Question

The coefficient of linear expansion of a crystalline substance in one direction is 2 x ${10}^{-4}{/}^0$C and in every direction perpendicular to it is 3 x ${10}^{-4}{/}^0$C. The coefficient of cubical expansion of crystal is equal to

• A. 5 x ${10}^{-4}{/}^0$C
• B. 4 x ${10}^{-4}{/}^0$C
• C. 8 x ${10}^{-4}{/}^0$C
• D. 7 x ${10}^{-4}{/}^0$C

Answer 1

The correct option is C 8 x ${10}^{-4}{/}^0$C

Given,

${\alpha }_x=2\times {10}^{-4}{/}^{0}C$

${\alpha }_y={\alpha }_z=3\times {10}^{-4}{/}^{0}C$

The coefficient of cubical expansion of the crystal is sum of the coefficient of linear expansion in three mutually perpendicular direction.

$\gamma ={\alpha }_x+{\alpha }_y+{\alpha }_z$

$\gamma =2\times {10}^{-4}+3\times {10}^{-4}+3\times {10}^{-4}=8\times {10}^{-4}{/}^{)}C$

The correct option is C.