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 goes to 48°C? Coefficient of linear expansion of iron = 11 ×10^-6 °C^-1

0.4cm

Explanation:

Given:

The initial length of the iron track, L₀, is 12 m

The initial temperature of the iron track is 18^oC

The final temperature of the iron track is 48^oC

The final length of the iron track be L_t

Formula used:

The relation connecting the length at a specified temperature () and that of with a standardized temperature can be written as,

L₀= Length at a reference temperature, α= coefficient of linear expansion, θ= Change in temperature.

12m =11 × °C^-1

Case 1: At temperature 18°C,

Case 2: At temperature 48°C

Now the difference between these two lengths should be the value of the gap.

So,

(Ans.)

So then there must be a gap of 0.4cm between the rails.