Question

A cuboid ABCDEFGH is anisotropic with

${\alpha }_x=1\times {10}^{-5}°C^{-1}$

${\alpha }_y=2\times {10}^{-5}°C^{-1}$

${\alpha }_z=3\times {10}^{-5}°C^{-1}$

Coefficient of superficial expansion of faces can be

• A. ${\beta }_{ABCD}=5\times {10}^{-5}{\left(°C\right)}^{-1}$
• B. ${\beta }_{BCHG}=4\times {10}^{-5}{\left(°C\right)}^{-1}$
• C. ${\beta }_{CDEH}=3\times {10}^{-5}{\left(°C\right)}^{-1}$
• D. ${\beta }_{CDEH}=5\times {10}^{-5}{\left(°C\right)}^{-1}$

Answer 1

The correct option is C ${\beta }_{CDEH}=3\times {10}^{-5}{\left(°C\right)}^{-1}$

${\beta }_{ABCD}={\beta }_{EFGH}=\alpha x+\alpha z=4\times {10}^{-5}°C^{-1}$

${\beta }_{BGHC}={\beta }_{AFED}=\alpha Y+\alpha z=5\times {10}^{-5}°C^{-1}$

${\beta }_{CDEH}={\beta }_{BAFG}=\alpha Y+\alpha X=3\times {10}^{-5}°C^{-1}$