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Question #42543

Difficulty: 8/10 | 🟢 Free

The Question

An ideal monatomic gas ( $\gamma = 5/3$ ) flows steadily through a horizontal, thermally insulated pipe of constant cross-sectional area. At section 1, the gas velocity is $v_0$ , pressure is $P_0$ , and density is $\rho_0$ . Due to viscous dissipation, the pressure drops to $P_0/4$ at section 2. If the initial state satisfies $\frac{\gamma}{\gamma-1} \frac{P_0}{\rho_0} = 16 v_0^2$ , what is the gas velocity $v$ at section 2?

Options

A.
$3 v_0$
B.
$4 v_0$
C.
$\sqrt{\frac{53}{5}} v_0$
D.
$2^{6/5} v_0$

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

First Law Application|Bernoulli’s Energy Balance|Reynolds Number Transition

Why This Question Is Tricky

Common Mistakes

This question tests the application of the First Law of Thermodynamics to open systems (Steady Flow Energy Equation) in the presence of viscous dissipation.

A common trap for JEE Advanced students is to apply the mechanical Bernoulli equation, incorrectly assuming that viscous friction causes a 'loss' of total energy that must be subtracted.

However, in an adiabatic pipe, the mechanical energy dissipated by viscosity is entirely converted into internal thermal energy, meaning the total stagnation enthalpy ( $h + v^2/2$ ) remains strictly conserved.

Furthermore, students must correctly couple the continuity equation with the ideal gas law to account for the density variation as the gas expands and accelerates.

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