The area of cross-section of a railway track is 0.01 m2. The temperature variation is 10$^\circ$C. Coefficient of liner expansion of material of track is 10$-$5/$^\circ$C. The energy stored per meter in the track is ____________ J/m.
(Young's modulus of material of track is 1011 Nm$-$2)
Answer (integer)
5
Solution
As the tracks won't be allowed to expand linearly, the rise in temperature would lead to developing thermal stress in track.<br><br>${{(Stress)} \over y} = \alpha \Delta T$ or $\sigma = Y\alpha \Delta T$<br><br>Energy stored per unit volume = ${1 \over 2}{\sigma \over Y}$<br><br>$\Rightarrow$ Energy stored per unit length = ${{A{\sigma ^2}} \over {2Y}}$<br><br>$= {A \over 2} \times Y{\alpha ^2}\Delta {T^2}$<br><br>$$ = {{{{10}^{ - 2}} \times {{10}^{11}} \times {{10}^{ - 10}} \times 100} \over 2} = 5$$ J/m
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
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