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-int_(T_(0))^(T)alpha(T)dT]`
D. `L gt L_(0)`

Answer

B

Explanation

As, `(dL)/(L_(0))=alpha(T)dT " " int_(L_(0))^(L)dL=L_(0) int_(T_(0))^(T) alpha(T) dT`
`L-L_(0)=L_(0) int_(T_(0))^(T) alpha(T)dT" " L=L_(0)[1+int_(T_(0))^(T) alpha(T)dT]`