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
Show Answer
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
