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The coefficient of linear expansion of c...

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

A

`alpha_1 + alpha_2`

B

`2 alpha_2 + alpha_2`

C

`alpha_1 + 2 alpha_2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`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`
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