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Question #42181

Difficulty: 8/10 | 🟢 Free

The Question

Two identical rigid bulbs of volume $V_0$ are connected by a thin tube of negligible volume. The system contains $N$ moles of an ideal monoatomic gas of molar mass $M$ and is placed in a zero-gravity environment. The entire assembly rotates with a constant angular velocity $\omega$ about an axis passing through the center of Bulb 1, such that Bulb 2 is at a distance $L$ from the axis. The gas is heated reversibly while a motor maintains the angular velocity $\omega$ constant. If $x = \frac{M \omega^2 L^2}{2 R T}$ , what is the molar heat capacity $C$ of the gas during this process?

Options

A.
$\frac{3}{2}R + R x^2 \frac{e^x}{(e^x+1)^2}$
B.
$\frac{3}{2}R - R x^2 \frac{e^x}{(e^x+1)^2}$
C.
$\frac{3}{2}R + R x \frac{e^x}{e^x+1}$
D.
$\frac{3}{2}R$

Check Your Answer

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

Molar Heat Capacity (Cv vs Cp)|Orbital Velocity Energy Balance|Accelerated Frame Hydrostatics

Why This Question Is Tricky

Common Mistakes

This question tests the coupling between thermodynamic internal energy and rotational kinetic energy in a non-inertial frame.

Students often incorrectly assume $C = C_v$ by ignoring the work done by the motor to maintain constant $\omega$ as the gas redistributes.

The trap lies in failing to recognize that heating the gas causes radial mass transfer (due to the temperature dependence of the Boltzmann distribution in the centrifugal potential field), which changes the system's moment of inertia and requires external work.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermodynamics - Class 11 Part 2
Concept	Molar Heat Capacity (Cv vs Cp)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free