Question:
A non-isotropic solid metal cube has coefficients of linear expansion as :
5 \( \times \) 10-5/oC along the x-axis and 5 \( \times \) 10-6/oC along the y and the z-axis. If the coefficient of volume expansion of the solid is C \( \times \) 10-6/oC then the value of C is
A non-isotropic solid metal cube has coefficients of linear expansion as :
5 \( \times \) 10-5/oC along the x-axis and 5 \( \times \) 10-6/oC along the y and the z-axis. If the coefficient of volume expansion of the solid is C \( \times \) 10-6/oC then the value of C is
5 \( \times \) 10-5/oC along the x-axis and 5 \( \times \) 10-6/oC along the y and the z-axis. If the coefficient of volume expansion of the solid is C \( \times \) 10-6/oC then the value of C is
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For a small temperature change the volume coefficient of expansion is the sum of the three linear coefficients: \(\gamma=\alpha_x+\alpha_y+\alpha_z\).
Updated On: Oct 31, 2026
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Correct Answer: 60
Solution and Explanation
Volume \(V=L_xL_yL_z\) with \(L_i=L_0(1+\alpha_i\Delta T)\).
\(V\approx L_0^3\left[1+(\alpha_x+\alpha_y+\alpha_z)\Delta T\right]\) (neglecting higher-order products).
So \(\gamma=\alpha_x+\alpha_y+\alpha_z=5\times10^{-5}+5\times10^{-6}+5\times10^{-6}=6\times10^{-5}=60\times10^{-6}\ /^\circ\text{C}\).
Comparing with \(C\times10^{-6}\): C = 60.
Answer: 60
\(V\approx L_0^3\left[1+(\alpha_x+\alpha_y+\alpha_z)\Delta T\right]\) (neglecting higher-order products).
So \(\gamma=\alpha_x+\alpha_y+\alpha_z=5\times10^{-5}+5\times10^{-6}+5\times10^{-6}=6\times10^{-5}=60\times10^{-6}\ /^\circ\text{C}\).
Comparing with \(C\times10^{-6}\): C = 60.
Answer: 60
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