Question

A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed one after the other. How much gap should be left between two such sections, so that there is no compression during summer when the maximum temperature rises to 48°C? Coefficient of linear expansion of iron = 11 × 10–6 °C–1.

Answer 1

Explanation:    

Step 1:

According to linear expansion equation  

$L=L_{0}(1+\alpha t)$

Where,  L= length at final temperature

$L_{0}=$ length at initial temperature

t= temperature difference (final temperature – initial temperature)

α = coefficient of linear expansion

At $t=18^{\circ} \mathrm{C}$

Step 2:

Length during winter

$L_{w}=12\left(1+11 \times 10^{-6} \times 18\right)$

$L_{w}=12.002376 \mathrm{m}$

$\text { At } t=48^{\circ} \mathrm{C}$

Step 3:

Length during summer

$L_{s}=12\left(1+11 \times 10^{-6} \times 48\right)$

$L_{s}=12.006336 \mathrm{m}$

Step 4:

Expansion in length  

$\Delta L=L_{s}-L_{w}$

Change in length = length in summer- length in winter

$\Delta L=0.003960 \mathrm{m}$

$\Delta L \approx 0.4 \mathrm{cm}$

This should be the gap between two section so that there is no compression during summer.

Answer 2

$\huge{\boxed{\mathcal\pink{\fcolorbox{red}{yellow}{Answer}}}}$

0.4 cm