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Thermal Stress And Thermal Strain - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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Thermal stress and thermal strain is considered one of the most asked concept.
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A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by T. The net change in its length is zero. Let $l$ be the length of the rod, A its cross-section area, Y its Young’s modulus, and α its linear expansion coefficient. Then, F is equal to :

$l^{2}Y\alpha \Delta T$

$lA\:\: Y\alpha \: \: \Delta T$

$A\: Y\alpha \: \Delta T$

$\frac{AY}{\alpha \Delta T}$

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Concepts Covered - 1

Thermal stress and thermal strain

Thermal stress in a rod which is rigidly fixed : When a rod which rigidly fixed at ends such as to prevent expansion or contraction, when its temperature is increased or decreased. Due to preventing its thermal expansion or contraction, a compressive or tensile stress is developed in it. As the rod try to expand or contracts, then it apply a reaction force on the rigid support. If the change in temperature of a rod of length L is $\Delta \theta$ then -

$\text { Thermal strain }=\frac{\Delta L}{L}=\alpha \Delta \theta \quad\left[\text { As } \alpha=\frac{\Delta L}{L} \times \frac{1}{\Delta \theta}\right]$

As, If we know the strain then with the help of Hooke's law, we can find the stress also. If we know the stress , then we can find the force by multiplying cross-sectional area with stress. Both stress and force can be written as -

$\\ {\text { So, Thermal stress }=Y \alpha \Delta \theta} \\ {\text { or, Force on the supports } F=Y A \alpha \Delta \theta}$

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Thermal stress and thermal strain

Physics Part II Textbook for Class XI

Page No. : 283

Line : 17

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