The coefficient of linear expansion for a certain metal varies with temperature as `alpha(T)`. If `L_0` is the initial length of the metal and the temperature of metal is changed from `T_0` to `T(T_0gtT)`, then

Options

A. `L=L_(0)int_(T_(0))^(T)alpha(T)dT`
B. `L=L_(0)[1+int_(T_(0))^(T)alpha(T)]dT`
C. `L=L_(0)[1+underset(T_(0))overset(T)(int)alpha(T)dT]`
D. `L gtL_(0)`

Answer

C

Explanation

`(dL)/(L_(0)) = -alpha(T)dt,` integrate the equation