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Area and Volume Expansion

A non-isotrop...

Question

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

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Solution

We know that,
$V = x y z$
$\begin{matrix} \frac{Δ v}{v} = \frac{Δ x}{x} + \frac{Δ y}{y} + \frac{Δ z}{z} \frac{1}{T} \frac{Δ v}{v} = \frac{1}{T} \frac{Δ x}{x} + \frac{1}{T} \frac{Δ y}{y} + \frac{1}{T} \frac{Δ z}{z} y = α_{n} + α_{y} + α_{z} y = 50 \times 10^{- 6} /^{\circ} C + 5 \times 10^{- 6} /^{\circ} C + 5 \times 10^{- 6} /^{\circ} C y = 60 \times 10^{- 6} /^{\circ} C ∴ C = 60 \end{matrix}$

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