The area of cross-section of railway track is `0.01 m^(2)`. The temperature variation is `10^(@)C`. Coefficient of linear expansion of steel `=10^(-5)//""^(@)C`. (Young's modulus of steel `= 10^(11) Nm^(-2)`). Calculate the energy stored per meter in the track.

Explanation

Let `alpha`= Coefficient of linear expansion.
`:.` Elastic energy `=(1)/(2) xx "stress " xx "strain " xx "volume"`
or `U= (1)/(2) xx (Y xx "strain") xx` strain `xx` volume
or `U= (1 xx Y xx ("strain")^(2) xx "volume")/(2)`
`alpha= (l)/(L xx t) = ("strain")/(t)`
`:. alpha= ("Change in length")/("original length" xx "temperature change")`
or strain `= alpha t`
`:. U = (Y xx alpha^(2) t^(2) xx ("area" xx "length"))/(2)`
or `U= (10^(11) xx (10^(-5))^(2) xx (10)^(2) xx 0.01xx 1)/(2) = 5J`
`:.` Energy stored `=5J`