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_(1) + alpha_(2)`
C. `alpha_(1) + 2 alpha_(2)`
D. None of above

Explanation

`V = V_(0) (1 + gamma T)`
or `L^(3) = L_(0) (1 + alpha_(1) T) L_(0)^(2) (1 + alpha_(2) T)^(2)`
or `= L_(0)^(3) (1 + alpha_(1) T) (1 + alpha_(2) T)^(2)`
or `V = V_(0) (1 + alpha_(1) T) (1 + alpha_(2) T)^(2)`
Hence `1 + gamma T = (1 + alpha_(1) T) (1 + alpha_(2) T)^(2)`
or ` 1 + gamma T = (1 + alpha_(1) T) (1 + 2alpha_(2) T)`
= `1 + (alpha_(1) + 2alpha_(2) )T`
Hence `gamma = alpha_(1) + 2 alpha_(2)`