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Question #42511

Difficulty: 8/10 | 🟢 Free

The Question

A closed cylindrical container of height $H$ is filled with an ideal gas of molar mass $M$ at a constant temperature $T$ . The container is placed in an elevator moving upwards with a constant acceleration $a$ . Two identical small orifices are punctured simultaneously at the bottom ( $y=0$ ) and the top ( $y=H$ ) of the container, allowing the gas to effuse into a surrounding vacuum. Which of the following expressions represents the ratio of the initial mass leakage rate at the bottom orifice to that at the top orifice? (Assume $g$ is the acceleration due to gravity and $R$ is the universal gas constant)

Options

A.
$\exp\left[\frac{M(g+a)H}{RT}\right]$
B.
$\exp\left[\frac{M(g-a)H}{RT}\right]$
C.
$\exp\left[\frac{MgH}{RT}\right]$
D.
1

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Ideal Gas Assumptions|Pascal’s Law Limitations|Apparent Weight in Accelerating Elevators

Why This Question Is Tricky

Common Mistakes

This question tests the limits of the 'Ideal Gas' assumption of uniform pressure by placing the gas in a non-inertial reference frame.

A common trap is assuming Pascal's Law implies uniform pressure throughout the container (leading to an incorrect ratio of 1), ignoring the hydrostatic pressure gradient caused by the gas's own weight.

Furthermore, students often forget to include the pseudo-force contribution to the effective gravity in the accelerating elevator.

By linking the pressure gradient to the kinetic theory concept of effusion (collision frequency), it forces the realization that local number density, and hence leakage rate, depends exponentially on the effective gravitational potential.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Kinetic Theory - Class 11 Part 2
Concept	Ideal Gas Assumptions
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free