Question 606: Thermodynamics & KTG

Question

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)

Accepted Answer

As the tracks won't be allowed to expand linearly, the rise in temperature would lead to developing thermal stress in track.
$${{(Stress)} \over y} = \alpha \Delta T$$ or $$\sigma  = Y\alpha \Delta T$$
Energy stored per unit volume = $${1 \over 2}{\sigma  \over Y}$$
$$\Rightarrow$$ Energy stored per unit length = $${{A{\sigma ^2}} \over {2Y}}$$
$$ = {A \over 2} 	imes Y{\alpha ^2}\Delta {T^2}$$
$$ = {{{{10}^{ - 2}} 	imes {{10}^{11}} 	imes {{10}^{ - 10}} 	imes 100} \over 2} = 5$$ J/m

Thermodynamics & KTG

The area of cross-section of a railway track is 0.01 m2. The temperature variation is 10$^\circC. Coefficient of liner expansion of material of track is 10-5/^\circC. The energy stored per meter in the track is ____________ J/m.(Young's modulus of material of track is 1011 Nm-$2)

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