Question

A non-isotropic solid metal cube has coefficients of linear expansion as: $5\times {10}^{–5}{/}^{\circ }C$ along the $x$ axis and $5\times {10}^{–6}{/}^{\circ }C$ along the $y$ and the $z$ axis. If the coefficient of volume expansion of the solid is $C\times {10}^{–6}{/}^{\circ }C$ then the value of C is

Answer 1

We know that: $\gamma ={\alpha }_x+{\alpha }_y+{\alpha }_z$
Given: ${\alpha }_x=5\times {10}^{-5}{/}^{\circ }C$
${\alpha }_y={\alpha }_z=5\times {10}^{-6}{/}^{\circ }C$
The coeffiecient of volume expansion
$\gamma =5\times {10}^{-5}+{10}^{-6}+5\times {10}^{-6}$
$\gamma =60\times {10}^{-6}$
Comparing with $C\times {10}^{-6}$
$C=60$
Final Answer: 60