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=V_0(1+gammaDeltatheta)`
or `L^3=L_0(1+alpha_1Deltatheta)L_0^2(1+alpha_2Deltatheta)^2`
`impliesL^3=L_0^3(1+alpha_1Deltatheta)(1+alpha_2Deltatheta)^2`
since `L_0^3=V_0`, hence
`1+gammaDeltatheta=(1+alpha_1Deltatheta)(1+alpha_2Deltatheta)^2`
`cong(1+alpha_1Deltatheta)(1+2alpha_2Deltatheta)`
`cong 1+alpha_1Deltatheta+2alpha_2Deltatheta`
`:. gamma_(1) + 2 alpha_(2)`.