A piece of steel has a length 2 m at 200K . At 250 K its length increases by 0.1 m. Find the coefficient of cubical expansion of steel.

Explanation

Given: Coefficient of linear expansion `alpha_(L) = (DeltaL)/(L) xx(1)/(DeltaT)`
Length of a steel piece L = 2m
Initial temperature `(T_(i))` = 200K
Final temperature `(T_(f))` = 250k
`DeltaT = T_(f)-T_(i)`
Increase in temperature , `DeltaT = 250-200`
=50k
Increase in length , `Delta L` = 0.1m
To find : Coefficient of cubical expansion.
`alpha_(L) = ?`
`alpha_(L) = (0.1)/(2)xx(1)/(50)`
`alpha_(L) = 0.001K^(-1)`
Coefficient cubical expansion = `3xx"coefficient linear expansion"`
`alpha_(L) = 3xxalpha_(L)`
`alpha_(v) = 3xx0.001`
Coefficient of cubical expansion.
`alpha_(v) = 0.003 K^(-1)`