1.

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 isA. `alpha_(1) + alpha_(2)`B. `2alpha_(1) + alpha_(2)`C. `alpha_(1) + 2alpha_(2)`D. None of these

Answer» Correct Answer - C
`V=V_(0)(1+gamma Delta theta)`
`L^(3) = L_(0)(1+alpha_(1) Delta theta)L_(0)^(2) (1+alpha_(2)Delta theta)^(2)`
`L_(0)^(3)(1+alpha_(1)Delta theta)(1+alpha_(2)Delta theta)^(2)`
Since `L_(0)^(3) = V_(0)` and `L^(3) =V`
Hence `1+gamma Delta theta = (1+alpha_(1)Delta theta)(1+alpha_(2)Delta theta)^(2)`
`~=(1+alpha_(1)Delta theta) (1+2 alpha_(2)Delta theta)`
`~=(1+alpha_(1)Delta theta+2 alpha_(2)Delta theta)`
`rArr gamma = alpha_(1)+ 2 alpha_(2)`.


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