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Question #42574
The Question
A parallel beam of ideal gas atoms, each of mass , strikes a freely movable, initially stationary flat wall of mass at a constant rate of atoms per second. The atoms move with a speed perpendicular to the wall. Assume all collisions between the atoms and the wall are perfectly elastic and independent. Let be the actual initial average force exerted on the wall. Let be the theoretical force calculated using the standard Kinetic Theory of Gases assumption (which treats the wall as infinitely massive and static). What is the value of the relative difference ?
Options
- A.
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- D.
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Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Intuition_Breaker
Train your brain to resist "obvious" answers that are designed to deceive your intuition.
Concepts Behind This Question
Ideal Gas Assumptions|Recoil of Atom|Vector Cross-Products
Why This Question Is Tricky
Common Mistakes
This question tests the fundamental assumptions of the Kinetic Theory of Gases (KTG) against the rigorous application of the Impulse-Momentum theorem and Conservation of Energy.
Students often blindly apply the standard KTG result () for pressure and force, forgetting that it relies on the assumption of an infinitely massive, static wall.
By introducing a freely movable wall of finite mass , the problem forces students to abandon the static wall approximation and calculate the true momentum exchange using elastic collision kinematics.
The trap lies in either using the standard KTG formula directly without accounting for recoil, or calculating the fractional error relative to the wrong base value.
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 |