The coefficient of linear expansion of crystal in one direction is `alpha_(1)` and that in every direction perpendicular to it is `alpha_(2)`. The coefficient of cubical expansion is

Options

A. `alpha_(1)+alpha_(2)`
B. `2alpha_(1)+alpha_(2)`
C. `alpha_(1)+2alpha_(2)`
D. none of these

Answer

C

Explanation

`V_(theta)=V_(0)(1+gammatheta)`
`L^(3)=L_(0)(1+alpha_(1)theta)L_(0)^(2)(1+alpha_(2)theta)^(2)`
`=L_(0)^(3)(1+alpha_(1)theta)(1+2alpha_(1)theta)`
`L^(3)=L_(0)^(3)[1(alpha_(1)+2alpha_(2))theta]`
(neglecting smaller terms)
`gamma=alpha_(1)+2alpha_(2)`