Question 810: Thermodynamics & KTG

Question

Railway track is made of steel segments separated by small gaps to allow for linear expansion. The segment of track is 10 m long when laid at temperature $17^{\circ} \mathrm{C}$. The maximum temperature that can be reached is $45^{\circ} \mathrm{C}$. Increase in length of the segment of railway track is ' $x$ ' $	imes 10^{-5} \mathrm{~m}$. The value of ' $x$ ' is $\left(\alpha_{	ext {steel }}=ight.$ $\left.1.2 	imes 10^{-5} /{ }^{\circ} \mathrm{C}ight)$

Accepted Answer

The increase in length of a segment of railway track due to thermal expansion can be calculated using the formula for linear expansion:
$$ \Delta L = L_0 \cdot \alpha \cdot \Delta T $$
where:
$ \Delta L $ is the change in length of the track,
$ L_0 = 10 \, 	ext{m} $ is the original length of the segment,
$ \alpha = 1.2 	imes 10^{-5} \, /{}^\circ\mathrm{C} $ is the coefficient of linear expansion for steel,
$ \Delta T = 45^\circ\mathrm{C} - 17^\circ\mathrm{C} = 28^\circ\mathrm{C} $ is the change in temperature.
Plugging the values into the formula gives:
$$ \Delta L = 10 \, 	ext{m} 	imes 1.2 	imes 10^{-5} \, /{}^\circ\mathrm{C} 	imes 28^\circ\mathrm{C} $$
Calculating further:
$$ \Delta L = 10 	imes 1.2 	imes 10^{-5} 	imes 28 = 3.36 	imes 10^{-3} \, 	ext{m} $$
The increase in length in terms of $ x 	imes 10^{-5} \, 	ext{m} $ is:
$$ \Delta L = 336 	imes 10^{-5} \, 	ext{m} $$
Thus, the value of $ x $ is 336.
The correct option is
Option C: 336
.

Answer

168

Answer

204

Answer

336

Answer

530

Thermodynamics & KTG

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