Question 754: Thermodynamics & KTG

Question

Rails of material of steel are laid with gaps to allow for thermal expansion. Each track is 10 m long, when laid at temperature $17^{\circ} \mathrm{C}$. The maximum temperature that can be reached is $45^{\circ} \mathrm{C}$. The gap to be kept between the two segments of railway track is
$$\left(\alpha_{	ext {steel }}=1.3 	imes 10^{-5} /{ }^{\circ} \mathrm{C}ight)$$

Accepted Answer

To find the gap that should be left between the two segments of the railway track to accommodate for thermal expansion, we use the formula for linear expansion:
$$ \Delta L = L 	imes \alpha 	imes \Delta T $$
where:
$ \Delta L $ is the change in length,
$ L $ is the original length of the rail,
$ \alpha $ is the coefficient of linear expansion for steel,
$ \Delta T $ is the change in temperature.
Given:
$ L = 10 \, 	ext{m} = 10,000 \, 	ext{mm} $
$ \alpha = 1.3 	imes 10^{-5} /{}^\circ \mathrm{C} $
Initial temperature: $ T_1 = 17^\circ \mathrm{C} $
Final temperature: $ T_2 = 45^\circ \mathrm{C} $
Now, calculate the change in temperature:
$$ \Delta T = T_2 - T_1 = 45 - 17 = 28^\circ \mathrm{C} $$
Next, substitute these values into the formula for linear expansion:
$$ \Delta L = 10,000 	imes 1.3 	imes 10^{-5} 	imes 28 $$
Calculating further:
$$ \Delta L = 10,000 	imes 1.3 	imes 28 	imes 10^{-5} $$
$$ \Delta L = 10,000 	imes 0.000364 $$
$$ \Delta L = 3.64 \, 	ext{mm} $$
Therefore, the gap to be kept between the two segments of the railway track is
3.64 mm
.
The correct answer is
Option C: 3.64 mm
.

Answer

1.68 mm

Answer

2.06 mm

Answer

3.64 mm

Answer

4.32 mm

Thermodynamics & KTG

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