A railway track (made of iron) is laid in winter when the average temperature is `18^@C`. The track consists of sections of 12.2 m placed one after the other. How much gap should be left between two such sections so that there in no compression during summer when the maximum temperature goes to `48^@C`? Coefficient of linear expansion of iron `= 11 xx 10^(-5 @)C^(-1)`.

Explanation

(a) `Deltal=l_(theta0)alphaDeltatheta`
`=12xx11xx10^(-6)xx(48-18)`
`=3.96xx10^(-3)m`
`=0.40cm`
(b) `d_(100)=_(0)(1+alphaDeltatheta)`
`2[1+2.3xx10^(-5)xx(100-0)]`
`=2.0046cm`