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Question #81558

Difficulty: 5/10 | 🟢 Free

The Question

A cylindrical metallic wire of length $L$ and cross-sectional area $A$ is subjected to a cyclic tensile stress. Due to the elastic after-effect, the longitudinal strain $\epsilon$ lags behind the applied stress $\sigma$ , forming a hysteresis loop in the $\sigma-\epsilon$ plane. The area of this hysteresis loop is $S$ (in $\text{J m}^{-3}$ ). The wire is maintained at a constant temperature $T$ by a surrounding heat bath. Which of the following statements regarding one complete cycle is INCORRECT?

Options

A.
The net work done by the external force on the wire per cycle is $S A L$ .
B.
The net heat absorbed by the wire from the heat bath per cycle is $S A L$ .
C.
The change in the internal energy of the wire over one complete cycle is exactly zero.
D.
The internal elastic forces are non-conservative, making the cyclic process thermodynamically irreversible.

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

Elastic After-Effect|First Law Application|State Function vs Path Function

Why This Question Is Tricky

Examiner Levers

Negative Thinking

Uses "NOT", "EXCEPT", or "INCORRECT" to flip the logic gate.

Difficulty Boost : +2

Common Mistakes

This question tests the intersection of solid mechanics and thermodynamics, specifically exploiting the misconception that 'elastic' deformation is always perfectly conservative.

The elastic after-effect (viscoelasticity) causes strain to lag stress, creating a hysteresis loop whose area represents mechanical energy dissipated as internal heat per unit volume.

Students often misapply the First Law of Thermodynamics ( $\Delta Q = \Delta U + W$ ) by either assuming $\Delta Q = 0$ for an 'elastic' cycle or by messing up the sign convention for work.

Because net positive work is done ON the material ( $W_{\text{ext}} > 0$ ), the material must reject an equivalent amount of heat to the surroundings to return to its initial internal energy state ( $\Delta U = 0$ ).

The trap uses 'Negative Thinking' to force students to identify the physically flawed statement regarding heat absorption.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Mechanical Properties of Solids - Class 11 Part 2
Concept	Elastic After-Effect
Difficulty	5
Cognitive Load	6
Target Solve Time	140 sec
Access	Free