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Question #42516

Difficulty: 8/10 | 🟢 Free

The Question

An ideal gas flows through a cylindrical pipe of diameter $D$ with a constant uniform velocity $v$ and at a constant pressure $P$ . At an initial temperature $T_0$ , the mean free path of the gas molecules is $\lambda_0$ and the Reynolds number of the flow is $Re_0$ . The gas is then heated to a higher temperature such that the mean free path of the molecules becomes $4\lambda_0$ . Assuming the flow velocity $v$ and pressure $P$ remain unchanged, what is the new Reynolds number of the flow? (Assume the gas molecules are hard spheres and follow the standard kinetic theory of gases).

Options

A.
$\frac{Re_0}{8}$
B.
$\frac{Re_0}{4}$
C.
$\frac{Re_0}{2}$
D.
$4 Re_0$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Mean Free Path|Reynolds Number Transition|Variation of Density with Temperature

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to connect macroscopic fluid dynamics (Reynolds number) with microscopic kinetic theory.

A common trap is assuming that the dynamic viscosity of a gas is independent of temperature, which would incorrectly lead to $Re \propto \rho \propto 1/T$ , yielding $Re_0/4$ .

Another trap is ignoring the density variation and only considering viscosity, yielding $Re_0/2$ .

By forcing the derivation of both $\rho \propto 1/T$ and $\eta \propto \sqrt{T}$ from kinetic theory principles, the problem elegantly exposes superficial dimensional analysis and rote memorization.

Quick Facts About This Question

Question Information

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