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. `2 alpha_2 + alpha_2`
C. `alpha_1 + 2 alpha_2`
D. None of these

Answer

C

Explanation

`V= V_(0) (1 + gamma Delta theta) = rArr L^(3) = L_0 (1 + alpha_1 Delta theta) L_(0)^(2) (1 + alpha_(2) Delta theta)^(2)`
` 1 + gamma Delta theta = (1 + alpha_1 Delta theta) (1 + alpha_2 Delta theta)^(2)`
`therefore gamma = alpha_(1) + 2alpha_2`