Before You Begin

Question #42547

Difficulty: 8/10 | 🟢 Free

The Question

A rigid, thermally insulated cylindrical container of fixed volume contains $n$ moles of an ideal diatomic gas at an initial temperature $T_0$ . A rigid rotor of moment of inertia $I$ is mounted inside the container on a frictionless axle. An external mechanism applies a sudden angular impulse $J$ to the rotor via a thin shaft, causing it to spin rapidly. Due to the viscosity of the gas, the rotor eventually comes to rest. Assuming the heat capacity of the rotor and the container to be negligible, what is the final equilibrium temperature $T_f$ of the gas?

Options

A.
$T_0 + \frac{J^2}{5 n R I}$
B.
$T_0$
C.
$T_0 + \frac{J^2}{7 n R I}$
D.
$T_0 + \frac{J^2}{n R I}$

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

First Law Application|Impulsive Torque and Angular Momentum|Work Done in Non-PV Diagrams

Why This Question Is Tricky

Common Mistakes

This question tests the generalized application of the First Law of Thermodynamics, specifically distinguishing between boundary-displacement work ( $P\Delta V$ ) and non-PV work (shaft work).

A common trap is assuming that in a rigid, adiabatic container, both heat exchange and work are zero, leading to the incorrect conclusion that the temperature remains constant (Option B).

Students must recognize that the impulsive torque injects rotational kinetic energy into the system from the outside, which is subsequently dissipated into internal energy via viscous forces, thereby raising the gas temperature.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermodynamics - Class 11 Part 2
Concept	First Law Application
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free