Question

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

• A. $5\times {10}^{-4}{/}^{\circ }\text{C}$
• B. $4\times {10}^{-4}{/}^{\circ }\text{C}$
• C. $8\times {10}^{-4}{/}^{\circ }\text{C}$
• D. $7\times {10}^{-4}{/}^{\circ }\text{C}$

Answer 1

The correct option is C $8\times {10}^{-4}{/}^{\circ }\text{C}$

If a crystal has different coefficients of linear expansion along three mutually perpendicular directions, the formula $[\gamma =3\alpha ]$ can be written as
$\gamma ={\alpha }_1+{\alpha }_2+{\alpha }_3$
$\Rightarrow \gamma =2\times {10}^{-4}+3\times {10}^{-4}+3\times {10}^{-4}$
$\Rightarrow \gamma =8\times {10}^{-4}{/}^{\circ }\text{C}$
Hence, option (c) is the correct answer.