A rod has length `L_(0)` at a reference temperature `T_(0)`, coefficient of linear expansion `alpha`, Young's modulus Y, area of cross section A. Rod lie unconstrained on a smooth surface temperature of rod is increased bby `Delta T`. Mark the correct statement

Options

A. Final length of rod is given by `L = L_(0) (1 + alpha Delta T)` for all the range of values of `alpha`.
B. If average coefficient of linear expansion is constant as L varies the general expression for the final length is `L = L_(0) e^(alpha Delta T)`
C. Rod is unstrained as it expands
D. Coefficient of expansion is defined as `alpha = (1)/(L) (dL)/(dt)`

Answer

B, C, D

Explanation

(B) `alpha = (dL)/(dt)`
`alpha.dt = (dL)/(dL)`
`alpha Delta T = [ln L]_(L_(0))^(L)`
`alpha Delta T = ln L - ln L_(0)`
`alpha Delta T = "ln" (L)/(L_(0)) rArr (L)/(L_(0)) = e^(alpha Delta T)`
`rArr L = L_(0) e^(alpha Delta T)`
(C) Thermal stresses does not produces any strain as the rod lies unconstrained on a smooth surface
(D) from definition `alpha = (1)/(L) (d L)/(dt)`