Thermal expansion

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By Expert Faculty of Sri Chaitanya
Question

A non- isotropic solid metal cube has coefficients of linear expansion as:$5×{10}^{-5}/{\text{\hspace{0.17em}}}^{0}C$   along the x-axis and  $5×{10}^{-6}/{\text{\hspace{0.17em}}}^{0}C$ along the y and the z-axis. If coefficient of volume expansion of the solid $C×{10}^{-6}/{\text{\hspace{0.17em}\hspace{0.17em}}}^{0}C$ then the value of C is _________

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Solution

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The coefficient of linear expansion of brass and steel are ${\mathrm{\alpha }}_{1}$ and ${\alpha }_{2}$. If we take a brass rod of length ${l}_{1}$ and steel rod of length ${l}_{\mathit{2}}$ at 0oC, their difference in length $\left({l}_{2}-{l}_{1}\right)$will remain the same at all temperatures if