A $$non-$$ isotropic solid metal cube has coefficients of linear expansion as:$$5$$×$$10$$−$$5/$$ $$0C$$ along the $$x-axis$$ and $$5$$×$$10$$−$$6/$$ $$0C$$ along the y and the $$z-axis$$. If coefficient of volume expansion of the solid C×$$10$$−$$6/$$ $$0C$$ then the value of C is $$_________$$

coefficient of volume expansion γ$$=$$α$$x+$$α$$y+$$αz⇒γ$$=2$$α$$y+$$α$$x=25$$×$$10$$−$$6+5$$×$$10$$−$$5=10$$×$$10$$−$$6+50$$×$$10$$−$$6=60$$×$$10$$−$$6$$ C −$$1$$ $$0$$

Thermal expansion

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Question

A non- isotropic solid metal cube has coefficients of linear expansion as: $5 \times 10^{- 5} /^{0} C$ along the x-axis and $5 \times 10^{- 6} /^{0} C$ along the y and the z-axis. If coefficient of volume expansion of the solid $C \times 10^{- 6} /^{0} C$ then the value of C is _________

Moderate

Solution

$\begin{array}{l} c o e f f i c i e n t o f v o l u m e e x p a n s i o n γ = α_{x} + α_{y} + α_{z} \\ \Rightarrow γ = 2 α_{y} + α_{x} = 2 (5) \times 10^{- 6} + 5 \times 10^{- 5} = 10 \times 10^{- 6} + 50 \times 10^{- 6} = 60 \times 10^{- 6} {}^{0}C^{- 1} \end{array}$

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