
$30 \pi R_0 \gamma c$
D.
$6 \pi R_0 \gamma c$

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

Radiation Pressure|Excess Pressure (Laplace Law)|Calculus (Optimization)

Why This Question Is Tricky

Common Mistakes

This question tests the synthesis of thermodynamics, optics, and fluid mechanics while setting multiple physical traps.

The primary trap is failing to account for the volumetric expansion of the trapped gas; students often erroneously use the initial gas pressure or assume an incorrect thermodynamic process (like adiabatic) despite the 'slow' expansion cue.

Additionally, students frequently misapply the Laplace law by using $2\gamma/R$ instead of $4\gamma/R$ for a soap bubble (which has two air-liquid interfaces) or incorrectly use the perfect reflection formula ( $P_r = 2I/c$ ) instead of the absorption formula ( $P_r = I/c$ ) explicitly dictated by the problem.

The problem requires setting up a differential pressure balance where both the internal gas pressure and the radiation pressure are dynamically coupled to the changing radius.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Waves - Class 12
Concept	Radiation Pressure
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free