Question

The coefficient of expansion of a crystal in one direction (x-axis) is $2.0\times {10}^{-6}{K}^{-1}$ and that in the other two perpendicular directions (y and z-axes) is $1.6\times {10}^{-6}{K}^{-1},$What is the coefficient of cubical expansion of the crystal?

• A. $1.6\times {10}^{-6}{K}^{-1}$
• B. $1.8\times {10}^{-6}{K}^{-1}$
• C. $2.0\times {10}^{-6}{K}^{-1}$
• D. $5.2\times {10}^{-6}{K}^{-1}$

Answer 1

The correct option is D

$5.2\times {10}^{-6}{K}^{-1}$

Coefficient of cubical expansion, $\gamma ={\alpha }_x+{\alpha }_y+{\alpha }_z={\alpha }_x+2a_y=2.0\times {10}^{-6}+2\times 1.6\times {10}^{-6}=5.2\times {10}^{-6}{K}^{-1}$
Hence, the correct choice is (d).