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Question #42172

Difficulty: 8/10 | 🟢 Free

The Question

A longitudinal compression pulse of small pressure amplitude $\Delta P$ ( $\Delta P \ll P_0$ ) travels through an ideal diatomic gas ( $\gamma = 1.4$ ) at equilibrium pressure $P_0$ and temperature $T_0$ . The pulse strikes a perfectly rigid, thermally insulated wall at normal incidence and reflects completely. Let $\Delta T$ be the maximum transient increase in temperature of the infinitesimally thin gas layer immediately adjacent to the wall during the reflection. Which of the following expressions correctly represents $\Delta T$ ?

Options

A.
$\frac{4}{7} \frac{\Delta P}{P_0} T_0$
B.
$2 \frac{\Delta P}{P_0} T_0$
C.
$\frac{2}{7} \frac{\Delta P}{P_0} T_0$
D.
$\frac{\Delta P}{P_0} T_0$

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

Sign Convention Trap|Boundary Condition Reflection|Instantaneous Nature

Why This Question Is Tricky

Common Mistakes

This question tests the thermodynamic nature of wave reflection at a rigid boundary.

A common lethal mistake is assuming that because the boundary is rigid, the gas layer adjacent to it undergoes an isochoric process ( $dV=0$ , $dW=0$ ).

If students apply the ideal gas law at constant volume, they incorrectly find $\Delta T = 2(\Delta P/P_0)T_0$ .

In reality, while the wall doesn't move, the gas layer itself is compressed against the wall by the incoming wave.

The process is rapid and adiabatic, requiring the use of the adiabatic relation between temperature and pressure, combined with the acoustic principle that pressure amplitude doubles at a displacement node.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermodynamics - Class 11 Part 2
Concept	Sign Convention Trap
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free