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Question #42478

Difficulty: 8/10 | 🟢 Free

The Question

An ideal monoatomic gas ( $\gamma = 5/3$ ) is confined in a horizontal, perfectly insulated cylinder by a frictionless, insulated piston of mass $M$ and cross-sectional area $A$ . Initially, the gas is at pressure $P_0$ and volume $V_0$ . The external atmospheric pressure is constant at $P_{ext} = \frac{P_0}{16}$ . The piston is released from rest. What is the speed $v$ of the piston when the volume of the gas becomes $8V_0$ ?

Options

A.
$\sqrt{ \frac{11 P_0 V_0}{8 M} }$
B.
$\sqrt{ \frac{105 P_0 V_0}{8 M} }$
C.
$\frac{3}{2} \sqrt{ \frac{P_0 V_0}{M} }$
D.
$\sqrt{ \frac{5 P_0 V_0}{8 M} }$

Check Your Answer

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

Work-Energy Theorem Validity|Adiabatic Process Constraint|Molecular Degrees of Freedom

Why This Question Is Tricky

Common Mistakes

This question tests the application of the Work-Energy Theorem coupled with the First Law of Thermodynamics for an adiabatic process.

A common trap is assuming the gas exerts a constant force during expansion (leading to $W = P_0 \Delta V$ ) or completely neglecting the negative work done by the external atmospheric pressure on the piston.

Furthermore, students must correctly evaluate the adiabatic work integral, recognizing that the internal energy decrease of the gas dictates the macroscopic work done on the piston, which ultimately manifests as the piston's kinetic energy.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Work-Energy Theorem Validity
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free