Properties Of Solids And Liquids Question 115

Question: The coefficient of linear expansion of crystal in one direction is $ {\alpha _{1}} $ and that in every direction perpendicular to it is $ {\alpha _{2}} $ . The coefficient of cubical expansion is

Options:

A) $ {\alpha _{1}}+{\alpha _{2}} $

B) $ 2{\alpha _{1}}+{\alpha _{2}} $

C) $ {\alpha _{1}}+2{\alpha _{2}} $

D) None of these

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Answer:

Correct Answer: C

Solution:

$ V=V _{0}(1+\gamma \Delta \theta ) $

$ L^{3}=L _{0}(1+{\alpha _{1}}\Delta \theta )L _{0}^{2}{{(1+{\alpha _{2}}\Delta \theta )}^{2}} $

$ =L _{0}^{3}(1+{\alpha _{1}}\Delta \theta ){{(1+{\alpha _{2}}\Delta \theta )}^{2}} $

Since $ L _{0}^{3}=V _{0} $ and $ L^{3}=V $

Hence $ 1+\gamma \Delta \theta =(1+{\alpha _{1}}\Delta \theta ){{(1+{\alpha _{2}}\Delta \theta )}^{2}} $

$ \tilde{=}(1+{\alpha _{1}}\Delta \theta )(1+2{\alpha _{2}}\Delta \theta ) $

$ \tilde{=}(1+{\alpha _{1}}\Delta \theta +2{\alpha _{2}}\Delta \theta ) $

therefore g = a1 + 2a2



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