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 18oC


The final temperature of the iron track is 48oC


The final length of the iron track be Lt


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.


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